Fundamentals of Hydrogen Embrittlement [2nd ed. 2023] 9789819909919, 9819909910

Table of contents :
Preface to the Second Edition
Preface to the First Edition
Contents
1 Solid Solution
1.1 Solubility
1.2 Lattice Location
1.3 Partial Molar Volume and Strain Field
1.4 Atomistic Calculations of the Heat of Solution
References
2 Hydrogen Trapping and Its Direct Detection
2.1 Manifestations and Analyses of Hydrogen Trapping
2.1.1 Solid Solubility at Low Temperatures
2.1.2 Equilibrium Partition of Hydrogen Among Different Traps
2.1.3 Kinetics of Hydrogen Trapping
2.2 Detection of Hydrogen Trapping and Distribution
2.2.1 Hydrogen Thermal Desorption Analysis
2.3 Visualization of Hydrogen Distribution
2.3.1 Tritium Autoradiography and Hydrogen Microprint Technique
2.3.2 Methods Using Stimulated Hydrogen Desorption
2.4 Indirect Detection of Hydrogen Distribution
2.4.1 Neutron Tomography
2.4.2 Scanning Kelvin Prove Microscopy
References
3 Interactions of Hydrogen with Lattice Defects
3.1 Dislocations
3.1.1 Experimental Facts
3.1.2 Theoretical Estimation of Hydrogen–Dislocation Interactions
3.2 Vacancies
3.2.1 Elementary Attributes
3.2.2 Vacancy Clustering and Migration
3.2.3 Interaction of Hydrogen with Vacancies
3.3 Precipitates
3.3.1 TiC
3.3.2 NbC and VC
3.3.3 Fe3C
3.4 Grain Boundaries
3.4.1 Experimental Works
3.4.2 Theoretical Works
3.5 Voids and Surfaces
References
4 Diffusion and Transport of Hydrogen
4.1 Determination of Diffusion Coefficient
4.1.1 Diffusion Coefficient Data
4.1.2 Measurement of Diffusion Coefficient
4.1.3 Theoretical Interpretation
4.2 Stochastic Theories of Hydrogen Diffusion
4.3 Hydrogen Transport by Moving Dislocations
4.3.1 Release of Internal Hydrogen During Straining
4.3.2 Effects on Electrochemical Permeation
4.3.3 A Kinetic Model
4.4 Accelerated Diffusion Along Grain Boundaries
References
5 Deformation Behaviors
5.1 Elastic Moduli
5.2 Flow Stress
5.2.1 Hardening
5.2.2 Softening
5.2.3 Explanations of Experimental Results
5.3 Stress Relaxation and Creep
5.3.1 Stress Relaxation
5.3.2 Creep
5.3.3 Implications of Surface Effects
5.4 Direct Observation of Dislocation Activity
5.5 Elastic and Atomistic Calculations
5.5.1 Elastic Shielding of Stress Centers
5.5.2 Mobility of Screw Dislocations—Atomistic Calculations
References
6 Macroscopic Manifestations of Hydrogen Embrittlement
6.1 Tensile Tests
6.1.1 Effects of Test Conditions
6.1.2 Damage Generation During Straining
6.2 Fracture Mechanics Tests
6.2.1 Crack Initiation
6.2.2 Crack Growth
6.3 Fatigue
6.3.1 Fatigue Limit
6.3.2 Crack Initiation and Growth-Rate Near Threshold
6.3.3 Stage II Crack Growth in Steel
6.3.4 Fatigue in Austenitic Stainless Steel
6.3.5 High-Cycle Fatigue Near Threshold
6.3.6 Models of Fatigue Crack Extension
6.4 Delayed Fracture
6.4.1 Characterization
6.4.2 Effects of Materials Factors
6.4.3 Effects of External Factors
6.4.4 Laboratory Test Methods
6.4.5 Concept of the Critical Hydrogen Concentration
References
7 Microscopic Features Characterizing Hydrogen Embrittlement
7.1 Crack Nucleation Sites
7.2 Fractographic Features
7.2.1 Cleavage
7.2.2 Dimple Patterns
7.2.3 Quasi-cleavage
7.2.4 Intergranular Fracture
7.2.5 Alteration of Fracture Morphology on Crack Extension
7.2.6 Fatigue Fracture
7.3 Strain Localization
7.3.1 Surface Morphology
7.3.2 Internal Structures
7.3.3 Plastic Instability
7.4 Damage Accumulation Precursory to Crack Nucleation
7.4.1 Damage Precursory to Crack Initiation
7.4.2 Effects of Stress History—Damage Accumulation
References
8 Microstructural Effects in Hydrogen Embrittlement of Steel
8.1 Martensitic and Bainitic Steel
8.1.1 Tempering of Martensite and Bainite
8.1.2 Precipitates
8.1.3 Grain-Size Effects
8.1.4 Impurities and Alloying Elements
8.1.5 Microscopic Features of Fracture
8.2 Multiphase Steel
8.2.1 Dual Phase Steel
8.2.2 Retained Austenite—TRIP Steel
8.3 Austenitic Stainless Steel
8.3.1 Hydrides and Phase Changes
8.3.2 Compositional Effects on Hydrogen Embrittlement
8.3.3 Fractographic Features
8.3.4 Deformation Microstructures
References
9 Mechanistic Aspects of Fracture I—Brittle Fracture Models
9.1 Internal Pressure Theory
9.2 Surface Adsorption Theory
9.3 Lattice Decohesion Theory
9.3.1 Stress-Controlled Criterion
9.3.2 Local Stress Intensity Approach
9.4 Theories of Intergranular Fracture
9.4.1 Interface Decohesion
9.4.2 Meaning of Surface Energy in Fracture Criteria
9.5 Summary of Brittle Fracture Models
References
10 Mechanistic Aspects of Fracture II—Plasticity-Dominated Fracture Models
10.1 Outline of Elemental Concepts of Ductile Fracture
10.1.1 Void Nucleation
10.1.2 Void Growth and Coalescence
10.1.3 Model of Plastic Instability
10.2 Hydrogen-Enhanced Localized Plasticity Theory
10.3 Adsorption-Induced Dislocation Emission Theory
10.4 Autocatalytic Void Formation and Shear Localization Theory
10.5 Hydrogen-Enhanced Strain-Induced Vacancy Theory
10.5.1 Brief Summary of Findings on Involvement of Strain-Induced Vacancies in HE
10.5.2 Mechanistic and Microscopic Functions of Vacancies
10.6 Summary of Ductile Fracture Models
References
11 Delayed Fracture After Long Exposure in Atmospheric Environments
11.1 Background
11.2 Peculiar Situations of Delayed Fracture as Material Failure
11.3 Fractographic Features and Microscopic Process of Cracking
11.3.1 Material
11.3.2 Entire Cracking Process
11.3.3 Crack Initiation Site—Frail Zone
11.3.4 Crack Propagation
11.4 Assessment of the Susceptibility to Delayed Fracture
11.5 Concluding Remarks
References

Citation preview

Fundamentals of Hydrogen Embrittlement

Michihiko Nagumo

Fundamentals of Hydrogen Embrittlement Second Edition

Michihiko Nagumo (Emeritus Professor) Laboratory for Materials Science and Technology Waseda University Tokyo, Japan

ISBN 978-981-99-0991-9 ISBN 978-981-99-0992-6 (eBook) https://doi.org/10.1007/978-981-99-0992-6 1st edition: © Springer Science+Business Media Singapore 2016 2nd edition: © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore

Preface to the Second Edition

Hydrogen embrittlement is an interdisciplinary problem covering materials science, mechanics, and electrochemistry, and its manifestation is diverse according to materials, environments, and loading methods. Studies of hydrogen embrittlement have a long history. The intention of the first edition, in 2016, was primarily to share fundamental and comprehensive knowledge, including retrospective works, for smooth discussion on hydrogen embrittlement of steel. Disputes about the function of hydrogen in embrittlement have not yet been settled. However, establishing reliable principles for materials design and assessing their performance are recent urgent industrial needs in developing high-strength steel for hydrogen energy equipment and weight-reducing vehicles. Fortunately, progress in the past decade in experimental and theoretical tools is remarkable and has nearly unveiled characteristic features of hydrogen embrittlement. Proposed models have almost covered feasible aspects of the function of hydrogen. In this second edition, the contents are enriched with recent crucial findings, chapters are reorganized, and the description is revised for readers’ convenience to provide a more systematic and unified view of hydrogen embrittlement. A new chapter is created for delayed fracture in long-time atmospheric exposure as a conclusive subject of critical ideas on the mechanism of hydrogen embrittlement presented in this book. Understanding the function of hydrogen in a general scheme of fracture events is this book’s latent but vital intention. Following the first edition, previous studies are critically reviewed, and supplemental descriptions of fundamental ideas are presented when necessary. Emphases are placed on experimental facts, with particular attention to their implication rather than phenomenological appearance. The adopted experimental conditions are also noted since the operating mechanism of hydrogen might differ by material and environment. For theories, employed assumptions and premises are noted to examine their versatility.

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The author would like to thank Drs. A. N. Itakura, K. Ebihara, M. Kawamori, A. Shibata, M. Koyama, and Y. Ogawa for providing their articles and checking the manuscript. Tokyo, Japan

Michihiko Nagumo

Preface to the First Edition

Hydrogen embrittlement or degradation of mechanical properties by hydrogen is a latent problem for structural materials. The problem is serious particularly for high-strength steels, and its importance is increasing with recent needs for hydrogen energy equipment. Hydrogen embrittlement has been studied for many decades, but its nature is still an unsettled issue. Two reasons are most likely: one is its interdisciplinary attribute covering electrochemistry, materials science, and mechanics, making comprehensive understanding difficult. The other is experimental difficulty in detecting hydrogen behaviors directly. Hydrogen, the lightest element on the periodic table, is mobile and insensitive to external excitations. Coupled with normally very low concentrations of hydrogen, information on its states in materials is limited and most notions must remain speculative about the function of hydrogen. However, recent remarkable advances in experimental techniques in analyses of hydrogen states and of microstructures of materials are unveiling the entity of embrittlement and stimulating new aspects on the mechanism of hydrogen embrittlement. Now is the time to put in order diverse results and notions on hydrogen embrittlement and to prepare the direction to establish principles for materials design and usage against hydrogen problems. This book provides students and researchers engaging in hydrogen problems with a comprehensive view on hydrogen embrittlement, reviewing previous studies and taking in recent advances. Hydrogen effects must be considered along operating principles in each field, and basic rather than phenomenological stances are adopted in referring to the literature. Emphases are put on experimental facts, but their meanings rather than phenomenological appearance are paid particular attention. Experimental facts are noticed on adopted conditions since the operating mechanism of hydrogen might differ by materials and environments. For theories, assumptions and premises employed are given attention so as to examine their versatility. Consecutive rather than fragmental setup of contents is attempted so as to facilitate readers’ systematic understanding of the problem. The interdisciplinary attribute of the subject requires an understanding of elementary concepts in the wider field. The

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task demands textbooks for each field, but brief descriptions of fundamental ideas are presented when necessary. This book consists of roughly two parts. The first part, from Chaps. 1, 2, 3, 4, and 5, covers basic behaviors of hydrogen in materials after the entry into materials, and the second part, from Chaps. 6, 7, 8, 9, and 10, deals with characteristics of the degradation of mechanical properties and fracture caused by hydrogen. I am pleased to acknowledge my colleagues, particularly my former students at Waseda University, many of whom are coauthors of my works. I also appreciate works by Prof. K. Takai of Sophia University in devising ingenious methods to clarify the function of hydrogen in embrittlement. A book of the same title in Japanese was published by Uchida Rokakuho Publishing, Tokyo, Japan, in 2008. The present book fully revised and reorganized the former one, removing some of its contents and adding recent advances. I would like to acknowledge the courtesy of Uchida Rokakuho for permitting the publication of this new book in the present form. Tokyo, Japan

Michihiko Nagumo

Contents

1

Solid Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Solubility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Lattice Location . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Partial Molar Volume and Strain Field . . . . . . . . . . . . . . . . . . . . . . . 1.4 Atomistic Calculations of the Heat of Solution . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 1 5 6 7 9

2

Hydrogen Trapping and Its Direct Detection . . . . . . . . . . . . . . . . . . . . . 2.1 Manifestations and Analyses of Hydrogen Trapping . . . . . . . . . . . 2.1.1 Solid Solubility at Low Temperatures . . . . . . . . . . . . . . . . 2.1.2 Equilibrium Partition of Hydrogen Among Different Traps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.3 Kinetics of Hydrogen Trapping . . . . . . . . . . . . . . . . . . . . . 2.2 Detection of Hydrogen Trapping and Distribution . . . . . . . . . . . . . 2.2.1 Hydrogen Thermal Desorption Analysis . . . . . . . . . . . . . 2.3 Visualization of Hydrogen Distribution . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Tritium Autoradiography and Hydrogen Microprint Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3.2 Methods Using Stimulated Hydrogen Desorption . . . . . . 2.4 Indirect Detection of Hydrogen Distribution . . . . . . . . . . . . . . . . . . 2.4.1 Neutron Tomography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.2 Scanning Kelvin Prove Microscopy . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11 11 11

Interactions of Hydrogen with Lattice Defects . . . . . . . . . . . . . . . . . . . 3.1 Dislocations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.1 Experimental Facts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1.2 Theoretical Estimation of Hydrogen–Dislocation Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Vacancies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Elementary Attributes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.2 Vacancy Clustering and Migration . . . . . . . . . . . . . . . . . . . 3.2.3 Interaction of Hydrogen with Vacancies . . . . . . . . . . . . . .

41 41 41

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15 18 20 20 32 33 35 38 38 38 39

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3.3

Precipitates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.1 TiC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.2 NbC and VC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3.3 Fe3 C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Grain Boundaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.1 Experimental Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4.2 Theoretical Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Voids and Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

67 68 69 71 71 71 72 73 74

4

Diffusion and Transport of Hydrogen . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Determination of Diffusion Coefficient . . . . . . . . . . . . . . . . . . . . . . 4.1.1 Diffusion Coefficient Data . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.2 Measurement of Diffusion Coefficient . . . . . . . . . . . . . . . 4.1.3 Theoretical Interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Stochastic Theories of Hydrogen Diffusion . . . . . . . . . . . . . . . . . . 4.3 Hydrogen Transport by Moving Dislocations . . . . . . . . . . . . . . . . . 4.3.1 Release of Internal Hydrogen During Straining . . . . . . . . 4.3.2 Effects on Electrochemical Permeation . . . . . . . . . . . . . . . 4.3.3 A Kinetic Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Accelerated Diffusion Along Grain Boundaries . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

77 77 77 78 82 83 86 86 88 90 91 93

5

Deformation Behaviors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Elastic Moduli . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Flow Stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.1 Hardening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.2 Softening . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.3 Explanations of Experimental Results . . . . . . . . . . . . . . . . 5.3 Stress Relaxation and Creep . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.1 Stress Relaxation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.2 Creep . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.3 Implications of Surface Effects . . . . . . . . . . . . . . . . . . . . . 5.4 Direct Observation of Dislocation Activity . . . . . . . . . . . . . . . . . . . 5.5 Elastic and Atomistic Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5.1 Elastic Shielding of Stress Centers . . . . . . . . . . . . . . . . . . 5.5.2 Mobility of Screw Dislocations—Atomistic Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

95 95 96 96 100 102 105 105 108 110 113 114 114

Macroscopic Manifestations of Hydrogen Embrittlement . . . . . . . . . 6.1 Tensile Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1.1 Effects of Test Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1.2 Damage Generation During Straining . . . . . . . . . . . . . . . . 6.2 Fracture Mechanics Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.1 Crack Initiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

123 123 123 127 129 130

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6.2.2 Crack Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fatigue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.1 Fatigue Limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.2 Crack Initiation and Growth-Rate Near Threshold . . . . . 6.3.3 Stage II Crack Growth in Steel . . . . . . . . . . . . . . . . . . . . . . 6.3.4 Fatigue in Austenitic Stainless Steel . . . . . . . . . . . . . . . . . 6.3.5 High-Cycle Fatigue Near Threshold . . . . . . . . . . . . . . . . . 6.3.6 Models of Fatigue Crack Extension . . . . . . . . . . . . . . . . . . 6.4 Delayed Fracture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.1 Characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.2 Effects of Materials Factors . . . . . . . . . . . . . . . . . . . . . . . . 6.4.3 Effects of External Factors . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.4 Laboratory Test Methods . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.5 Concept of the Critical Hydrogen Concentration . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

135 139 140 142 144 150 152 152 155 155 158 159 162 164 167

Microscopic Features Characterizing Hydrogen Embrittlement . . . 7.1 Crack Nucleation Sites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Fractographic Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.1 Cleavage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.2 Dimple Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.3 Quasi-cleavage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.4 Intergranular Fracture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.5 Alteration of Fracture Morphology on Crack Extension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.6 Fatigue Fracture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3 Strain Localization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3.1 Surface Morphology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3.2 Internal Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3.3 Plastic Instability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.4 Damage Accumulation Precursory to Crack Nucleation . . . . . . . . 7.4.1 Damage Precursory to Crack Initiation . . . . . . . . . . . . . . . 7.4.2 Effects of Stress History—Damage Accumulation . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

171 171 174 174 175 176 179

Microstructural Effects in Hydrogen Embrittlement of Steel . . . . . . 8.1 Martensitic and Bainitic Steel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1.1 Tempering of Martensite and Bainite . . . . . . . . . . . . . . . . 8.1.2 Precipitates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1.3 Grain-Size Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1.4 Impurities and Alloying Elements . . . . . . . . . . . . . . . . . . . 8.1.5 Microscopic Features of Fracture . . . . . . . . . . . . . . . . . . . 8.2 Multiphase Steel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.1 Dual Phase Steel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.2 Retained Austenite—TRIP Steel . . . . . . . . . . . . . . . . . . . . 8.3 Austenitic Stainless Steel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

205 206 206 209 212 216 221 223 224 227 230

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9

Contents

8.3.1 Hydrides and Phase Changes . . . . . . . . . . . . . . . . . . . . . . . 8.3.2 Compositional Effects on Hydrogen Embrittlement . . . . 8.3.3 Fractographic Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3.4 Deformation Microstructures . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

230 233 237 238 242

Mechanistic Aspects of Fracture I—Brittle Fracture Models . . . . . . 9.1 Internal Pressure Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2 Surface Adsorption Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.3 Lattice Decohesion Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.3.1 Stress-Controlled Criterion . . . . . . . . . . . . . . . . . . . . . . . . . 9.3.2 Local Stress Intensity Approach . . . . . . . . . . . . . . . . . . . . 9.4 Theories of Intergranular Fracture . . . . . . . . . . . . . . . . . . . . . . . . . . 9.4.1 Interface Decohesion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.4.2 Meaning of Surface Energy in Fracture Criteria . . . . . . . 9.5 Summary of Brittle Fracture Models . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

245 245 248 249 249 251 253 253 258 261 263

10 Mechanistic Aspects of Fracture II—Plasticity-Dominated Fracture Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.1 Outline of Elemental Concepts of Ductile Fracture . . . . . . . . . . . . 10.1.1 Void Nucleation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.1.2 Void Growth and Coalescence . . . . . . . . . . . . . . . . . . . . . . 10.1.3 Model of Plastic Instability . . . . . . . . . . . . . . . . . . . . . . . . . 10.2 Hydrogen-Enhanced Localized Plasticity Theory . . . . . . . . . . . . . 10.3 Adsorption-Induced Dislocation Emission Theory . . . . . . . . . . . . 10.4 Autocatalytic Void Formation and Shear Localization Theory . . . 10.5 Hydrogen-Enhanced Strain-Induced Vacancy Theory . . . . . . . . . . 10.5.1 Brief Summary of Findings on Involvement of Strain-Induced Vacancies in HE . . . . . . . . . . . . . . . . . . 10.5.2 Mechanistic and Microscopic Functions of Vacancies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.6 Summary of Ductile Fracture Models . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Delayed Fracture After Long Exposure in Atmospheric Environments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Peculiar Situations of Delayed Fracture as Material Failure . . . . . 11.3 Fractographic Features and Microscopic Process of Cracking . . . 11.3.1 Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.3.2 Entire Cracking Process . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.3.3 Crack Initiation Site—Frail Zone . . . . . . . . . . . . . . . . . . . 11.3.4 Crack Propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.4 Assessment of the Susceptibility to Delayed Fracture . . . . . . . . . . 11.5 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

265 265 265 267 276 277 281 282 283 284 286 289 291 293 293 294 296 296 297 299 304 308 310 310

Chapter 1

Solid Solution

1.1 Solubility Hydrogen that causes deterioration of mechanical properties of metallic materials comes from environments during fabrication and service. Hydrogen adsorbs on the surface of metals as H2 molecules or H3 O+ ions, dissociates to atoms, and diffuses into the bulk. The hydrogen content depends on the type of the material, its internal and surface states, and environmental conditions such as temperature, humidity, and the presence of corrosive species. Hydrogen atoms locate in metals at various sites with respective energies, as schematically shown in Fig. 1.1. The role of hydrogen in embrittlement is the central subject of this book, and hydrogen interactions with lattice defects are crucial. Hydrogen atoms in solid solution, i.e., at interstitial sites of the regular crystalline lattice, are intrinsic to a metallic material but are only a part of the total number of hydrogen atoms in most cases at thermal equilibrium. However, interstitial sites are dominant for the number and control of the transport and partition of hydrogen at various trap sites. Solid solubility—the atomic fraction of hydrogen in the lattice at thermal equilibrium—is a function of temperature and hydrogen environments. Figure 1.2 [1] compares the temperature dependence of the solid solubility θ of hydrogen in various metals in hydrogen gas of 0.1 MPa. Both positive and negative dependencies on temperature are present in metals. The negative slope in the Arrhenius plot for iron means an endothermic reaction for hydrogen absorption, i.e., the hydrogen energy in the solid solution is higher than that in the hydrogen molecule, as Fig. 1.1 indicates. It contrasts with Ti and V, of higher affinities with hydrogen than Fe. The amount of absorbed hydrogen in iron at high temperatures is readily measurable by chemical analysis. The solid solubility data thus determined for pure iron under hydrogen gas environments above 573 K are shown in Fig. 1.3 [2]. The ordinate denotes θ in atomic √ ratio normalized by p, where p is the hydrogen gas pressure in the unit of 0.1 MPa. Solubility data for iron at lower temperatures are in Sect. 2.1 concerning trapping of hydrogen in lattice defects. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 M. Nagumo, Fundamentals of Hydrogen Embrittlement, https://doi.org/10.1007/978-981-99-0992-6_1

1

2 Fig. 1.1 Energies of hydrogen in gas-metal equilibria. E s Energy of solid solution. E m Migration energy. E b Trap binding energy

1 Solid Solution

GAS

METAL Em

Es

Eb

Fig. 1.2 Temperature dependence of hydrogen solubility in various metals in equilibrium at 0.1 MPa hydrogen gas (Huang et al. [1]. Reprinted with permission from The Japan Inst. Metals)

In Fig. 1.3, the level of θ in face-centered cubic (fcc) γ -iron is higher than that in body-centered cubic (bcc) α-iron, and a slight departure from linearity in the Arrhenius plot, i.e., the log C versus 1/T relation, appears at temperatures lower than about 773 K. The departure was discussed to originate in simultaneous occupations of tetrahedral and octahedral sites in α-iron [2]. Definitive values of θ in α-iron in the room temperature regime are few. Hirth collected reliable data and gave a useful expression of θ (in atomic ratio) in hydrogen gas of pressure p (in 0.1 MPa) in the form √ θ = 0.00185 p exp(−3440/T )

(1.1)

1.1 Solubility

3 1300 1100

900

700

500

300ºC

Fe-H Solid Solubility, θ/p1/2

δ γ α

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

T-1, (104 K-1)

Fig. 1.3 Solid solubility of hydrogen in iron above 573 K (Different marks are by literatures in the original paper) (Da Silva et al. [2])

with T in Kelvin [3]. The heat of solution of hydrogen in α-iron obtained from the temperature dependence of θ is 28.6 kJ/mol-H. √ The p dependence of θ is known as Sieverts’ law. It is originally an experimental relation for diatomic molecular gases, but thermodynamics also derives the law in the following way. The entry of hydrogen into metal starts from the dissociation of adsorbed hydrogen molecules on the metal surface, followed by the diffusion of hydrogen atoms into the metal. For the equilibrium reaction 1 H2  Hsol , 2

(1.2)

where the chemical potential μ is equal in both sides, i.e. 1 μH = μHsol . 2 2

(1.3)

The expression of μ using its value at the standard state, μ0 , and the hydrogen concentration in terms of the activity, a, is μ = μ0 + RT ln a,

(1.4)

where R is the gas constant. By definition of μ, the change of the Gibbs energy associated with the absorption of hydrogen is −ΔG0 =

aHsol 1 0 . μ − μ0Hsol = RT ln 1/2 2 H2 aH2

(1.5)

4

1 Solid Solution

Since ΔG0 = ΔH0 − T ΔS0 ,

(1.6)

where H and S denote respectively enthalpy and entropy, Eq. (1.5) is rewritten as aHsol =

1/2 aH2

  0  ΔS ΔH0 exp , exp − RT R

(1.7)

leading to the form of Sieverts’ law. An increase in the hydrogen partial pressure augments the hydrogen concentration. The associated change in the volume differs between ideal and real gases, and the change in the chemical potential in a real gas is expressed by defining and introducing fugacity f instead of pressure p in an ideal gas, i.e., dμ = RT d ln f .

(1.8)

From Eqs. (1.8) and (1.4), an expression of the hydrogen activity a in terms of fugacity f is a=

ϕp f = 0 0, 0 f ϕ p

(1.9)

where ϕ is the fugacity coefficient and the superscript “0 ” denotes the standard state. Accordingly, for estimating the equilibrium hydrogen concentration using Eq. (1.1), p should be replaced by f . The conversion is necessary for practice in high pressures since ϕ increases with p. Calculated values of ϕ are tabulated in Ref. [4], e.g., 1.06, 1.41, and 2.06 for p of 10, 50, and 100 MPa hydrogen gas at 300 K, but the values vary according to the equation of state employed for the calculation. The equilibrium hydrogen concentration in α-iron at room temperature expected from Eq. (1.1) is minimal, ca 2 × 10–8 (in atomic ratio), in 0.1 MPa hydrogen gas. Then, usually observed hydrogen concentrations of the order of mass ppm in ferritic steels are mostly of trapped hydrogen in various lattice defects except under non-equilibrium situations. The solubility of hydrogen in steel is substantially altered by alloying. In austenitic stainless steels, the heat of solution of hydrogen is about 16 kJ/mol-H [5], much less than that in pure γ -iron. Solubility data for stainless steels are shown in Fig. 1.4 [5]. Higher solubilities in austenitic stainless steels than those in ferritic stainless steels are due not only to the crystal structures but also to alloying elements such as Ni and Cr. Most data in Fig. 1.4 are by permeation experiments. It is to be noticed that the distributions of hydrogen in austenitic stainless steel are often very inhomogeneous because of the low diffusivity of hydrogen, as described in Sect. 4.1.1. At elevated temperatures, the increased diffusivity favors homogeneous distribution, and the hydrogen content in Type 316L stainless steel directly measured using thermal desorption is about 40 mass ppm in 70 MPa hydrogen at 363 K [6].

1.2 Lattice Location

5

Fig. 1.4 Solid solubility data of hydrogen in stainless steel (Caskey [5])

1.2 Lattice Location Hydrogen atoms locate at interstitial sites in the elementary lattice of α-iron. Direct determination of the location is difficult because of the hydrogen’s low solubility and high diffusivity. However, calculations of the total energy of the solution, described in Sect. 1.4, showed preferential occupancy at the tetragonal site (T-site) than at the octahedral site (O-site). Analyses of thermodynamic data also showed a favored occupancy at the T-site at low temperatures, while the O-site occupancy increased with the temperature rise [2, 7]. A powerful method to directly detect the lattice location of hydrogen in metals is a channeling analysis utilizing a nuclear reaction 1 H(11 B, α)αα using 11 B beam. The location of hydrogen can be precisely determined by measuring the angular profile of emitted α particles on tilting a single crystal specimen against the incident 11 B beam. Hydrogen occupancy at the T-site was successfully confirmed for bcc single crystals of the group V a metals (Nb, V, Ta) and their alloys [8–11]. In vanadium, a reversible displacement of hydrogen from the normal T-site occurred when compressive stress of 70 MPa was applied along the axis [8]. In Nb-Mo alloys with Mo of less than 10%, the position of the hydrogen atom shifts from the center of the T-site to a neighboring Mo atom, as shown schematically in Fig. 1.5 [10]. The shift decreases with increasing Mo concentrations and disappears at 20 at.% of Mo, directly showing hydrogen trapping by alloying elements.

6

1 Solid Solution

Fig. 1.5 Location of hydrogen atom in Nb–Mo alloy determined by a 1 H(11 Bα)αα nuclear reaction channeling method (Yagi [10]. Reprinted with permission from The Iron and Steel Institute Japan)

1.3 Partial Molar Volume and Strain Field The entry of hydrogen into metals accompanies volume expansion, and dilatation measurements are available for direct determination of the partial molar volume of hydrogen, V H . While a substantial scatter of data is inevitable, a reliable V H value for α-iron wires exposed to hydrogen gas is 2.0 × 10–6 m3 /mol-H in the temperature range from 873 to 1073 K [12]. Electrochemical hydrogen permeation experiments are alternative methods for determining V H at room temperature. The applied elastic stress affects the steady-state permeation current in iron due to the change in the hydrogen solubility. The chemical potential of hydrogen in metal alters by the applied stress, and an additional hydrogen flow occurs to keep equilibrium. The hydrogen concentration evaluated from the permeation-current density gives V H as [13],  V H = RT

 ∂ ln (Cσ /C0 ) , ∂ σh

(1.10)

where C σ and C 0 are respectively hydrogen concentrations with and without the application of external hydrostatic stress σh . A method to evaluate C σ and C 0 is to measure reversible permeation current densities on cyclic stressing, and the obtained V H for pure iron and AISI 4340 steel are 2.66 × 10–6 and 1.96 × 10–6 m3 /mol-H, respectively [13], which are close to the value obtained from dilatation measurements at high temperatures. The value of V H is insensitive to temperature and microstructures. The value of 2.0 × 10–6 m3 /mol-H, i.e., about 0.3 nm3 /H-atom, is almost common for all metals [7]. However, Hirth noticed [3] that the value of V H included an effect associated with elastic relaxation at the free surface and that the internal volume change δv for calculating interactions with the hydrostatic elastic fields of lattice defects was 1.22 × 10–6 m3 /mol-H. The volume change around the hydrogen atom is crucial in the interaction energies of hydrogen with various types of lattice defects, described in Chap. 3. In α-iron, the local strain field around a single hydrogen interstitial atom has tetragonal symmetry in both the T- and O-sites [3], but the tetragonality is considered small. Accordingly, in the elastic regime, the hydrogen concentration, C h , under hydrostatic stress σ h , or C σ under a uniaxial stress σ, at a constant hydrogen fugacity f is given respectively as

1.4 Atomistic Calculations of the Heat of Solution



σh V H C h = C0 exp RT

7

 ,

(1.11)

,

(1.12)

f

or 

σVH Cσ = C0 exp 3RT

 f

where C 0 is the value at zero stress [14]. Stress fields in materials are generally inhomogeneous and result in localized hydrogen distributions. An example is the hydrogen accumulation in stressconcentrated areas such as notch root [15]. Visualizing hydrogen distributions is described in Sect. 2.3. It should be careful that the local increase in the hydrogen concentration by stress is not only for hydrogen in solid solution but also for hydrogen trapped in various lattice defects created by plastic strain. In embrittlement, generation and activation of lattice defects deteriorate materials, and the crucial role of strain-induced defects, rather than hydrogen itself, is described in later chapters.

1.4 Atomistic Calculations of the Heat of Solution In the crystalline lattice of metals, the electronic state of hydrogen differs from that of a free atom because of the partial sharing of electrons with host metallic ions. The heat of solution, Hs, is the difference between the energy of hydrogen atom in solid solution and half of the energy of hydrogen molecule as shown in Fig. 1.1. Atomistic calculations of binding energies of hydrogen with metals have been conducted by various methods. The first-principles calculations are generally time-consuming, and some approximate methods have been devised. The effective medium theory (EMT) replaces the complicated inhomogeneous host with an effective host consisting of a homogeneous electron gas. The embedding energy ΔE of an atom is the energy difference between the combined atom–host system minus the energies of the separated atom and the host. The host density is not homogeneous in general, and the core regions of host atoms have substantial variations in the electrostatic potential. Nørskov took into account the interaction of the hydrogen 1s level with the valence bands, mainly 3d band, of the host and calculated ΔE of hydrogen at the T-site of α-iron in transition metals [16]. The calculated value of ΔE for α-iron was -212 kJ/mol. The heat of solution is the embedding energy minus the binding energy of a hydrogen molecule (−232 kJ/mol), and the resultant 20 kJ/mol is about two-thirds of the experimentally obtained heat of solution of 29 kJ/mol [3, 17]. A generalization of the EMT using a pair-wise interaction is the embedded atom method (EAM) [18, 19]. It considers each atom in a system as embedded in a host

8

1 Solid Solution

lattice consisting of all other atoms. An employed approximation is that the embedding energy depends only on the environment immediately around the impurity or locally uniform electron density. The energy of an impurity atom in a host consists of two terms; one is a function of the electron density of the host without impurity, and the other is the short-range electrostatic interaction. The total energy is a sum of all individual contributions of the host and the impurity. Daw and Baskes determined the embedding energies semiempirically and calculated the adsorption energies on the surfaces of Pd and Ni. Agreements with experimental values were fairly good for Pd, but calculated values were much smaller than experiments for Ni. For the bcc iron–hydrogen system, Wen et al. proposed a new potential to use in the EAM calculation [20]. Using empirically determined parameters for fitting, Wen et al. obtained good agreements between calculated and experimental values for the heat of solution, migration energy, and hydrogen binding energy with vacancies. On the other hand, Itsumi and Elis calculated electronic structures for bcc iron clusters with or without hydrogen and also involving a vacancy [21]. The calculations used local-density functional theory, implemented by the Discrete Variational Method (DV-Xα). Calculations of the density of states for α-Fe clusters of 32 atoms with and without one hydrogen atom showed that the main bonding peak was due to H-1 s and Fe-4 s hybridization with smaller contributions of Fe-3d and 4p. The charge transfer of about 0.6e from the first and second neighbor Fe atoms to H decreased metallic bond strength. Itsumi and Elis used the concept of the bond orders, defined as the sum of overlap populations between two atoms, as a measure of interatomic bonding strength. Interstitial hydrogen notably decreases Fe–Fe bond strength, but the acting area is over a small distance within 0.3 nm. The Fe–H bond strength increases by nearby vacancies associated with a shift of the position of the hydrogen atom toward the vacancy. The total energy of the many-electron system at the ground state is a function of the spatially dependent electron density. Tateyama et al. applied the density functional theory (DFT) to calculate the total energy of the H–α–Fe system using a pseudopotential and a plane-wave basis set [22]. A supercell consisting of 54 atoms (53 Fe-atoms + 1 H-atom) was adopted, locating hydrogen at a T-site as the ground state. The calculated heat of solution was 32.8 kJ/mol-H, which corresponded to an experimentally determined value of 29 kJ/mol-H. Effects of the supercell size or applied pressure on the system’s total energy were also calculated [23]. The calculated heat of solution was a decreasing function of hydrostatic tensile stress that increased cell volume, a natural consequence of the repulsive nature of the solid solution. It was deduced that the hydrogen concentration in a stress-concentrated region, e.g., ahead of a crack tip, increases about 100-fold when applied hydrostatic tensile stress of 2–5 GPa. Another calculation of the heat of solution using DFT with different computational supercell sizes, i.e., different hydrogen concentrations, showed the heat of solution of 28.9 kJ/mol in the T-site of α-iron [24]. The energy difference between hydrogen in the O-site and T-site converged as the hydrogen concentration decreased, suggesting the operation of a repulsive interaction between hydrogen atoms.

References

9

Calculations of the formation energy of a Fe–H complex using DFT were also conducted with a supercell of 54 Fe atoms [25]. The formation energy was defined, similarly to the embedding energy, as the energy of the complex minus the total energy of Fe atoms in a cell and the energy of one hydrogen atom in the isolated hydrogen molecule. The calculated formation energies for the T-site and O-site occupancy were 20.3 and 32.8 kJ/mol, respectively. The value of 20.3 kJ/mol corresponds to 20 J/mol obtained by the EMT method [16] but differs from the experimental heat of solution of around 28.6 kJ/mol. Counts et al. ascribed the gap to the zero-point-energy of the lattice vibration for hydrogen in α-iron and corrected the value to 28.9 kJ/mol in agreement with the experimental one [25].

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25.

Y.G. Huang, K. Fujita, H. Uchida, Bull. Jpn. Inst. Metals 18, 694–703 (1979) J.R.G. da Silva, S.W. Stafford, R.B. McLellan, J. Less Common Metals 49, 407–420 (1976) J.P. Hirth, Metall. Trans. A 11A, 861–890 (1980) H P. van Leeuwen, in Hydrogen Degradation of Ferrous Alloys, eds. by R.A. Oriani, J.P. Hirth, M. Smialowski (Noyes Pub., Park Ridge N.J. 1985), pp. 16–35 G.R. Caskey, Jr., in Hydrogen Degradation of Ferrous Alloys, eds. by R.A. Oriani, J.P. Hirth, M. Smialowski (Noyes Pub., Park Ridge N.J., 1985), pp. 822–862 K. Takai, K. Murakami, N. Yabe, H. Suzuki, Y. Hagiwara, J. Jpn. Inst. Metals 72, 448–456 (2008) K. Kiuchi, R.B. McLellan, Acta Metall. 31, 961–984 (1983) Y. Yagi, T. Kobayashi, S. Nakamura, F. Kano, K. Watanabe, Y. Fukai, S. Koike, Phys. Rev. B 33, 5121–5123 (1986) Y. Yagi, T. Kobayashi, Y. Fukai, K. Watanabe, J. Phys. Soc. Jpn. 52, 3441–3447 (1983) E. Yagi, ISIJ Int. 43, 505–513 (2003) C. Sugi, E. Yagi, Y. Okada, S. Koike, T. Sugawara, T. Shishido, K. Ogiwara, J. Phys. Soc. Jpn. 82, 074601 (2013) H. Wagenblast, H.A. Wriedt, Metall. Trans. 2, 1393–1397 (1971) J. O’M Bockris, P.K. Subramanyan, Acta Metall. 19, 1205–1208 (1971) H.A. Wriedt, R.A. Oriani, Acta Metall. 18, 753–760 (1970) K. Ichitani, M. Kanno, S. Kuramoto, ISIJ Int. 43, 496–504 (2003) J.K. Nørskov, Phys. Rev. B 26, 2875–2885 (1982) W.J. Arnoult, R.B. McLellan, Acta Metall. 21, 1396–1397 (1973) M.S. Daw, M.I. Baskes, Phys. Rev. Lett. 50, 1285–1288 (1983) M.S. Daw, M.I. Baskes, Phys. Rev. B 29, 6443–6453 (1984) M. Wen, X.-J. Xu, S. Fukuyama, K. Yokogawa, J. Mater. Res. 16, 3496–3502 (2001) Y. Itsumi, D.E. Ellis, J. Mater. Res. 11, 2206–2213 (1996) Y. Tateyama, T. Miyazaki, T. Ohno, Phys. Rev. B, 67, 174105-1-0 (2003) Y. Tateyama, T. Ohno, ISIJ Int. 43, 573–578 (2003) D.E. Jiang, E.A. Carter, Phys. Rev. B 70, 064102 (2004) W.A. Counts, C. Wolverton, R. Gibala, Acta Mater. 58, 4730–4741 (2010)

Chapter 2

Hydrogen Trapping and Its Direct Detection

2.1 Manifestations and Analyses of Hydrogen Trapping 2.1.1 Solid Solubility at Low Temperatures The hydrogen concentration in steel is crucial to the evolution of embrittlement, but its values at failure substantially differ by the steel and the case of failure. The equilibrium hydrogen concentration in steel varies not only by the environment but also by the microstructures of the steel. The main reason is hydrogen trapping in various lattice defects that directly concern the fracture process. Trapping of hydrogen appears in the temperature dependence of the equilibrium hydrogen content. Observed hydrogen contents are usually of the order of 1 mass ppm in α-iron at room temperature under ordinary environments, far exceeding the solid solubility of hydrogen. Figure 2.1 [1] is the extension of Fig. 1.2 for iron to lower temperatures. Data in the temperature range 1/T > 20 × 10−4 substantially scatter, and most specimens are given cold-straining and subsequent annealing that produce various types of lattice defects. Direct measurements of hydrogen solubility are difficult because of very low concentrations at low temperatures. The measurements often utilize hydrogen diffusivity, which is strongly affected by trapping in lattice defects, even weak binding with hydrogen. Permeation techniques are conventional for this purpose, and the following briefly describes the procedure. The steady-state flow of hydrogen, J ∞ , in metal is described by Fick’s first law of diffusion, J∞ = −DH

dC , dx

(2.1)

where DH is the diffusion coefficient of hydrogen and C is the hydrogen concentration. Assuming Sieverts’ law for hydrogen concentrations at the input and output surfaces of the specimen, the total flux jt of hydrogen permeating through a disk of area A and thickness L is expressed in terms of the permeability coefficient F as, © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 M. Nagumo, Fundamentals of Hydrogen Embrittlement, https://doi.org/10.1007/978-981-99-0992-6_2

11

12

2 Hydrogen Trapping and Its Direct Detection 10-3

Fe-H Fe-D Fe-T

Solid Solubility (θ/p1/2)

10-4

10-5

α 10-6

10-7 8

10

12

14

16

18

20

22

24

26

28

30

32

34

T (10 /K) -1

4

Fig. 2.1 Solid solubility of hydrogen in iron in the temperature range from 293 to 1173 K (da Silva et al. [1])

jt = ϕ

) A ( 1/2 pi − po1/2 , L

(2.2)

where pi and po are pressures in the input and output surfaces, respectively. The numerical value of F obtained for α-iron above 373 K is [2] ϕ = (2.9 ± 0.5) × 10−3 exp[(−35 ± 1.8kJ/mol)/RT ],

(2.3)

where the units of F is [cm3 (ntp H2 )·cm−1 ·sec−1 ·atm−1/2 ]. Electrochemical techniques are also used for hydrogen permeation from the gas phase through sheet specimens [3]. The permeability coefficient for pure iron thus obtained in temperature and pressure ranges of 273–333 K (0–60 °C) and 0.01–1 atm, respectively, is ϕ = 2.6 × 1017 exp[(−36 ± 2.5 kJ/mol)/RT ],

(2.4)

where the unit of F is [atom-H·cm−1 ·sec−1 ·atm−1/2 ]. When the hydrogen pressure at the output surface is negligible, the hydrogen concentration at the input surface C i in equilibrium with hydrogen gas of pressure pi is obtained from Eqs. (2.1) and (2.2) using observed F and DH as Ci =

√ ϕ pi . DH

(2.5)

2.1 Manifestations and Analyses of Hydrogen Trapping

13

Equation (2.5) is also applied to the hydrogen entry by cathodic polarization, where C i [atoms-H·cm−3 ] is calculated from the steady-state current J ∞ [atomsH·cm−2 ·sec−1 ] as Ci =

J∞ L . DH

(2.6)

Figure 2.2 [4] shows the result of an electrochemical permeation experiment with α-iron single crystal specimens with/without prestraining. Tensile prestrain of 4.3% was given at liquid nitrogen temperature, and the hydrogen concentration was calculated from the steady-state hydrogen flux. The temperature dependence of C i for specimens without prestrain is consistent with the lower limit of the solubility data in Fig. 2.1 and shows the endothermic nature of the solid solution. On the contrary, the prestrain increases the hydrogen content to a large extent and also changes the hydrogen dissolution from endothermic to exothermic. The hydrogen concentration C i in Eqs. (2.5) and (2.6) determined in this way is conventionally termed diffusible or diffusive hydrogen. It must be careful that C i is a quantity calculated from the boundary condition of the diffusion equation, and C i includes hydrogen both in solution and weakly trapped, reversibly to the solid solution to keep local equilibrium. The driving force of diffusion is the concentration gradient of lattice hydrogen, but reversibly trapped hydrogen compensates for the loss of lattice hydrogen by diffusion. In electrochemical permeation experiments, the electrolyte and the applied cathodic polarization potential control the entry of hydrogen. The condition for electrolysis is crucial not only for the concentration of hydrogen in solution but also for trapped states of hydrogen. In this respect, the effective hydrogen fugacity in electrochemical experiments is a significant quantity. Table 2.1 lists some reported Temperature (ºC)

(gr-atom/cm3)

70

55

40

25

10

Strained by 4.3%

Hydrogen Content

Fig. 2.2 Temperature dependence of hydrogen content in iron with (◯) and without (●) plastic strain of 4.3% (Yamakawa et al. [4]. Reprinted with permission from The Japan Society of Corrosion Engineering)

2.8

3.0

3.2

T (10 / K) -1

3

3.4

3.6

14

2 Hydrogen Trapping and Its Direct Detection

values of hydrogen fugacity for iron and AISI 1045 steel estimated using Eq. (2.2) and permeability coefficients [3, 5]. Under corrosive atmospheric environments, electrochemical reactions on the surface control the hydrogen entry into materials, and the equivalent hydrogen fugacity varies with ambient atmospheres. Figure 2.3 [6] shows records of hydrogen permeation currents for a high-strength Cr–Mo steel foil specimen, the outer side of which is exposed to atmospheric environment. The variation of the permeation current corresponds to daily humidity alternations. Permeation experiments are used for the measurement of the hydrogen diffusion coefficient that manifests hydrogen trapping. Details of the procedures and thus obtained information are described in Sect. 4.1.2. Table 2.1 Effective hydrogen fugacity on the surface of electrode at cathodic electrolysis Materials

Electrolyte

Current density (mA/cm2 )

Hydrogen fugacity (atm)

Hydrogen pressure (atm)

99.5 iron

25 °C, distilled water

–

5.7 × 10–5

5.7 × 10–5

Armco iron

25 °C, 0.1 N NaOH 8.1

2.2 × 101

2.2 × 101

99.8 iron

25 °C, 0.1 N H2 SO4 0.4

5.4 ×

102

4.5 × 102

99.9965 iron

24 °C, 1 N H2 SO4 + 5 g/L As2 O3

4.5

1.2 × 108

1.8 × 104

99.8 iron

25 °C, 0.1 N NaOH 1.8

1.1 × 100

1.1 × 100

99.8 Ferrovac E

25 °C, 0.1 N NaOH 11.3

2.9 ×

2.9 × 101

AISI 1045

0.1 N H2 SO4 + 0.5 mg/L As2 O3

0.4

> 1.4 ×

AISI 1045

0.1 N NaOH + 10 mg/L As2 O3

0–0.6

0–3 × 103

101 104

Kumnick et al. [3] and Oriani et al. [5]

0.6

SCM440 5 min/point

Current Density (µA/cm2)

Fig. 2.3 Alternating variation of the permeation current density through iron specimen exposed to outer atmospheric environment (Yamakawa et al. [6]. Reprinted with permission from The Iron and Steel Institute Japan)

0.4

0.2

0

4 8 Exposure Period (days)

2.1 Manifestations and Analyses of Hydrogen Trapping

15

2.1.2 Equilibrium Partition of Hydrogen Among Different Traps Hydrogen atoms interact with various lattice defects, such as point defects, dislocations, grain boundaries, during migration in the lattice. The potential energy of a hydrogen atom varies by its sites, and the hydrogen atom preferentially stays, i.e., trapped, at sites close to defects where the potential energy is lower than that at interstitial sites in the regular lattice. The binding energy of hydrogen, E b , with a type of defect is the energy difference between the trapped site and the regular lattice, as shown in Fig. 1.1. The trapping of hydrogen is tighter at sites of higher E b , making the location more stable. The total number of trapped hydrogen atoms is the product of the number of sites and the fractional occupancy by hydrogen, and the binding energies with traps determine the distribution of hydrogen atoms. The distribution function for the partition of hydrogen among different sites was discussed by Hirth and Carnahan [7] concerning the adsorption of hydrogen at dislocations and cracks in iron. From a thermodynamics viewpoint, McLellan derived the distribution of hydrogen among trap sites and neighboring regular lattice sites in terms of the Fermi–Dirac distribution, i.e., a maximum of one particle permitted in one state, provided that the fractional occupancy was low and mutual interactions of trapped hydrogen atoms were negligible [8]. The Fermi–Dirac distribution expresses the probability f (E) that a particle will have energy E as f (E) =

1 , 1 + exp[(E − E F )/kB T ]

(2.7)

where k B is the Boltzmann constant and E F is the Fermi energy. Following Beshers [9], the partition of N H hydrogen atoms in two distinct energy states, E 0 and E 1 = E 0 − E b , under Fermi–Dirac statistics is written as ) ) ( ) ( ( NH1 EF NH0 E0 E1 = = exp . (2.8) exp − exp − N0 − NH0 kB T N1 − NH1 kB T kB T Denoting the state 0 and 1 for the regular lattice and trapped state, respectively, Eq. (2.8) is rewritten in terms of fractional occupancy, θ, as ) ) ( ( θx θL Eb Eb ≈ θL exp , = exp 1 − θx 1 − θL kB T kB T

(2.9)

showing an approximate Boltzmann distribution when θ x direction toward a nearest-neighbor vacancy site [49].

58

3 Interactions of Hydrogen with Lattice Defects

Table 3.3 Binding energies of deuterium with vacancies produced by ion implantation

Material

E V-H (kJ/mol)

Type of vacancies

References

Fe

46

Monovacancy

[48]

Fe

51

Monovacancy

[49]

Fe

68

Cluster

[49]

Fcc stainless steel

22

Cluster

[50]

Ni

23

Monovacancy

[51]

Ni

41

Multivacancy

[51]

Cu

41

Monovacancy small cluster

[52]

Mo

111

Cluster

[53]

Mo

99

Monovacancy (Low occupancy)

[53]

Mo

77

Monovacancy (High occupancy)

[53]

The displacement is because a deuterium atom seeks the optimum electron density to minimize its energy. The binding energy of the hydrogen atom calculated using an effective medium theory (EMT) was consistent with the observed one when a displacement of 0.05 nm was assumed [55]. There are 6 O-sites and 8 or 24 T-sites in the fcc or bcc structure, respectively, around a vacant lattice site. Multiple occupations by hydrogen were deduced experimentally from ion implantation experiments of deuterium with different fluencies. Figure 3.8 [56] shows the effects of deuterium fluence on the retained concentrations of deuterium in the implanted zone in iron after a linear temperature ramp. The deuterium concentration decreased at 220 K, and the decrease was enhanced by increasing the deuterium fluence. The shift of the start of deuterium migration to lower temperatures was ascribed to the release of deuterium from multitrapped states at monovacancy when the binding energy decreased with the increasing number of trapped deuterium atoms. Binding enthalpies were also calculated using EMT for occupancy of 1–6 deuterium atoms for a vacancy in transition metals [57]. In EMT calculations, the binding energy is defined as the energy required to embed a hydrogen atom into the host metal, and the hydrogen trapping energy in multiple occupancies is defined, for the last hydrogen atom in a VHN complex, as △E(N ) = E(N ) − E(N − 1) − E sol ,

(3.17)

where E sol denotes the interstitial binding energy [57]. The observed profiles in Fig. 3.8 agree with those calculated using trapping enthalpies of 61 kJ/mol for N =

3.2 Vacancies

59

Fig. 3.8 D retention versus temperature profile of 15-keV D in Fe. Strong He traps located at 1.2 μm act as sinks for the released (Besenbacher et al. [56]. Reprinted with permission from AIP Publishing LLC)

D in Fe : ▲ 4×1016 D/cm2 × 3×1016 D/cm2 ● 2×1016 D/cm2 ○ 1×1016 D/cm2 −−− Theoretical fit.

Vacancies (1.1×1016/cm2) for 4×1016D/cm2

Fig. 3.9 Hydrogen trapping energy in α-Fe calculated using DFT (filled circle) and EMT (open circle) (Tateyama et al. [58]. Reprinted with permission from American Physical Society)

-Etrap (n) kJ/mol-H

1–2 and 41 kJ/mol for N = 3–6 [55]. The results implied decreasing trapping strength with increasing occupancy. Trapping energies calculated afterward using a modified EMT are included in Fig. 3.9 [58] with open circles. Trapping energies for multiple hydrogen occupancy for a monovacancy were calculated for iron using the density functional theory (DFT) [58, 59]. Calculated trapping energies of VHN complexes in iron are shown in Fig. 3.9, together with the former results of EMT calculations [56]. The DFT calculation shows that the trapping energies of VH1 and VH2 are about 60 kJ/mol and that VH6 is unstable. The calculation also shows that up to three hydrogen atoms are exothermically bound to monovacancy. Accordingly, very high site occupancies of hydrogen are expected for VH and VH2 , and most vacancies may exist in the form of VH2 [59]. Another atomistic calculation using DFT combined with molecular dynamics (MD) and Monte Carlo methods [60] showed that a three-dimensional tetrahedral configuration has the lowest energy for VH4 and that the binding is exothermic.

60

3 Interactions of Hydrogen with Lattice Defects

An explanation of the stability, deduced by the DFT analysis, was that Fe3d-H1s hybridization causes charge transfer to the region around the hydrogen atom from neighboring iron atoms. Resulted negatively charged hydrogen atoms might repel each other, and calculations showed that distances between hydrogen atoms and the corresponding O-sites in the VHN complexes decrease with increasing N [58]. The hydrogen binding energy for multiple trapping in vacancy clusters was calculated by Ebihara et al., using the molecular static simulation [61]. The number of trap sites of an i-size vacancy cluster increases with the vacancy cluster size. Table 3.4 lists the calculated hydrogen trapping energies.

3.2.3.2

Hydrogen Enhancement of Strain-Induced Generation of Vacancies

(a) Results of thermal desorption analysis TDA of hydrogen introduced into deformed iron, used as the tracer of defects, Figs. 3.2 and 3.4, revealed the strain-induced generation of lattice defects. Figure 3.10 [62] is a complemental result of Fig. 3.4, to demonstrate the hydrogen effects on the strain-induced generation of lattice defects. The ordinate of Fig. 3.10 is the amount of tracer hydrogen introduced to saturation into a commercial pure iron given various amounts of tensile-straining after hydrogen precharging. Cathodic hydrogen charging was at a current density of 50 A m2 in an aqueous solution of H2 SO4 of 2.5 in pH added 0.09 mass% NH4 SCN as a catalysis [62]. In Fig. 3.10, the tracer hydrogen is denoted as [strain], [H + strain], and [H + strain + 200 °C], each respectively indicating “strained”, “strained after hydrogen precharging”, and “annealed at 200 °C (473 K) after hydrogen precharging and straining”. The amount of tracer hydrogen was measured using TDA that showed a single desorption peak, and the annealing effect indicates that most of the increment of tracer hydrogen by hydrogen precharging is due to the enhanced generation of vacancies. LTDS that starts temperature ramp from a temperature as low as 70 K is a powerful tool to exhibit a complete hydrogen thermal desorption profile, as described in Sect. 2.2.1.5(a). In the experiment for Fig. 3.10, a conventional TDA technique could not exhibit a complete desorption profile. Figure 3.11 [63] shows LTDS profiles of tracer-hydrogen introduced into pure iron tensile strained up to 20% with and without hydrogen precharging. Charging of tracer hydrogen was by immersing specimens in an aqueous solution of 20% NH4 SCN at 323 K. The amount of the tracer-hydrogen increases with strain, and hydrogen precharging evolved a new peak at a higher temperature. The LTDS profiles corresponding to Fig. 3.2 are shown in Fig. 2.5 for the hydrogen-precharged and 25% strained specimen. The existence of a subpeak is evident at the higher temperature side. Figure 3.2 indicates that hydrogen precharging enhances the strain-induced generation, prominently at strain of more than 25%., i.e., when the dislocation density is substantial. In the LTDS profiles shown in Fig. 2.5, the lower temperature peak is ascribed to the desorption from dislocations, as described

3.2 Vacancies

61

Table 3.4 H-Trapping energy for vacancies and vacancy clusters (Ebihara et al. [61]) Trapped H atom

V1

V2

V3

V4

V5

V6

V7

V8

V9

1

53.3

56.9

54.9

55.3

55.4

55.4

55.9

55.9

56.8

2

50.0

53

54.5

55.4

55.4

55.4

55.7

55.9

55.9

3

32.5

52.7

54.3

55.1

55.1

55.4

55.7

55.9

55.9

4

27.5

36.5

50.9

55.1

55.1

55.4

55.4

55.9

55.9

5

17.6

37.8

50.1

50.8

54.8

54.9

55.1

55.4

55.5

6

10.6

38.6

44.9

50.9

51.1

54.9

55.1

55.4

55.4

28.1

34.8

50.3

51.2

52.4

54.9

55.2

55.5

7 8

28.4

34.4

50.4

50.6

52.5

51.5

55.2

55.2

9

19.1

33.4

30.9

50.0

50.1

51.2

51.5

55.1

10

18.2

26.0

31.1

37.0

50.1

47.0

51.6

52.4

11

10.1

24.3

30.5

38.0

37.1

47.4

50.4

51.6

12

7.9

27.6

35.5

37.1

51.1

50.7

51.4

13

13.1

23.9

29.8

40.0

42.5

45.9

51.1

14

18.2

24.5

34.6

36.8

45.7

51.1

15

17.6

26.6

30.0

34.5

36.6

50.2

16

13.8

21.5

29.4

32.9

36.0

37.4

17

20.6

26.4

32.9

35.5

38.8

18

14.8

26.3

30.9

34.1

35.8

19

10.6

16.5

28.3

33.6

33.1

20

14.8

25.5

29.0

33.3

21

12.7

21.3

26.7

30.9

17.7

26.4

31.4

22 23

15.9

24.3

29.4

24

13.1

22.4

25.8

25

16.9

22.6

26

12.6

22.2

27

20.1

28

16.0

29

13.4

in Sect. 3.1.1.3. Figure 3.12 [17] shows the hydrogen enhancement of the two peaks in Fig. 2.5, expressed as the ratio of the peak intensities with and without hydrogen precharging. Obviously, the hydrogen enhancement appears in the higher temperature peak 2, while the lower temperature peak 1, which originates in trapping in dislocations, appears at a strain of more than 25%. It implies that hydrogen enhancement is more prominent for vacancies than for dislocations in the early stage of plastic deformation.

62

3 Interactions of Hydrogen with Lattice Defects

Hydrogen Content (mass ppm)

Iron [H+strain]

4

[H+strain+200º] 2

[strain] 0 0

0.1 0.2 Applied Strain

0.3

Fig. 3.10 Amounts of the tracer-hydrogen introduced to iron specimens after straining [strain], strained after hydrogen-precharging [H + strain], and further annealing at 473 K (200 ºC) [H + strain + 200 ºC] (Takai et al. [62]) 25

(a)

20%

10%

2

M/z=2

(b)

M/z=2 H+20% Strain

A) (10 10

1% 0%

5 0 -200

H+10% Strain

-11

15

Ion Intensity

-11

Ion Intensity (10

A)

20

100 -100 0 Temperature (ºC)

200

1 H+1% Strain

No Strain

0 -200

-100

0 100 Temperature (ºC)

200

Fig. 3.11 LTDS profiles of hydrogen introduced into iron specimens given strain up to 20% (a) without and (b) with hydrogen precharging. The thickness of specimen and the concentration of NH4 SCN are 0.3 mm and 20% at 323 K (50 ºC) for (a) and 0.4 mm and 0.05% at 303 K (30 ºC) for (b), respectively (Sato et al. [63]. Reprinted with permission from The Iron and Steel Institute Japan)

Ebihara et al. simulated the LTDS profile shown in Fig. 2.5 for α-iron using a model incorporating vacancies and vacancy clusters [61]. The model considered up to nine-vacancies cluster, V9 , and employed parameters, including the hydrogen trapping energy of vacancies and vacancy clusters based on atomistic calculations. The solution of the McNabb–Foster equation used the finite difference method. Simulations were initially conducted for the degassing, annealing, polishing, and charging

3.2 Vacancies

63

Hydrogen Content ratio, CH+ε/Cε

Fig. 3.12 Ratio of tracer hydrogen contents introduced to strained iron specimens with and without hydrogen precharging. Two peaks in Fig. 2.5 are separated by Gaussian fitting as a function of applied plastic strain (Sugiyama et al. [17])

Peak 1 Peak 2

Applied Strain (%)

processes before the LTDS measurements. Annihilation, dissociation, and clustering proceed during the processes. Figure 3.13 compares the densities of vacancy clusters during heating process for strained specimens with and without hydrogen charging [61]. V4 and V5 are relatively more stable compared with V2 and V3 , and hydrogen favors the stability. However, the results strongly depend on presumptions for the simulation, and a quantitative comparison with experimental results is difficult. The thermal stability is a measure for identifying the type of lattice defects. Figure 3.4(b) shows that tritium trap-sites are annihilated by annealing at temperatures as low as 473 K (200 °C) as described about Fig. 3.4. Figure 3.14 [17] shows similar aging results for the LTDS peaks of tracer hydrogen shown in Fig. 2.5. The specimens were strained to 25% with/without hydrogen precharging and were subsequently aged at various temperatures up to 423 K for 1 h. Cathodic electrolysis to

(a) Concentration, CVi (at.%)

(b)

Temperature, T/K

Temperature, T/K

Fig. 3.13 Calculated densities of vacancy clusters during the heating process in LTDS of 25% tensile-strained iron. Straining is at 303 K (a) without and (b) with hydrogen precharging (Ebihara et al. [61])

Fig. 3.14 Tracer hydrogen contents in Peak 1 and 2 of LTDS profile, shown in Fig. 2.5, after aging at various temperatures of 25% strained pure iron with and without hydrogen precharging (Sugiyama et al. [17])

3 Interactions of Hydrogen with Lattice Defects

Tracer Hydrogen Content, CH (wt.ppm)

64

Peak 1: H+25%ε Peak 1: 25%ε

Peak 2: H+25%ε

Peak 2: 25%ε

Aging Temperature, T/ºC

introduce tracer-hydrogen was in a 0.1 N NaOH aqueous solution with 20 g · L−1 of NH4 SCN. The trap sites composing the higher temperature peak gradually deceased by elevating the aging temperature and almost totally annihilated at 373 K. On the other hand, the lower temperature peak was hardly affected by aging at temperatures up to 423 K. The results are consistent with identifying the trap sites, dislocations, and vacancies to the lower and higher temperature peaks, respectively. Hydrogen enhancement was preferential for the generation of vacancies rather than dislocations. TDA in Fig. 3.10 started the temperature ramp from room temperature without showing separation of the peak. A substantial loss of diffusive hydrogen before the start of TDA might have failed to detect the desorption peak from dislocations. (b) Results of positron annihilation spectroscopy Positron annihilation spectroscopy (PAS), sensitive to vacancies, is a more direct method than TDA to investigate the nature of lattice defects. Some applications are described in Sects. 3.2.1 and 3.2.2. Figure 3.15 [64] shows the mean positron lifetime τ m in pure iron on isochronal annealing after tensile straining at room temperature with and without hydrogen precharging. The increase in τ m by straining is enhanced by the presence of hydrogen at the time of straining. Annealing at 900 K reduced τ m to 100 ± 2 ps which is coincident to the calculated τ in the α-Fe lattice [46]. The variances, χ 2 /q, larger than 2.0 for τ m in deformed iron indicate that τ m is composed of multicomponents. Significant recoveries of τ m that appear at about 400 K, 550 K, and 650 K were analyzed for components. Figure 3.16 [64] shows results for specimens deformed by 20% (a) without and (b) with hydrogen precharging. In the annealing temperature range from 400 to 625 K, the longer lifetime in two-component analyses was 150 ps, coincident with a calculated τ in dislocations [65]. At temperatures lower than 375 K for (a) and 575 K for (b), three-component analyses gave the longest life component

3.2 Vacancies

6 4 2 0 160

2

χ /q

Positron Mean Lifetime τm (ps)

Fig. 3.15 Positron mean lifetime during isochronal annealing of iron deformed with and without hydrogen precharging. Filled marks denote hydrogen-precharged specimens (Sakaki et al. [64])

65

150 140 130 120 110 100

400

500

600

700

800

Annealing Temperature (K)

τ 3 exceeding 400 ps. The recovery stage corresponds to the annihilation of vacancies, and τ 3 indicates positron lifetime likely in large vacancy clusters. Figures 3.15 and 3.16 exhibit hydrogen effects, i.e., increasing τ m and retaining the longest lifetime component τ 3 at high temperatures. The relative intensity of the τ i component is related to the positron-trapping probability κ i in Eq. (3.14), and κ i is proportional to the concentration of the i-th defect C i [36, 65]. The estimated densities of dislocations and vacancies are listed in Table 3.5 [64]. The density of dislocations increases with the amount of plastic strain, as expected, but hydrogen does not affect the increase in the dislocation density. On the other hand, a substantial enhancement by hydrogen is evident for the strain-induced generation of vacancies. These PAS measurements are consistent with the TDA results shown in Figs. 3.10 and 3.12, manifesting the preferential effect of hydrogen on the strain-induced generation of vacancies rather than dislocations. The hydrogen-enhanced increase in positron lifetime has been observed for various deformed materials; AISI 410 martensitic steel [66], Ni single crystal and Ni-alloy [67], α-iron [68], Type 316L stainless steel [69, 70], Type 304 stainless steel [71], and martensitic steel [72]. The clustering of vacancies is crucial to the nanovoid nucleation in the fracture process. TDA in Fig. 3.5 and PAS in Fig. 3.15 exhibited the presence of clusters of strain-induced vacancies. Sugita et al. analyzed positron lifetime data for martensitic steel and showed that hydrogen promoted the clustering of vacancies [66]. Chiari et al. showed for α-iron that decreasing the strain rate increases the lifetime, and that clustering is prominent at temperatures over 350 K [68].

66

3 Interactions of Hydrogen with Lattice Defects (a) Without H -c harging

2

χ /q

2 //

1

1

0 // 100 //

Relative Intensity (%)

0 // 100 //

Positron Lifetime (ps)

(b) With H-charging

2 //

80

80

60

60

40

40

20

20 0 // 500 //

0 // 500 //

vacancy cluster dislocations 400 matrix

400 300

vacancy cluste dislocations matrix

300

200

200

100

100

0 // 300

400

500

600

700

800

0 // 300

Annealing Temperature (K)

400

500

600

700

800

Annealing Temperature (K)

Fig. 3.16 Components of mean positron lifetimes τ m shown in Fig. 3.15 and their relative intensities (Sakaki et al. [64])

Table 3.5 Densities of dislocations (C d ) and vacancies (C V ) in iron deformed with/without hydrogen precharging

Strain (%)

Hydrogen

C d (1010 /cm2 )

C V (10–7 )

10

None

1

Not detected

Charged

0.9

1.7

None

2.2

1.7

Charged

1.9

8.2

20

Measurements by positron annihilation spectroscopy (Sakaki et al. [64])

Hydrogen hardly affected the positron capture at dislocations [66], but a grain size dependence of positron lifetime and its relative intensity was observed in Nialloys given hydrogen precharging and straining [67]. The evolution of the long-time life component of the lifetime is preferential in small grain size specimens, and the suggested origin was vacancy agglomeration on grain boundaries and in the adjacent volumes [67].

3.3 Precipitates

3.2.3.3

67

Theoretical Background for a High Density of Vacancies

The thermal equilibrium density of vacancies increases with the decrease in the formation enthalpy of vacancies, as Eq. (3.13) states. When the DEFACTANT mechanism by Kirchheim, described in Sect. 3.1.2, is applied to vacancies that combine with hydrogen, the formation enthalpy of vacancies H f is related to the logarithm of hydrogen activity as expressed in the form ∂Hf = −RT Z , ∂ ln a

(3.18)

where Z is the average number of hydrogen atoms per vacancy [31]. A DFT calculation of the total energy of vacancy–hydrogen complex by Tateyama and Ohno [58] showed a substantial decrease in H f of a VHN complex, occasionally to negative values, under high hydrogen pressures of 1–2 GPa and Z of 5 or 6. However, the expected densities of vacancies are still very low in thermal equilibrium in most situations where hydrogen embrittlement appears. Another mechanism of realizing high densities of vacancies is kinetic effects. Excess vacancies generated by mutual interactions of dislocations are unstable and tend to annihilate at various sinks such as dislocations, grain boundaries and surfaces. Migration of vacancies is requisite for this annihilation process. However, the formation of immobile clusters and complexes with impurity atoms impede the migration, as described in Sect. 3.2.2, and retard annihilation, keeping high densities before reaching thermal equilibrium. The mobility of a single vacancy in bcc iron under a hydrogen environment has been calculated using the DFT and the nudged elastic band method to find the diffusion path of the minimum energy [59]. A configuration, i.e., two hydrogen atoms trapped at opposite O-sites across a vacancy, has the highest binding energy, and the fraction of the VH2 complex is predominant at room temperature. In that configuration, the activation energy of vacancy diffusion increases from 60 to 103 kJ/mol, and the frequency decreases from 1.71 × 10–2 to 1.62 × 10–8 s−1 , showing almost immobile vacancies. Consequently, for the generation of vacancies by jog dragging of screw dislocations, high densities of vacancies are expected to remain behind moving screw dislocations [59]. Luna et al. conducted some first principles calculations of positron lifetimes and momentum distributions for vacancy clustering in pure metals [73].

3.3 Precipitates Fine carbides or nitrides are widely utilized for grain refinement and precipitation hardening of steel. Interactions of hydrogen with such precipitates are crucial for hydrogen embrittlement of high-strength steel, and many studies have been reported. Experiments to obtain binding energies mainly address diffusion or permeation

68

3 Interactions of Hydrogen with Lattice Defects

processes in which hydrogen trapping and de-trapping occur, as described concerning TDA in Sect. 2.2.1.3.

3.3.1 TiC TiC is the most extensively studied precipitate. Asaoka et al. visualized the distribution of tritium introduced into a Fe-0.15%Ti alloy using tritium autoradiography and examined the thermal desorption and associated changes of the distribution of tritium [74]. A release of tritium from an incoherent TiC/matrix interface occurred at 873 K, and the trapping enthalpy calculated using Oriani’s diffusion equation [13] was 71–79 kJ/mol. The calculation, however, neglected the entropy term, and higher enthalpy values ~ 130 kJ/mol were estimated when the entropy term was taken into account. Lee and Lee applied hydrogen TDA to Fe–Ti–C alloys in which the amounts of Ti and C varied in a wide range while fixing the Ti/C mass ratio at 4:1 [75]. Hydrogen charging was at 673 K under 0.1 MPa hydrogen gas, and successive aging at room temperature released the diffusive part of hydrogen. TDA of remaining hydrogen showed three desorption peaks at 473, 773, and 996 K at a heating rate of 3 K/min, and the 996 K peak was assigned to de-trapping from the incoherent TiC/matrix. The activation energy of de-trapping obtained from Kissinger’s equation, Eq. (2.15), was 86.9 kJ/mol. The binding energy of hydrogen with TiC was calculated using the relation between the TDA peak area and the hydrogen-charging temperature T H of the form,   Eb − E0 , (3.19) C x = N x C0 exp RT H where C x and C 0 are respectively concentrations of hydrogen trapped at TiC and in solid solution, N x is the trap density, and E 0 is the heat of solution [75]. The estimated binding energy E bTiC and N x are 28.1 kJ/mol and 1023 /cm3 -Fe, respectively. Successively, TDA was applied to specimens with controlled TiC/matrix interfaces [76]. Hydrogen introduced to a ferritic Fe–Ti–C alloy heat-treated at different austenitizing temperatures showed four desorption peaks at 383, 473, 748, and 880 K at a heating rate of 3 K/min. Two peaks at 748 K and 800 K were assigned to detrapping from semicoherent and incoherent interfaces, respectively. It implies that the trapping strength of TiC increases associated with the loss of the particle/interface coherency. The hydrogen trapping energy at the incoherent interface is not always unique. The peak temperature assigned to the incoherent interface shifted to higher temperatures when specimens were further heat-treated to increase the TiC particle size. In ferritic Fe–Ti–C alloys, incoherent TiC particles and Ti atoms in solution act as irreversible and reversible traps, respectively. The apparent hydrogen diffusion coefficient, obtained by the permeation transient, is often used to estimate the hydrogen

3.3 Precipitates

69

binding energy with traps as described in Sect. 3.1.1.2 concerning hydrogen permeation. A method devised to separate trapping parameters of reversible and irreversible traps was a sequential permeation method [77]. Both types of trapping take place in the first permeation, but reversible trapping dominates diffusivity in the second transient after irreversible traps have been filled. The difference between the first and the second transients gives irreversible trapping parameters. The obtained binding energies were 94.6 kJ/mol for incoherent TiC and 26 kJ/mol for reversible trap assigned to solute Ti atom [77]. Precipitation of TiC on tempering of martensitic steel brings about a substantial increase in hydrogen absorption capacity. Hydrogen trapping of a TiC particle associated with its coherent-to-incoherent interfacial character transition was extensively studied for low-carbon steel [78]. Using TDA and transmission electron microscopy (TEM) together, Wei and Tsuzaki revealed that the broad semicoherent interface of the disk-like TiC traps 1.3 atoms/nm2 hydrogen during cathodic charging for 1 h. The activation energy for hydrogen desorption from this semicoherent interface was 55.8 kJ/mol, the misfit dislocation core likely being the trap site. On the other hand, the hydrogen binding energy of incoherent TiC particles increased from 68 to 137 kJ/mol as the tempering temperature was raised from 737 to 973 K. A further increase in the tempering temperature to 1073 K decreased the binding energy to 85 kJ/mol. The amount of trapped hydrogen decreases with the increasing tempering temperature above 823 K, and TiC particles likely trap in themselves.

3.3.2 NbC and VC NbC and VC of NaCl-type structures are also common precipitates in high-strength low-alloy steel, and their precipitation increases the hydrogen absorption capacities of steel. Desorption peak temperatures on TDA relevant to NbC and VC are generally lower than the peak temperature due to TiC [79, 80] but are often in the same range as the desorption from other traps. Determining the specific trapping parameters is then difficult, but lower peak temperatures imply lower binding energies of hydrogen with NbC and VC than that with TiC. Figure 3.17 [81] shows TDA profiles of hydrogen introduced to 0.37C–1.0Mo–0.54 V martensitic steel tempered at different temperatures. The precipitation of fine VC particles causes a prominent secondary hardening of martensite. Separately conducted hardness measurements and transmission electron microscopy revealed increased hydrogen absorption capacity associated with secondary hardening [80]. A distinct shoulder in the high-temperature side of the desorption peak for the 923 K (650 °C) tempering is ascribed to trapping at fine VC precipitates. The Atom-Probe tomography to visualize hydrogen trapping at TiC and VC in precipitation-hardened steel is described in Sect. 2.3.2.3 [82, 83]. Hardening proceeded with time on isothermal aging at 883 K, showing a maximum at the aging time of 8 h. The trapping sites in the peak-aged steel with large trapping energy are around the (001) broad interface between VC precipitate and ferrite matrix. However,

Fig. 3.17 TDA profiles of hydrogen introduced to 0.37C-1.0Mo-0.54 V martensitic steel tempered at temperatures shown in the insert (Nagumo et al. [81])

3 Interactions of Hydrogen with Lattice Defects Hydrogen Desorption Rate (10 3 ppm/min)

70

120

◊ 450ºC Δ 500ºC □ 550ºC × 600ºC ○ 650ºC

100

80

60

40

20

0

0

50

100

150

200

250

300

Temperature (ºC (

no hydrogen trapping was observed in the under-aged steel with the small trapping energy. In simultaneously conducted TDA measurements, the evolution of a large desorption peak corresponded to peak aging. Fine VC precipitates trap hydrogen at their interface with the ferrite matrix and in the surrounding stress fields, induced by both coherency of the interface and stress intensification by the precipitates. Figure 3.18 shows TDA profiles of hydrogen introduced to the same steel as used in Fig. 3.17, tempered at 550 °C (823 K) and 650 °C (923 K) [81]. The specimens were applied stress of 0.4 of the ultimate tensile strength before introducing the tracer hydrogen and aged at room temperature before TDA. In Fig. 3.18, the filled marks indicate TDA profiles after degassing at room temperature for 24 h. The difference between the open and filled marks is the amount of diffusive hydrogen. TDA curves exhibit a single peak, but the peak widths are substantially wide. Room temperature degassing showed that hydrogen composing the higher temperature side of the peak is non-diffusive. A separately conducted measurement showed that the applied stress increased densities of both diffusive and non-diffusive hydrogen trap sites, the increase being more prominent for non-diffusive hydrogen [81]. In the case of fine precipitates, the number of hydrogen trap sites is high, and their distribution is uniform, increasing the average hydrogen absorption capacity of the steel. It must be careful that overall or average information from a specimen does not always represent local situations. Strongly trapped non-diffusive hydrogen is irrelevant to embrittlement, and hydrogen behaviors concerning hydrogen embrittlement in martensitic steel are described in Sect. 8.1.2.

3.4 Grain Boundaries

71

Hydrogen Desorption Rate (10-3 ppm/min)

120

120

(a) 550ºC

(b) 650ºC

□ 0h ■ 24h

100 80

80

60

60

40

40

20

20

0

0

50

100

150

200

Temperature (ºC)

250

□ 0h ■ 24h

100

300

0

0

50

100

150

200

250

300

Temperature (ºC)

Fig. 3.18 TDA profiles of hydrogen introduced to 0.37C-1.0Mo-0.54 V martensitic steel tempered at (a) 550 ºC (823 K) and (b) 650 ºC (923 K). Hydrogen charging is conducted under applied stress of 0.4 tensile strength. Filled marks denote specimens kept for 24 h at 30 ºC (303 K) to remove diffusive hydrogen (Nagumo et al. [81])

3.3.3 Fe3 C Precipitation of fine Fe3 C hardly affects the hydrogen absorption capacity on the tempering of 0.42% C martensitic steel [78]. TDA profiles of hydrogen in eutectoid steel do not show trapping of hydrogen to pearlitic Fe3 C when cold-working is not applied, as shown in Fig. 2.8. It suggests that Fe3 C and its interface are not strong trap sites. On the other hand, two TDA peaks appeared by cold-drawing originating in fine lamellar Fe3 C. The cause of the evolution of the higher-temperature peak, increasing by cold-drawing, is the strain-induced formation of irreversible traps in the interface or within Fe3 C. A noteworthy fact is that such irreversibly trapped hydrogen or trapping defects are almost immune to hydrogen embrittlement.

3.4 Grain Boundaries 3.4.1 Experimental Works Accumulation of hydrogen along grain boundaries has been revealed directly using autoradiography, shown in Fig. 2.16 for low-carbon ferritic steel. However, the type and structure of grain boundaries are diverse, and reported values of hydrogen binding energies with grain boundaries substantially scatter. Thermal desorption kinetics and

72

3 Interactions of Hydrogen with Lattice Defects

tritium autoradiography for ferritic Fe–Ti–C alloys showed that the release of tritium from grain boundaries took place below 573 K, and the calculated trapping energy was 59 kJ/mol neglecting the entropy term in the free energy change [74]. The hydrogen binding energy with ferrite grain boundaries was formerly reported by Choo and Lee using TDA for cold-worked and recrystallized iron with grain size controlled from two to nine in the ASTM numbers [15]. Hydrogen introduced at 673 K was partially degassed by room temperature aging. A TDA peak that appeared around 373 K, preceding the evolution of a large desorption peak, was assigned to grain boundaries. The activation energy of desorption obtained using Kissinger’s equation was 17.2 kJ/mol, giving 9.6 kJ/mol for the binding energy after subtracting the saddle point energy of 7.6 kJ/mol. However, Kissinger’s equation addresses the dissociation-controlled desorption of hydrogen, and the value of 9.6 kJ/mol is too small to apply the dissociation-controlled analysis. The experiment used the specimen of 8 mm in diameter and degassing at room temperature for six hours, likely diffusive hydrogen remaining in solution. Alternatively, modeling of TDA profiles of hydrogen from pure iron with different grain sizes was conducted, assuming diffusion-controlled desorption [16], described in Sect. 2.2.1.3. The desorption-rate peak at 415 K was assigned to grain boundaries, and the binding energy of 49 kJ/mol gave the best fit between simulated and experimental TDA profiles.

3.4.2 Theoretical Works Matsumoto et al. calculated the cohesive energy of symmetrical tilt grain boundaries in α-Fe under a gaseous hydrogen environment using density functional theory (DFT) [84]. The definition of the binding energy of hydrogen at a site x was the difference in the heat of solution between the position x and far from grain boundaries. Large gaps in high-energy grain boundaries capture many hydrogen atoms in these spaces. Calculated binding energies were 47.3, 32.8, and 45.3 kJ/mol for ∑3(111), ∑3(112), and ∑9(114) symmetrical tilt grain boundaries, respectively. However, the binding energy between hydrogen and grain boundaries is negligible when carbon and nitrogen atoms segregate at grain boundaries at their solubility limit, i.e., carbon and nitrogen atoms exclude hydrogen atoms from the grain boundaries. The local coordination and the volume of the available interstitial sites influence hydrogen solubility within grain boundary regions. Du et al. examined the interaction of hydrogen with close-packed and open grain boundary structures in α- and γ -Fe, using DFT [85]. The structures or types of grain boundaries strongly affect the heat of solution of hydrogen within grain boundaries. Within the open grain boundary structures, like ∑5 bcc and ∑11 fcc, different interstitial sites are available, generally providing favorable binding sites for hydrogen atoms. Hydrogen accumulation at the grain boundary is energetically favored for those structures, implying hydrogen trapping in the grain boundary. The calculated hydrogen trap energies are ~ 40 and ~ 10 kJ/mol for ∑5 bcc and ∑11 fcc grain boundaries, respectively.

3.5 Voids and Surfaces

73

Grain-boundary-related results must be carefully examined in respect of situations surrounding boundaries, as described in Sect. 3.2.3.2(b) concerning observations of positron annihilation spectroscopy for Ni-alloys [67]. The presence of plastic strain is an item to be remarked on, and impurity segregation and precipitates often decorate grain boundaries. The role of grain boundaries in hydrogen embrittlement is to be considered, taking into account various associated factors, such as the cohesive strength of boundaries, their modifications by segregated impurities or precipitates, and concentrated plastic deformation in adjacent areas.

3.5 Voids and Surfaces The precipitation of molecular hydrogen under high hydrogen fugacity activates small voids or cracks occasionally formed in metallic materials. De-trapping of deuterium from helium bubbles formed by ion implantation of 15-keV 4 He into iron and austenitic stainless steels was investigated by measuring the release of deuterium [50, 51]. The size of the bubbles was about 1 nm in diameter, and the thermal release of deuterium from the implanted zone was analyzed in the same way as described in Sect. 3.2.3.1. For iron, three types of traps were assumed, and the strongest trap with the binding enthalpy of 75 kJ/mol was assigned to de-trapping from He bubbles [50]. Similarly, in Type 304 stainless steel, the corresponding value was 41 kJ/mol assuming two types of traps [51]. The precipitation of molecular hydrogen activates small voids. Adsorption on the void surface is an intermediate step in diffusing out of molecular hydrogen in voids, and the deuterium binding with the He bubble is considered a chemisorption-like interaction. The hydrogen binding energy with the bubble surface, E T , is the lowered hydrogen energy relative to the lattice site, as illustrated in Fig. 3.19 [86]. It is written as E T = E chem + E s −

1 EH , 2 2

(3.20)

where E chem is the chemisorption binding energy of hydrogen referred to as the free hydrogen atom in a vacuum, E s is the heat of solution, and E H2 is the energy of hydrogen molecule. Using experimental values of E chem = 259 kJ/mol and E s = 28 kJ/mol together with E 0 = 222 kJ/mol for α-Fe, a calculated E T is 77 kJ/mol [72]. The calculated value of E T is consistent with the value obtained from the deuterium implantation experiment [50]. Visualization of hydrogen desorption from 5%Ni–Fe alloy by Krieger et al. using SKPFM [44] is described in Sect. 2.4.2. SKPFM for hydrogen introduced into specimens revealed hydrogen trapping at the interface of oxide inclusions in the coldworked specimen. In a simultaneously conducted TDA measurement, Krieger et al. assigned the desorption peak of 38.5 ± 5 kJ/mol in the desorption binding energy to vacancies presumably generated along the interface of inclusions.

74 Fig. 3.19 Schematic illustration of hydrogen energies. E T is the lowering of hydrogen energy by moving from solid solution to surface site (Picraux [86])

3 Interactions of Hydrogen with Lattice Defects Surface

Bulk

Vacuum H Atom

E0

EC

H in Solution

Es H2 Molecule

ET

H Chemisorption

References 1. R. Gibara, A.J. Kumnick, in Hydrogen Embrittlement and Stress Corrosion Cracking, ed. by R. Gibara, R.F. Hehemann (ASM, Metals Park OH., 1984), pp. 61–77 2. T.S. Kê, Scr. Metall. 16, 225–231 (1982) 3. V. Hivert, P. Groh, W. Frank, I. Ritchie, P. Moser, Phys. Stat. Sol. (a) 46, 89–98 (1978) 4. G.M. Sturges, A.P. Miodownik, Acta Metall. 17, 1197–1207 (1969) 5. J.P. Hirth, Metall. Trans. A 11A, 861–890 (1980) 6. G. Schoek, Scr. Metall. 16, 233–239 (1982) 7. A. Seeger, Scr. Metall. 16, 241–247 (1982) 8. J.P. Hirth, Scr. Metall. 16, 221–223 (1982) 9. A. Zielinski, E. Lunarska, M. Smialowski, Acta Metall. 25, 551–556 (1977) 10. R. Gibara, Trans. Metall. Soc. AIME 239, 1574–1585 (1967) 11. S. Asano, M. Shibata, Scr. Metall. 16, 1171–1174 (1982) 12. L. Vandewalle, M.J. Konstantinovi´c, T. Depover, K. Verbeken, Steel Research Int. 92 (2021). https://doi.org/10.1002/srin.202100037 13. R.A. Oriani, Acta Metall. 18, 147–157 (1970) 14. A.J. Kumnick, H.H. Johnson, Acta Metall. 28, 33–39 (1980) 15. W.Y. Choo, J.Y. Lee, Metall. Trans. A 13A, 135–140 (1982) 16. K. Ono, M. Meshii, Acta Metall. 40, 1357–1364 (1992) 17. Y. Sugiyama, K. Takai, Acta Mater. 208, 116663 (2021) 18. J.P. Hirth, in Hydrogen Degradation of Ferrous Alloys, ed. by R.A. Oriani, J.P. Hirth, M. Smialowski (Noyes Pub., Park Ridge N.J. 1985), pp. 131–139 19. J.P. Hirth, B. Carnahan, Acta Metall. 26, 1795–1803 (1978) 20. S. Taketomi, R. Matsumoto, N. Miyazaki, Acta Mater. 56, 3761–3769 (2008) 21. J.W. Christian, Metall. Trans. A 14A, 1237–1256 (1983) 22. M.S. Duesbery, V. Vitek, Acta Mater. 46, 1481–1492 (1998) 23. M. Wen, A.H.W. Ngan, Acta Mater. 48, 4255–4265 (2000) 24. S.L. Frederiksen, K.W. Jacobsen, Phil. Mag. 83, 365–375 (2003) 25. M. Itakura, H. Kaburaki, M. Yamaguchi, Acta Mater. 60, 3698–3710 (2012) 26. M. Wen, S. Fukuyama, K. Yokogawa, Acta Mater. 51, 1767–1773 (2003) 27. M. Itakura, H. Kaburaki, M. Yamaguchi, T. Okita, Acta Mater. 61, 6857–6867 (2013) 28. V.G. Gavriljuk, V.N. Shivanyuk, B.D. Shanina, Acta Mater. 53, 5017–5034 (2005) 29. V.G. Gavriljuk, B.D. Shanina, V.N. Shivanyuk, S.M. Teus, J. Appl. Phys. 108, 083723 (2010) 30. R. Kirchheim, Acta Mater. 55, 5129–5138 (2007) 31. R. Kirchheim, Acta Mater. 55, 5139–5148 (2007) 32. R. Kirchheim, Scr. Mater. 62, 67–70 (2010)

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77. 78. 79. 80. 81.

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82. 83. 84. 85. 86.

Chapter 4

Diffusion and Transport of Hydrogen

Hydrogen diffusion, tolerating trapping and de-trapping at lattice defects during migration, is expressed by McNabb–Foster equation, Eqs. (2.11) and (2.12). The diffusion coefficient, including tapping parameters, is given in Eq. (2.31). The driving force of diffusion is the concentration gradient, and the diffusion coefficient in the equations is a quantity resulting from the jumping frequency of atoms in a crystalline lattice. The diffusion equation addresses the unit process of the transfer of hydrogen atoms across an atomic plane in a crystalline material and the time change of the hydrogen concentration in a volume element. However, in actual materials, various microstructural inhomogeneities in the diffusion path affect the long-distance transport of a hydrogen atom. Macroscopically observed diffusion coefficients are mostly averaged ones over diffusion paths. This chapter first describes the practice and principles of determining the hydrogen diffusion coefficient. Some factors affecting long-distance hydrogen transport are then presented.

4.1 Determination of Diffusion Coefficient 4.1.1 Diffusion Coefficient Data Published data on hydrogen diffusion in metals are collected in a book [1], and the range of data for iron and steel is shown in Fig. 4.1 according to the original compilation by McNabb and Foster [2]. A reported value of the hydrogen diffusion coefficient in a 99.99% purity iron specimen, which is almost free from dislocation trapping, is [3] ( ) D m2 /s = 5.8 × 10−8 exp(−4.5(kJ/mol)/RT ).

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 M. Nagumo, Fundamentals of Hydrogen Embrittlement, https://doi.org/10.1007/978-981-99-0992-6_4

(4.1)

77

4 Diffusion and Transport of Hydrogen

D e f f (H) (cm2/min)

78

103/T(K)

Fig. 4.1 Literature data range of effective diffusion coefficient of hydrogen in iron and steels. Data lines are shown in [2]

The diffusion coefficient in Fick’s first law, Eq. (2.1), is a function of temperature. A widespread over three orders of Deff at low temperatures in Fig. 4.1 corresponds to the scatter in the solid solubility shown in Fig. 2.1, resulting from hydrogen trapping at various lattice defects. Hydrogen atoms migrating in crystalline lattices tolerate various energy barriers. The diffusivity of hydrogen in close-packed fcc γ -iron is lower than that in bcc α-iron due to the higher activation energy of diffusion in fcc structures. Figure 4.2 [4] shows hydrogen diffusion coefficients from the literature in various austenitic stainless steels. The effects of alloying elements on diffusion coefficients are substantial in addition to those of crystal structures. The hydrogen diffusion coefficient reported for Type 304 stainless steel in the temperature range of 311–332 K is [5] ( ) D m2 /s = 4.41 × 10−7 exp(−53.5(kJ/mol)/RT ).

(4.2)

√ Migration distances of hydrogen in terms of Dt calculated using Eqs. (4.1) and (4.2) at room temperature for α-iron and austenitic stainless steel, roughly 100 μm and 20 nm per second, respectively, are drastically different.

4.1.2 Measurement of Diffusion Coefficient Hydrogen diffusivity is measured by various methods [6], like gas or electrochemical permeation techniques. Figure 4.3 shows the electrical circuit for the electrochemical cell employed by Devanathan and Stachurski [7]. The specimen is sandwiched

4.1 Determination of Diffusion Coefficient

10

10-2

D(H) (cm2/s)

10

1000 500

0

Temperature (ºC) 300 200

20ºC

100

δ-iron

-4

α-iron

304 304

10-6

79

347

316

321

10-8

304

304L 347

10-10

γ-iron Austenitic steel Kh18N10T

10-12 10-14

1.0

2.0

3.0

3

10 /T(K) Fig. 4.2 Hydrogen diffusion coefficients in austenitic stainless steel (Caskey [4])

between two individual electrolyte cells, and hydrogen generated electrochemically on one side of the specimen by cathodic polarization is absorbed into the bulk. Then, hydrogen diffusing through the specimen is oxidized at a constant potential. Zero coverage on the opposite side is maintained by anodic polarization, and the oxidation current is proportional to the amount of hydrogen penetrating through the specimen with time. The continuous current record in the anodic potentiostat circuit represents the instantaneous rate of hydrogen permeation. Figure 4.4 [8] illustrates schematically the permeation transient and its integration with time after the switch-on of galvanostatic cathodic potential. The diffusion coefficient of hydrogen is obtained from the transient curves, but somewhat different quantities are used according to experimental conditions. In the non-steady-state galvanostatic time lag method, a constant hydrogen flux is established at the entrance side by a constant cathodic current. Time lag t i shown in Fig. 4.4 is expressed from the solution of Fick’s second law as [8], ti =

L2 3 ln 3 L 2 ≈ , 2 2 π D 6D

(4.3)

where L and D are the thickness of the specimen and the hydrogen diffusion coefficient, respectively. ∫ The integral of the current with time, Jdt, becomes linear when a stationary linear concentration gradient is established in the specimen. Another time lag, t L , is the time required to obtain a steady-state flow after a sudden change of the boundary condition and is defined as the intercept on the t-axis of the extrapolation of the

80

4 Diffusion and Transport of Hydrogen

Fig. 4.3 Schematic diagram of the electrical circuit for hydrogen permeation experiment (Devanathan et al. [7]. Reprinted with permission from The Royal Society)

Fig. 4.4 Permeation current density or hydrogen flux J permeating with time after starting galvanostatic cathodic polarization (Boes et al. [8])

J , ∫ J dt

∫ J dt J

tb ti

tL

t

straight line [8], tL =

L2 . 2D

(4.4)

Further, the break-through time t b is defined as the intersection of the tangent at the inflection point with the initial level J = 0, tb = 0.76

L2 L2 ≈ 0.077 . π2D D

(4.5)

4.1 Determination of Diffusion Coefficient

81

In the case of the non-steady-state potentiostatic method with a constant hydrogen concentration at the entrance side, expressions for time lag are, ti =

ln 16 L 2 L2 ≈ 0.091 , 3 π2D D

(4.6)

L2 , 6D

(4.7)

tL = tb = 0.5

L2 L2 ≈ 0.05 . π2D D

(4.8)

In this condition, t L is simply obtained as the time at which the permeation rate is 0.63 of the steady-state value [7]. Determining t b is not always clear in practice. In electrochemical permeation curves for a high-strength medium-carbon martensitic steel, Frappart et al. defined an apparent diffusion coefficient Dapp as. Dapp =

L2 , Mt

(4.9)

where L and M are, respectively, the sample thickness and a constant depending on the time t chosen in the diffusion transient (M = 25, 15.3, 6 for 1%, 10%, 63% J ∞ ) [9]. Employing Dapp at a current density of 10% J ∞ , Frappart et al. examined Dapp ’s temperature and the cathodic polarization dependencies. Two domains for Dapp appear, as shown in Fig. 4.5 [9], in the dependence on the subsurface hydrogen concentration C H estimated using J ∞ and Dapp . Frappart et al. considered that hydrogen trapping and diffusion compete in domain I, while lattice hydrogen diffusion dominates in domain II, where all trapping sites are filled. ■ E xp er imen t al R e s u l ts Model

8x1011

D a p p (m 2 /s)

Fig. 4.5 Apparent diffusion coefficient in the Fe–C–Mo high-strength steel as a function of the apparent subsurface concentration of hydrogen at 293 K (Frappart et al. [9])

6x1011

4x1011

2x1011 0

0.2

0.4

0.6 0.8 1.0 C H (w t ppm)

1.2

1.4

82

4 Diffusion and Transport of Hydrogen

4.1.3 Theoretical Interpretation McNabb–Foster equation, Eqs. (2.11) and (2.12), describing diffusion accompanying trapping and de-trapping during migration, complements Fick’s law that considers the elementary process of atomic jumping. A general solution of the McNabb–Foster equation is complicated, and approximate solutions were derived for thick and thin specimens [2]. The case of thick specimens is described in Sect. 2.2.1.4, and the effective diffusivity is given in Eq. (2.31), including trapping parameters k and p. McNabb and Foster applied their equation to hydrogen permeation through a plate of thickness L under boundary conditions of constant C 0 and zero hydrogen concentrations on the input and output surfaces, respectively. In the permeation transient in the presence of traps, the time lag t L required to obtain a steady-state flow was derived in a modified form of Eq. (4.7) as [ ] ( 2) 1 L2 tL = (1 + α) 1 − αβ/(1 + α) + O β , 6D 2

(4.10)

where α = N x k/p, β = C 0 k/p [2]. Equations (3.6) and (3.7) are approximated forms of Eq. (4.10). Equation (4.10) is the same form as Eq. (4.7) when the notation of D in Eq. (4.10) is replaced by Deff , defined as Deff = D(1 + α)

−1

) ( k −1 , = DL 1 + N x p

(4.11)

where N x denotes the number of trap site per unit volume. Equation (4.11) is the same as Eq. (2.31). The definitions of p and k express the time required for one trapping or de-trapping event as 1/C L k or 1/p, while the time to pass through a specimen of the thickness a is a2 /D. “Thick” specimen means frequent trapping and de-trapping events during diffusion through the specimen, i.e., D/a2 > p, C L k, lattice hydrogen diffuses out readily, and trapping and de-trapping events occur independently. Desorption of hydrogen from a thin specimen then indicates the decrease in the amount of trapped hydrogen controlled by de-trapping, i.e., ∂C x = − pC x . ∂t

(4.12)

When thermal equilibrium is established at t = 0, the numbers of trapping and de-trapping hydrogen atoms are the same, i.e., ( ) kCL0 N x 1 − θ 0 = pθ 0 N x ,

(4.13)

4.2 Stochastic Theories of Hydrogen Diffusion

83

where θ denotes the fractional occupancy of the trap. The decrease in trapped hydrogen approximates the amount of remaining hydrogen, which is expressed in terms of trapping parameters as [2], C x = C x0 exp(− pt) = θ 0 N x exp(− pt) =

C L0 N x k/ p exp(− pt). 1 + C L0 k/ p

(4.14)

Casky and Pillinger simulated hydrogen permeation and evolution curves using the finite difference method for a plane sheet to solve the McNabb and Foster equation [10]. The trapping effect was explored for a range of trapping parameter values such as the trap density N, p, and kC. Casky and Pillinger noticed that analysis of the experimental data by the simple time lag or inflection point techniques does not of themselves detect trapping, leading to substantial errors in the calculations of diffusivity and solubility. Casky and Pillinger suggested conducting both permeation and evolution experiments in succession and comparing the two curves.

4.2 Stochastic Theories of Hydrogen Diffusion The diffusion coefficient has been derived more generally from stochastic viewpoints on the movement of atoms. According to Einstein’s relation [11], the mean square displacement of particles is proportional to Dt in Brownian motion. From the viewpoint of random walk, Koiwa assumed that the mean square displacement of a diffusing species after the same number of atomic jumps is the same irrespective of the presence of traps [12]. Since the time of stay at a trap may differ from that at a normal lattice site, the relation between apparent and normal lattice diffusion coefficients is expressed as [12] Deff tU' = DL tU ,

(4.15)

where tU' and t U denote the times required for a diffusing atom to make the same number of jumps with and without traps, respectively. When the saddle point energy change, ΔE, is zero in the energy diagram shown in Fig. 2.13, interstitial atoms visit all sites with an equal probability. In this case, tU' is the weighted mean of the mean stay times at a normal lattice site, t L , and a trap site, t T . Assuming that trap sites for interstitials in the bcc lattice are substitutional foreign atoms of c in atomic ratio, Eq. (4.15) is written for O-occupancy of hydrogen in bcc metals as tU' = (1 − 2c)tL + 2ctT . For T-occupancy of hydrogen, 2c in Eq. (4.16) is replaced by 4c.

(4.16)

84

4 Diffusion and Transport of Hydrogen

The jump frequency ν between the nearest neighbor sites with the activation energy E a is ν = ν0 exp(−Ea /RT ).

(4.17)

Since the time of stay is the inverse of ν, the form of Deff from Eqs. (4.15)–(4.17) is ]−1 [ Deff = DL 1 − 2c + 2c(νL /νT ) exp(Eb /RT ) ,

(4.18)

Fig. 4.6 Effects of the change in saddle point energy ΔE on effective diffusion coefficient of interstitial atoms in the bcc lattice. The straight line shows the normal diffusion coefficient (Koiwa [12])

Effective Diffusion Coefficient Deff (cm2/s)

where ν L and ν T are frequency factors of the jump from the normal lattice site and trap site, respectively. Equation (4.18) corresponds to Eq. (2.27) derived by Oriani for the case of local equilibrium. Koiwa further considered the case in which the interaction between trapping centers and hydrogen atoms extends to the nearest neighboring sites. In this case, a more general form of Deff was derived, considering a high probability of reverse trapping immediately after the release at the original trap center. Equation (4.18) is for the case of ΔE = 0 in Fig. 2.13, but it is to be noticed that the saddle point energy substantially affects Deff as shown in Fig. 4.6 [12]. An increase in ΔE, i.e., a decrease in the saddle point energy, increases Deff substantially at low temperatures in the negative curvature range. Surroundings of a defect, like networks, tangles, and cell structures of dislocations, may affect the saddle point energy. In this case, even for traps of the same E b , the diffusivity of hydrogen affected by dislocations may differ from that in the lattice of low dislocation densities. It is also to be noticed that the assumption of an equal probability for visiting all sites is invalid when ΔE /= 0.

10-3

Temperature (K) 1000 500 400

300

Em=0.1, Eb=0.3 C=2.577X10-3

10-4

10-5

10-6 0

0 0.03 ΔE= 0.05 0.07 (Eb = 0.25, ΔE = 0)

1

2 1000/T(K)

3

4.2 Stochastic Theories of Hydrogen Diffusion

85

Another stochastic approach to hydrogen diffusion was made by Kirchheim using Monte Carlo methods [13, 14]. The procedure is that interstitial atoms, P in number, are initially distributed randomly in a metal lattice, and each atom is given energy E generated as a random number by the computer. The probability p(E) that an atom has energy E is, p(E) = exp(−E/RT ).

(4.19)

If the energy E exceeds at least one of the surrounding energy barriers, a jump to a neighboring site is possible, and this step is repeated for a definite number (100 P or 1000 P) of jumps. In the first run during time 1 t, the diffusion coefficient for the ith interstitial atom is calculated in terms of the position vectors Ri and Ri0 for the final and the initial positions of the ith atom, respectively, as 1

Di =

(Ri − Ri0 )2 , 2d 1 t

(4.20)

where d is the dimension of the lattice considered. The 1 Di is averaged over all P interstitial atoms. Then, the whole procedure is repeated after the time k t with the atom, starting from the final position of the previous run until the average of 1 Di for over all n runs, n k ∑ D kt , D= t k=1

(4.21)

is constant. The effects of the site and the saddle point energies on diffusion coefficient and site occupancy were examined numerically for the fcc lattice. The calculation results for the effects of the saddle point energy on diffusion coefficient are shown in Fig. 4.7 [13] for dilute solutions, i.e., for low occupancy of the trap. Decreases in both the free energy of a trap site and the saddle point energy reduce the diffusion coefficient compared to the regular lattice, in contrast to Fig. 4.6. It was also shown that the occupancy of a site by an interstitial atom is determined not only by the binding energy in the equilibrium position but also by the heights of surrounding barriers. Equation 4.18 gives the ratio Deff /DL . The relation’s origin is in Eq. 4.15, i.e., the difference in the jumping frequency or the stay time at the trap and lattice sites. McLellan derived the Deff /DL of interstitial solute atoms in defected and defectfree crystals based on the nearest neighbor statistics and the reaction rate theory [15]. Defected crystals contain foreign substitutional atoms, grain boundaries, or dislocations. The calculated form of the ratio was slightly different from Eq. 4.18, though both forms fitted well with experimental data, and discussion was made about the difference [16–18].

86

0 Log (Diffusion Coefficient )

Fig. 4.7 Calculated diffusion coefficient in the fcc lattice with traps (1%, E t = −20 kJ/mol) having lower saddle point energies (ΔQ = −5 kJ/mol). The broken line is calculated with ΔQ = 0 (Kirchheim [13])

4 Diffusion and Transport of Hydrogen

-1 -2

Et = 0

-3 -4

-5

Et = -20kJ/mol ΔQ = 0

Et = -20kJ/mol ΔQ = -5kJ/mol

0

1

2

3 4 1000/T(K)

5

6

4.3 Hydrogen Transport by Moving Dislocations Fracture in hydrogen embrittlement occurs in most cases under applied strain. Hydrogen transport other than normal diffusion, if any, is a matter to be considered for hydrogen accumulation at a critical site. Hydrogen transport, in addition to diffusion through the lattice, is vital, especially for fcc and hcp metals and alloys in which intrinsic hydrogen diffusivity is low. The drag of hydrogen atoms by moving dislocations is a feasible mechanism, and some observations have been discussed in this respect.

4.3.1 Release of Internal Hydrogen During Straining Promoted evolutions of precharged tritium during tensile straining are general in various metals and alloys, such as iron, Type 304 stainless steel, nickel, Inconel 718, and 5086 aluminum alloys [19]. In all cases, the release rate increased rapidly at the proportional limit or yield point, reached a maximum with increasing strain, fell with additional strain, and finally showed a significant release at fracture. For iron, the release rate was constant during Lüder’s extension, and the rate was a function of temperature and strain rate. Activation energies for the release were about 8 kJ/ and 40 kJ/mol for iron and Type 304 stainless steel, respectively, but the corresponding thermally activated process was not definite. Similar strain-enhanced desorption of hydrogen was observed for iron and Inconel 625 alloy [20]. A quadrupole mass spectrometer detected hydrogen release during tensile straining of iron specimens. In the experiment, hydrogen was precharged to saturation by cathodic electrolysis, and the test was in a vacuum chamber at room temperature. Figure 4.8(a) shows the hydrogen desorption rate and (b) the stresstime curve for iron [20]. Extraneous hydrogen from dissociated water or molecular hydrogen on the specimen surface was subtracted from the total amount of desorbed

4.3 Hydrogen Transport by Moving Dislocations 5 4

Nominal Stress

Ion Current

(b) (b)

M/z=2

100

3 2 1 0 0

150 MPa)

M/z=2

-11

10 A)

(a) (a)

87

50

0 200

400 600 Time (s)

800 950

0

200

400 Time

600 (s)

800

Fig. 4.8 (a) Hydrogen desorption during elastic cyclic stressing and subsequent tensile straining until failure of a pure iron specimen. Hydrogen is precharged by cathodic electrolysis in poisoned H2 SO4 aq of pH 2.5 at a current density of 50 A/m2 . The tensile strain rate is 4.2 × 10–4 /s. The stress-time curve is shown in (b) (Shoda et al. [20]. Reprinted with permission from The Iron and Steel Institute Japan)

hydrogen. Cyclic stressing applied in the elastic range prior to tensile straining increased only slightly the desorption rate, but a rapid increase in the early stage of plastic deformation and the subsequent decrease was consistent with previously reported results [19]. The ratio of released hydrogen during tensile straining to the initial content differed by the strain rate. For iron, the ratios were not monotonic against the strain rates in the range from 4.2 × 10–3 /s to 4.2 × 10–5 /s, and the maximum release was 16% at 4.2 × 10–4 /s. On the other hand, for Inconel 625, the fraction of released hydrogen monotonically increased with decreasing strain rate, from almost 0% at 4.2 × 10–3 /s to 9% at 4.2 × 10–6 /s [20]. The hydrogen release from the surface during tensile deformation was directly observed for pure aluminum at different temperatures [21], using the hydrogen microprint technique described in Sect. 2.3.1. The emission of residual impurity hydrogen during tensile straining to 5% was prominent along coarse slip bands at room temperature, but the emission along grain boundaries, rather than slip bands, was preferential at 355 K. The emission along slip bands was reduced at 203 K. The results at room temperature and 355 K were ascribed respectively to the hydrogen transport by moving dislocations and thermal dissociation of accumulated hydrogen along grain boundaries. Diffusivities of hydrogen in fcc and hcp metals and alloys are very low at room temperature. Substantial hydrogen desorption implies that the desorption is not simply due to the diffusion of hydrogen but is likely associated with the movement of dislocations. However, the possibility cannot be ruled out that fresh metal surface and/or surface steps formed by slip-off dislocations act as active sites for desorption by reducing the barrier energy for the emission. The prominent tritium

88

4 Diffusion and Transport of Hydrogen

emission at the onset of Lüder’s band, shown in Fig. 4.8(a), is most likely due to the evolution of fresh surface on the specimen.

4.3.2 Effects on Electrochemical Permeation

Current

At the steady state of electrochemical permeation, straining of the electrode changes the anodic current. Figure 4.9 [22] is a schematic illustration of anodic current as a function of time when straining is applied to the polycrystalline nickel electrode. Δitot is the change of the total anodic current by straining, and its magnitude and even the sign differ by materials and experimental conditions. Various factors affect Δitot ; hydrogen transport by moving dislocations expects an increase in anodic current, but a large portion of Δitot is the background current to passivate the newly formed electrode surface by straining. The net current Δinet after subtracting the passivation current from Δitot still includes currents of various origins other than the transport by dislocations, feasibly dynamic trapping by newly created dislocations, an associated depletion of the lattice hydrogen concentration, the decrease in the thickness of the specimen, and the increased input hydrogen concentration by the fresh metal surface enhancing the hydrogen entry. Further, the concentration gradient at the output surface of the specimen is critical to the release of hydrogen diffusing through the lattice. The concentration gradient is not constant at dynamic trapping within the specimen [22]. For polycrystalline nickel electrodes, observed Δitot was complicated depending on experimental conditions. Δitot was positive at a strain rate as low as 1 × 10–6 /s

Passivation Start charging

Start deformation

Stop deformation

Δitotal

Hydrogen flux Passivation current

Δipass

Time Fig. 4.9 Schematic representation of anodic current for electrochemical permeation through nickel specimen measured as a function of time, illustrating experimental procedure (Frankel et al. [22])

4.3 Hydrogen Transport by Moving Dislocations

89

and increased with the amount of strain, but it was negative at strain rates higher than 1 × 10–5 /s [22]. Frankel and Lanision deduced dynamic hydrogen trapping by newly created dislocations, while dislocation transport of hydrogen to great depths is unlikely. However, the specimen for the contribution of the dislocation transport in the easy glide deformation was a thin (~ 100 μm) single-crystal slice [22]. The passivation current occupied about 90% of the total permeation current [23]. Hydrogen transport by dislocation at electrochemical permeation was also examined for single-crystal iron, concerning the effects of the type of dislocation [24]. Three combinations of the surface orientation and the tensile axis were prepared by slicing specimens of 2 mm in thickness to selectively give the primary slip system for edge, screw, and mixed dislocations, respectively. For all three orientations, applying tensile straining during the steady-state permeation did not affect the anodic current in the elastic range. However, the onset of plastic deformation discontinuously dropped anodic current, reaching nearly constant levels in easy glide regimes. In the strain range of less than 1%, small distinct peaks of anodic current appeared for the screw orientation, but the current fluctuated irregularly around a constant level without showing peaks for edge or mixed orientations. The decrease in anodic current associated with plastic deformation was mainly ascribed to the trapping of lattice hydrogen by newly generated defects. It was then assumed that hydrogen transport by dislocations gave rise only to small discontinuous peaks for the screw orientation. The increase in hydrogen transport rate per unit strain with decreasing strain rates is consistent with the notion that lattice diffusion of hydrogen, rather than dislocation transport, plays the dominating role in anodic current. Hydrogen transport by moving dislocations was discussed about the hydrogen-carrying capacity, which was dependent on the type of dislocations [24], but definite evidence was not available for dragging hydrogen atoms by moving dislocations. For polycrystalline iron, electrochemical permeation experiments were conducted using cylindrical specimens of 0.3 mm in wall thickness [25]. Permeation current after subtracting the passivation current is shown in Fig. 4.10 [25] as a function of time from the start of tensile straining during the steady-state permeation stage. The permeation current increased linearly in the elastic range, decreased discontinuously at the onset of plastic deformation, increased gradually, and increased rapidly by stopping the load increase. The discontinuous drop of the permeation current is consistent with a previous study for a single crystal [24] due to the trapping of lattice hydrogen by newly generated defects. Refilling of depleted hydrogen is likely the reason for the following gradual increase and the rapid increase at stopping the load rise. Geometrical thinning of the specimen also caused an increase of permeation current in elastic and also in the plastic ranges.

90

4 Diffusion and Transport of Hydrogen

P erm eati on Current Dens ity ( μA/c m 2 )

Fig. 4.10 Change in hydrogen permeation current with elastic and plastic deformation for pure iron (Huang et al. [25]. Reprinted with permission from The Iron and Steel Institute Japan)

3.2 3.2

3.1 3.1 Elastic range elastic

Plastic range plastic

Hold hold strain strain

Unload unloading

3.0 3.0 2.9 2.9 2.8 2.8 2.7 2.7 0 0

1 1

22

33 44 55 Time,Tim t/ks e, t /ks

66

77

88

4.3.3 A Kinetic Model Hydrogen transport by moving dislocations must be affected by increasing dislocation densities during deformation. Charles et al. considered hydrogen transport by dislocations and the trapping process in the apparent hydrogen diffusion. A model assumed was that hydrogen atoms are trapped at dislocations, then transported by dislocations across the sample, and potentially de-trapped to lattice sites. Charles et al. proposed to add a term expressing the time dependence of the trapped hydrogen concentration to the diffusion equation, adopting a model in which plasticity is described using a reaction–diffusion framework [26]. The proposed equation for the density of trapped hydrogen, C T , was ∂CT ∂CTr = ∇(DT ∇CT ) + , ∂t ∂t

(4.22)

where DT is the trap (= dislocations) diffusion coefficient. ∂CTr /∂t corresponds to the creation of dislocations. DT is modified by both strain rate and plasticity. Since the total hydrogen concentration, i.e., the sum of lattice C L and trapped C T hydrogen, is constant, the expression of ∂CTr /∂t using the McNabb–Foster equation is ∂CL k ∂CTr =− = CL (NT − CT ) − pCT , ∂t ∂t NL

(4.23)

where N T and N L are the trap and the normal interstitial lattice site densities, respectively, and k and p are trapping and de-trapping parameters in the McNabb–Foster equation.

4.4 Accelerated Diffusion Along Grain Boundaries

91

Using a finite element method, Charles et al. calculated the hydrogen repartition ahead of the crack tip and the acceleration of the hydrogen transport for various loading conditions and trapping parameters. However, experimental results to be compared were not shown.

4.4 Accelerated Diffusion Along Grain Boundaries Grain boundaries have two competitional effects on hydrogen transport; one is trapping hydrogen, and another is operating as short paths for diffusion. Hydrogen diffusivities in fcc and hcp metals and alloys are low, but short-circuit effects along grain boundaries are expected to promote hydrogen diffusion. Brass and Chanfreau compared electrochemical permeation curves of commercial high-purity nickel prepared to two grain sizes of 25 and 150 μm polycrystalline samples, 98% cold worked samples, and nickel single crystal [27]. The specimen thickness was 200 μm, giving straight diffusion paths through the sample. Analyses of the diffusion data showed an increase in the diffusion coefficient and the hydrogen flux in the smaller grain size samples of 25 μm, corresponding to short-circuit effects. The estimated intergranular diffusion coefficient was 2–7 times larger than the lattice diffusivity of hydrogen in pure nickel. At an early stage of permeation, the break-through time showed more rapid hydrogen diffusion through the large-grain material. As a factor operating in grain size effects, intrinsic dislocations accommodating angular misorientations between two grains operate as hydrogen trap sites. Oudriss et al. prepared high-purity polycrystalline nickel specimens of grain sizes ranging from 20 nm to 168 μm [28]. The specimen thickness was 180 μm. Figure 4.11 [28] shows the grain size dependence of the effective diffusion coefficient obtained using the electrochemical permeation technique. The sample preparation methods differ by domains, electrochemical deposition in domain III, and heat treatment for 10 and 150 μm grain sizes in domain II. Oudriss et al. considered the short-circuit diffusion and the hydrogen trapping mechanisms. In domain I, grain boundaries act as a preferential diffusion path. A peak that appeared at a grain size of about 50 μm in Fig. 4.11 was ascribed to the competition between the two mechanisms. The increased density of geometrically necessary dislocations associated with grain refinement likely disturbs hydrogen diffusion. The increase in short-circuit diffusion associated with triple junctions becomes prevalent in nanograin size [28]. On the other hand, permeation tests using polycrystalline high-purity nickel specimens of 10 and 150 μm grain sizes did not provide any evidence supporting enhanced hydrogen transport by grain boundaries [29]. Annealing conditions after cold rolling to prepare the two grain sizes were substantially different, suggesting a difference in intrinsic dislocation densities. Hydrogen diffusion coefficients decrease with decreasing hydrogen concentration in polycrystalline palladium, while it is constant in a single crystal [30]. A reason might be the filling of trap sites formed by dislocations.

92

4 Diffusion and Transport of Hydrogen 10-11

Fig. 4.11 Hydrogen diffusion coefficients in polycrystalline Ni (Oudriss et al. [28])

Deff (m2/s)

10-12

Domain III

Domain II

Domain I

10-13

10-14 0.01

0.1

1.0

10

100

1000

G r ai n S iz e , d/ μm

Turnbull and Hutchinson measured hydrogen permeation in duplex stainless steel, varying the volume fraction of γ -phase by heat treatments [31]. Obtained hydrogen Deff s decreased with increasing volume fraction of γ -phase, about a factor of 400 less than that for the fully ferritic steel at 44% γ -phase. Turnbull and Hutchinson deduced that diffusion through the γ -phase has no effect on hydrogen transport and that the trapping of hydrogen atoms at the α/γ interface is the most significant factor in reducing diffusivity. Electrochemical permeation tests are indirect for identifying the grain-boundary diffusion of hydrogen. Ladna and Birnbaum used secondary-ion mass spectrometry to measure the distribution of deuterium at the surface and grain boundaries of cathodically deuterium-charged nickel bicrystals [32]. The deuterium concentration at the grain boundary was higher than in the adjacent grains for high energy 39° symmetric tilt boundaries (∑ = 9), while 129° low energy grain boundaries (∑ = 11) did not have higher D concentration. The diffusivity enhancement along the 39° grain boundary was about 8 to 17 times, while the diffusivity along the 129° boundary was equal to the lattice diffusivity in the α solid solution. Tanaka et al. visualized the distribution of deuterium charged from the surface of an fcc Fe-30%Ni alloy using Ga-focused ion beam time-of-flight SIMS [33]. Deuterium was enriched in the layer of about 10 μm from the surface, but the enrichment further proceeded twice or so in depth along grain boundaries, indicating that grain boundaries can be a fast diffusion path. A more direct dynamic evidence of hydrogen diffusion along grain boundaries is shown in Fig. 2.19, which observed permeating deuterium supplied from the bottom of a Type 304 stainless steel specimen [34]. The areas of high deuterium concentration were sites where multiple grain boundaries were assembled or crossed.

References

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References 1. D.J. Fisher, ed., Hydrogen Diffusion in Metals—A 30-Year Retrospective (Scitec Pub., ZürichUetikon, Switzerland, 1999) 2. A. McNabb, P.K. Foster, Trans. Metall. Soc. AIME 227, 618–627 (1963) 3. H. Hagi, Mater. Trans. 35, 112–117 (1995) 4. G.R. Caskey, Jr., in Hydrogen Degradation of Ferrous Alloys, ed. by A. Oriani, J.P. Hirth, M. Smialowski (Noyes Pub., Park Ridge, N. J., 1985), pp. 822–862 5. Y. Sakamoto, H. Katayama, J. Jpn Inst. Metals 46, 805–814 (1982) 6. P. Kedzierzwawski, in Hydrogen Degradation of Ferrous Alloys, ed. by A. Oriani, J.P. Hirth, M. Smialowski (Noyes Pub., Park Ridge, N. J., 1985), pp. 251–270 7. M.A.V. Devanathan, Z. Stachurski, Proc. Roy. Soc. A 270, 90–103 (1962) 8. N. Boes, H. Züchner, J. Less Common Metals 49, 223–240 (1976) 9. S. Frappart, X. Feaugas, J. Creus, F. Thebault, L. Delattre, H. Marchebois, J. Phys. Chem. Solids 71, 1467–1479 (2010) 10. G.R. Caskey Jr., W.L. Pillinger, Metall. Trans. A 6A, 467–476 (1965) 11. J.L.Bocquet, G. Brebec, Y. Limoge, in Physical Metallurgy (vol. 1, 4th Ed) ed. by R.W. Cahn, P. Haasen (Elsevier Sci., Amsterdam, 1996), pp. 536–668 12. M. Koiwa, Acta Metall. 22, 1259–1268 (1974) 13. R. Kirchheim, Acta Metall. 35, 271–280 (1987) 14. R. Kirchheim, Prog. Mater. Sci. 32, 261–325 (1988) 15. R.B. McLellan, Acta Metall. 27, 1655–1663 (1979) 16. R.B. McLellan, Scripta Metall. 15, 1251–1253 (1981) 17. D. Farkas, Scripta Metall. 17, 837–839 (1983) 18. F.D. Fischer, J. Svoboda, E. Kozeschnik, Modell. Simul. Mater. Sci. Eng. 21, 025008 (2013) 19. J.A. Donovan, Metall. Trans. A. 7A, 1677–1683 (1976) 20. H. Shoda, H. Suzuki, K. Takai, Y. Hagiwara, ISIJ Int. 50, 115–123 (2010) 21. K. Koyama, G. Itoh, M. Kanno, J. Jpn. Inst. Metals 42, 790–795 (1998) 22. G.S. Frankel, R.M. Latanision, Metall. Trans. A 17A, 861–867 (1986) 23. G.S. Frankel, R.M. Latanision, Metall. Trans. A 17A, 869–875 (1986) 24. C. Hwang, I.M. Bernstein, Acta Metall. 34, 1001–1010 (1986) 25. Y. Huang, A. Nakajima, A. Nishikata, T. Tsuru, ISIJ Int. 43, 548–554 (2003) 26. Y. Charles, J. Mougenot, M. Gaspérini, Int. J. Hydrogen Energy 47, 13746–13761 (2022) 27. A.M. Brass, A. Chanfreau, Acta Mater. 44, 3823–3831 (1996) 28. A. Oudriss, J. Creus, J. Bouhattate, C. Savall, B. Peraudeau, X. Feaugas, Scripta Mater. 66, 37–40 (2012) 29. J. Yao, J.R. Cahoon, Acta Metall. Mater. 39, 119–126 (1991) 30. T. Mü¯ tschele, R. Kirchheim, Scripta Metall. 21, 135–140 (1987) 31. A. Turnbull, R.B. Hutchings, Mater. Sci. Eng., A 177, 161–171 (1994) 32. B. Landna, H.K. Birnbaum, Aeta Metall 35, 2537–2542 (1987) 33. T. Tanaka, K. Kawakami, S. Hayashi, J. Mater Sci 49, 3928–3935 (2014) 34. N. Miyauchi, K. Hirata, Y. Murase, H.A. Sakaue, T. Yakabe, A.N. Itakura, T. Gotoh, S. Takagi, Scripta Mater. 144, 69–73 (2018)

Chapter 5

Deformation Behaviors

5.1 Elastic Moduli Elastic moduli that characterize the linear relationship between stress and strain express the shape of the potential energy of an atom pair in materials. Hydrogen atoms, located at interstitial sites in the regular lattice, exert stress fields and alter electronic states around them. An expected alteration of the distance or the cohesive force between neighboring host atoms is to appear in the elastic moduli. Hydrogen effects on Young’s modulus of polycrystalline bcc tantalum, niobium, and vanadium were measured from the velocity of 100 kHz elastic wave in wire specimens [1]. Hydrogen charging was done by cathodic electrolysis in 4% H2 SO4 with small amounts of CS2 and As2 O3 . Numerical data of hydrogen contents were not shown, but a linear increase in Young’s modulus E with hydrogen content was reported for each metal. The increases in terms of ΔE/E were 0.07, 0.58, and 0.48% for Ta, Nb, and V, respectively, per 1 at.% of hydrogen. On the contrary, a linear decrease in Young’s modulus against the square root of the hydrogen concentration as low as 2.5 × 10–3 was reported for a Ti–Mo alloy accompanying solution softening and expansion of lattice parameter [2]. As described in Chap. 1, the solid solubility of hydrogen in α-iron at room temperature is very low, and expected moduli changes, if any, are also very small. Measurements of the shear modulus of hydrogen-charged polycrystalline α-iron using a torsion pendulum method showed a decrease of about 0.3% of the pendulum frequency at temperatures lower than 200 K [3]. For the experiment, hydrogen was introduced by the electric discharge of wet hydrogen gas. The hydrogen concentration was not exact, but an estimated decrease in the shear modulus of iron by 1 at.% hydrogen was about 8% at 100 K.

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 M. Nagumo, Fundamentals of Hydrogen Embrittlement, https://doi.org/10.1007/978-981-99-0992-6_5

95

96

5 Deformation Behaviors

5.2 Flow Stress Lattice distortion around solute hydrogen atoms and the resulted interactions between dislocations and hydrogen, described in Sect. 3.1, may cause the solid solution hardening or softening for the flow stress. However, an exact evaluation is difficult because of low hydrogen concentrations and various trapping lattice defects. For a Ti–Mo alloy cited above [2], the proportional limit and 0.2% proof stress decreased linearly against the square root of hydrogen concentration. For iron and steel, hydrogen effects on the flow stress are fairly complicated depending on materials, deformation stages, and testing conditions. Flow stress is a major controlling factor of mechanical properties, and many early studies addressed the effects of hydrogen on flow stress. Hydrogen effects on the flow stress of iron are not yet conclusive, and Table 5.1 summarizes reported results in the literature [4–15].

5.2.1 Hardening Hardening by hydrogen is the more general case than softening for commercially pure iron, low-alloyed, and stainless steels tested for bulky specimens at room temperature. For iron single crystals containing about 50 ppm or less carbon, the critical resolved shear stress for yielding increased on {110} slip system in a hydrogen-precharged specimen, while it was almost immune on {112} slip system [4]. The tensile straining, in that case, was at room temperature with strain rates of about 10–4 –10–5 /s, using specimens of 2 mm thickness. Hydrogen effects on hardening behaviors varied by carbon contents. For carbon-doped iron single crystals, flow stress on tensile straining in the presence of hydrogen increased with 165 ppm carbon but decreased with 10 ppm [7]. For an intermediate 90 ppm carbon, the flow stress was higher or lower than that of the hydrogen-free specimen according to strain ranges less or larger than 30%, respectively. In the experiments, the tensile straining was at room temperature under cathodic electrolysis, setting the tensile axis near . For polycrystalline iron containing 10 ppm carbon and ~ 30 μm grain size, the yield and flow stresses increased by hydrogen on tensile straining of specimens of 2 mm thickness [8]. In the experiments, ~ 2 ppm hydrogen was precharged in 0.1 MPa hydrogen gas at 1123 K (850 °C), and tensile tests were at 273 K and 193 K. Strain aging increases flow stress, and a noteworthy fact was that hydrogen enhanced the increase at a strain of less than 5%. The grain-size dependence of hydrogen effects was also examined in terms of the Hall–Petch relation, i.e., a linear increase in the flow stress against the square root of the grain size, for commercially pure iron of grain size ranging 10–150 μm [9]. Tensile tests were at room temperature under concurrent cathodic hydrogen charging to 2–7 ppm in the average hydrogen concentration. A hydrogen effect appeared on the slope of the Hall–Petch relation. The 0.5% offset stress decreased by hydrogen

Vacuum melt 30 μm electrolytic iron

5

Decarburized Ferrovac E

Zone-refined pure iron (varied C contents)

4

6

Zone-refined Single crystal pure iron (resistance ratio 4700)

3

10–150 μm

Single crystal

–

2 × 5 mm

– TA//

1 N H2 SO4 + As 10 A/m2

1 atm H2 , 850 °C × 1 h → liq. N2

1 N H2 SO4 + As2 O3

6.5 × 10–3

6 × 10–4

–

8.3 × 10–4

RT

0–-80 °C

RT

200 K

RT

4 × 10–4

1 N H2 SO4 + As2 O3 40 A/m2

Temperature RT

Strain rate (s−1 )

1 N HCl aq + hydrazine 3.3 × 10–4 , 3.3 × 10–5 30 A/m2

H charging

0.4 ϕ or 0.1 × 0.1 N 1.4 CH3 OH–H2 O–H2 SO4 20 or 40 A/m2

1.5 mmϕ

Single crystal

Zone-refined pure iron

2

Size (t × w)

2 × 2 mm

Grain size

Decarburized Single crystal Armco iron (C: 30–50 ppm)

1

Purity

Specimen

[8]

[7]

[6]

[5]

[4]

References

(continued)

Enhanced grain-size [9] dependence of proof stress. Hardening for fine grain size less than 30 μm

Hardening, prominently at ε < 8%

Softening in the 1st and 2nd work-hardening stages. Hardening when C is added

Softening, but hardening in the 3rd work-hardening stage

Softening

Hardening for: {110} , Small change for {112}

Hydrogen effects

Table 5.1 Effects of hydrogen on the flow stress of iron. The residual resistance ratio (RRR) is a measure of the purity of material defined as the ratio of electric resistivity at room temperature and that at 4.2 K [4–15]

5.2 Flow Stress 97

Remelt Plasitron (added 0.15%Ti)

Vacuum melt mild steel and pure iron

Zone-refined pure iron (resistance ratio 3500–6000)

Zone-refined pure iron (resistance ratio 1800–5000)

7

8

9

10

Purity

Specimen

Table 5.1 (continued)

0.06–0.8 × 6 mm

20 μm

0.1 mm (RRR 1800) 0.3 mm (RRR 3600) 1.0 mm (RRR 5000)

0.4 mmϕ

0.4 mmϕ

–

10–150 μm

0.3 mm (RRR 3600) 1.0 mm (RRR 5000)

Size (t × w)

Grain size

170–297 K

8.3 × 10–5

0.1 N CH3 OH–H2 O–H2 SO4 20 or 40A/m2

170–297 K

8.3 × 10–5

0.1 N NaOH + Na2 AsO2 100 or 300 A/m2

RT

RT

Temperature

3.3 × 10–5

6.5 × 10–3

Strain rate (s−1 )

1 N H2 SO4 + As2 O3 10 A/m2

1 N H2 SO4 + As 10 A/m2

H charging

[11]

[10]

[9]

References

(continued)

Softening reduced at [12] elevating temperatures. Hardening at room temperature for low-purity iron

Softening, but hardening even at 200 k for low-purity iron Enhanced softening at lower strain rate

Hardening, but softening for fine specimen size less than 0.19 mm

Softening

Hydrogen effects

98 5 Deformation Behaviors

Remelt Single crystal electrolytic iron

13

TA// (0.1–1.0) × 5 mm

0.4, 1.0, 2.0 mm 0.4 mmϕ

Zone-refined pure iron (Resistance ratio 3600–5200)

12

0.5 mmϕ

60–100 μm

Zone-refined pure iron + 0.6 at.% Ti Zone-refined pure iron + 0.2 at.% Mo

Size (t × w)

Grain size

11

Purity

Specimen

Table 5.1 (continued)

5 × 10–5

C2 H5 OH + H2 SO4 50 A/m2 195 K

170–297 K

1.7 × 10–3 – 8.3 × 10–5

ibid

Temperature 200–RT

Strain rate (s−1 ) 3.3 × 10–5

ibid

H charging [13]

References

Enhanced softening [15] for smaller specimen size

Softening reduced by [14] increasing strain rate and current density

Hardening for Fe–T. Hardening at RT but softening at below 0° C for Fe–Mo

Hydrogen effects

5.2 Flow Stress 99

100

5 Deformation Behaviors

for coarse-grain sizes over ~ 30 μm but increased for smaller grain sizes. However, effects of interstitial impurities were present, and for iron with reduced interstitial impurities by adding 0.15% titanium as a getter, the slope of the Hall–Petch relation was almost unaffected, and hydrogen reduced the strength for all grain sizes. The specimen size is also a vital factor. Effects of hydrogen on the flow stress at room temperature of decarburized rimmed steel containing ~ 40 ppm of carbon vary with of the specimen thickness [10]. Switching on cathodic current for hydrogen charging during tensile straining consistently increased the flow stress for specimens of 0.8 mm in thickness. However, reducing the specimen thickness decreased the flow stress increment, and softening appeared for the thickness of less than 0.20 mm. On the other hand, hardening was always the case for 17Cr steel. Hardening by hydrogen was also observed for a commercial quenched and tempered steel [8] and a Fe-0.5%Ti alloy [13] on tensile straining at temperatures below room temperature. Another demonstration of hardening was the appearance of two-stage Lüders deformation on tensile straining of commercial 1045 steel [16]. In the experiment, hydrogen was introduced into one-half of the gauge section, and the second-stage Lüders deformation was assigned to the yield in the hydrogen-charged portion.

5.2.2 Softening Softening by hydrogen generally appears for thin specimens of high-purity iron at temperatures below room temperature. Figure 5.1 [12] shows tensile stress–strain curves of zone-refined high-purity iron specimens as thin as 0.4 mm in diameter tested at low temperatures. Downward and upward arrows indicate switching on and off of cathodic current for hydrogen charging. While hydrogen caused only hardening at room temperature, a gradual decrease of flow stress after a small hump or a rapid decrease appeared at lower test temperatures. The decrease in the flow stress at the start of hydrogen charging was temporal at temperatures lower than 180 K, and the flow stress tended to increase again at 170 K. The initial decrease in the flow stress that appears on hydrogen charging at low temperatures was more prominent for high-purity iron. The amount of softening depends on test conditions. The higher charging current density, the lower strain rate, and the smaller specimen size increased the difference in the flow stresses between the final steady level and before charging [14]. It is to be noted that the microstructures of the coarse-grain specimens were bamboo-like. Softening by hydrogen was also reported in tensile straining of single-crystal iron specimens, as thick as 3 mm in diameter, within the easy glide region under continuous hydrogen charging at room temperature [17]. Slip markings on the specimen surface were finer for hydrogen-charged specimens than those of the hydrogenfree ones. The work-hardening rate soon after yielding increased in the presence of hydrogen, and shear stress exceeded that of hydrogen-free specimens, i.e., softening turned to hardening. However, the critical resolved shear stress for yielding

5.2 Flow Stress

101

300

Fig. 5.1 Effects of cathodic polarization on tensile curves of pure iron specimens at different temperatures (Matsui et al. [12])

250

Current on (20A/m 2 ) Current off

Tensile Stress

(MPa)

170K

200 180

150

190K 225

100

250K 80A/m 2

273

297K

40A/m 2

50 0

0

1

2 Strain (%)

3

was almost the same for specimens with and without hydrogen charging. Softening also appeared over a wide strain range at 200 K for a single-crystal iron specimen of 2 mm in thickness, but a polycrystalline iron showed hardening in small strain of less than 5% [18]. Softening by hydrogen is prominent for low strain rates. Figure 5.2 [11] shows the temperature dependence of the yield stress of high-purity iron tested at different strain rates. For the experiments, the specimens of 0.4 mm in diameter were given 1–2% prestrain and cathodic hydrogen precharging. The yield stress increased with decreasing temperature and exceeded the yield stress of the hydrogen-free specimens, i.e., turned to hardening by hydrogen at low temperatures. Prestrain introduced fresh dislocations in specimens, and aging of prestrained and hydrogen-precharged specimens at room temperature diminished hydrogen effects on the yield stress, or rather showed hardening at 200 K, even at the strain rate as low as 8 × 10–5 /s [11]. Prominent softening by hydrogen was reported earlier as a pronounced decrease of torque in torsion tests of mild steel tubes [19]. The specimen was a tube of 2 mm in wall thickness and 20 mm in outer diameter. The test was conducted at room temperature, and hydrogen was introduced by immersing the specimen in 5% H2 SO4 with small additions of poisons. The observed softening, coupled with transitions of fractographic feature presented in Sect. 7.2.5, was a basis of the hydrogen-assisted cracking (HAC) mechanism of hydrogen embrittlement, described in Sect. 10.2.

102

5 Deformation Behaviors

Fig. 5.2 Yield stress of prestrained and hydrogen-precharged iron at different strain rates and temperatures. The broken line is for specimens without hydrogen (Moriya et al. [11])

5.2.3 Explanations of Experimental Results As described above, observed hydrogen effects on flow stress are complicated, depending on the material purity, grain size, specimen size, testing temperature, strain rate, and hydrogen fugacity. For focusing discussion, dislocation dynamics is the primary player in the flow stress, and the applied flow stress τ app must overcome the sum of the intrinsic flow stress τ 0 and the internal stress τ int , i.e., τapp = τ0 + τint .

(5.1)

τ int is composed of short- and long-range stress fields. Further, under a given strain rate ε˙ , τ app keeps the average dislocation velocity v that satisfies ε˙ = bρv,

(5.2)

where b is the Burgers vector and ρ is the dislocation density. Any term in Eq. (5.1) and (5.2) is a candidate to tolerate hydrogen effects, not necessarily limited to the intrinsic mobility of dislocations. A fact to be noticed is that a decrease in the flow stress is remarkable at switching on hydrogen charging in a transient state, i.e., during a dynamic state of the specimen. Concerning the mechanism of hydrogen embrittlement, softening, rather than hardening, has been given much attention as hydrogen effects, as described in Sect. 10.2. Discussion on the effects of softening has been in the following aspects:

5.2 Flow Stress

103

(1) interactions of hydrogen with dislocations, (2) the increase in the density of mobile dislocations, and (3) the formation of damage in near-surface areas. The last aspect is vital in experiments using cathodic electrolysis under substantially high hydrogen fugacity. The authors of the original papers interpreted their results briefly as follows: (a) Kink-pair formation The motion of screw dislocations dominates plastic deformation after preyield strain for iron single crystal at low temperatures. The formation of a kink and its sideward movement energetically favors the slip of a dislocation line. The Peierls potential for screw dislocations in bcc metals is high, and strain rate is controlled by the kinkpair formation and the side-way movement of kinks. To explain softening observed for high-purity iron, Matsui et al. postulated that hydrogen enters the dislocation core and modifies the core structure to increase the double-kink nucleation rate [12]. A prompt response of the flow stress to cathodic polarization was ascribed to the hydrogen transportation by moving dislocations. Characteristic experimental conditions employed by Matsui et al. were high hydrogen fugacity, extremely high purity, and coarse-grain thin specimens. High concentrations of hydrogen far exceeding equilibrium may exhibit solid solution hardening or softening in similar ways as carbon and nitrogen play their role. However, Matsui et al. ruled out this possibility from tests at temperatures at which hydrogen was mobile together with dislocations. They assumed that interactions between hydrogen and impurities cause hardening at and above 273 K in impure specimens containing dissolved impurities of comparable concentrations as hydrogen. First-principles calculations for hydrogen interactions with the core of screw dislocations and their role in the mobility of dislocations are presented in Sects. 3.1.2 and 5.5.2, respectively. (b) Long-range internal stress On the other hand, Lunarska et al. suggested that softening by hydrogen in the easy glide region at room temperature was due to long-range internal stress rather than double-kink formation because the critical resolved shear stress for yielding was unaffected by hydrogen charging [17]. The proposed mechanism was that hydrogen segregation around dislocations lowered elastic interactions between dislocations. On the other hand, fine slip markings and higher work-hardening rates leading to hardening in Stage III feature hydrogen effects. Lunarska et al. also suggested the formation of some obstacles against dislocation motion. Hydrogen effects enhancing the mobility of dislocations are also discussed concerning elastic field shielding by hydrogen in Sect. 5.5.1 concerning direct observations by transmission electron microscopy. Hydrogen-enhanced strain localization (HELP) associated with the formation of defects is described in Sect. 7.2.3, concerning fractographic features.

104

5 Deformation Behaviors

(c) Surface effects High hydrogen fugacity eventually induces surface damage, and some blisters appear on the surface of hydrogen-charged specimens [12]. Oriani and Josephic noticed that the generation of blisters or microvoids causes softening by reducing localized stress at the sites and thus increasing the effective stress [16]. They also noticed that the surface of microvoids might facilitate plastic deformation by serving as an additional source and sink of dislocations, increasing the number of mobile dislocations and reducing the number of dislocation pileups. On the other hand, for the hardening effects of hydrogen, Oriani and Josephic proposed that hydrogen reduces stacking fault energy that impedes cross-slipping. Suppression of the dislocation nucleation from grain boundaries and their ledges was another mechanism Oriani and Josephic proposed for hardening. The specimen-size dependence of softening [10] supports the idea that surface effects originate in flaws induced by hydrogen charging. However, softening appeared even under mild hydrogen-charging conditions by which the formation of blisters is unlikely [11]. Changes in stress–strain curves associated with switching on and off charging current are too complicated to ascribe simply to the formation of blisters or voids. A viable viewpoint, though so far not paid so much attention to, on the flow stress under concurrent electrolysis is the decrease in surface energy due to the hydrogen adsorption on the surface. Surface effects are particularly critical in experiments using thin specimens. As described in the following sections, surface effects likely operate in stress relaxation, creep, and dislocation mobility under in situ transmission electron microscopy. The generation of dislocations from the surface, the release of dislocation pinning on the surface, and associated changes in internal dislocation structures must be considered. (d) Point lattice defects An indispensable aspect of hydrogen functions associated with the movement of dislocations is the creation of point defects. Moving dislocations multiply, and screw dislocations gliding on a slip plane generate jogs by intersecting screw dislocations on other slip planes. Transmission electron microscopy revealed large jogs, forming dipoles of edge dislocations in a single crystal of 3% Si iron [20], and the formation of tangles and cells of dislocations resulting from mutual interactions of dislocations in iron single crystals [21]. Interactions of dislocations with other lattice defects are vital factors controlling dislocation structures as well as flow stress. Interactions of hydrogen with lattice defects created by moving dislocations are crucial, particularly in areas where the density of dislocations is substantial, rather than in elementary slip processes of dislocations. Interactions of hydrogen with vacancies created by dragging jog are described in Sect. 3.2.3.

5.3 Stress Relaxation and Creep

105

5.3 Stress Relaxation and Creep 5.3.1 Stress Relaxation Stress relaxation is a partial release of external stress under a constant-strain condition. An example of stress relaxation in engineering practice is the loss of compacting force in prestressed steel structures. Stress relaxation eventually leads to fracture, and delayed fracture of steel components stressed at constant displacement in corrosive environments is a case where hydrogen-assisted stress relaxation occurs. Dislocation configurations, forming under rising stress, turn toward stable structures when the increase in stress is stopped. At a constant-strain condition, the macroscopic strain rate is zero, i.e., ε = εe + ε p const,

(5.3)

σ˙ e , E

(5.4)

then ε˙ p = −˙εe = −

where suffixes e and p denote elastic and plastic, respectively, and E is Young’s modulus. Equation (5.4) implies that the plastic strain rate associated with the rearrangement of dislocations appears as a decrease in elastic stress rate. Stress relaxation originates in microplasticity, a measure of the stability of microstructures, particularly dislocation configurations. The relaxation rate is very susceptible to temperature variation, and careful temperature control is necessary for stress-relaxation measurements. The plastic strain-rate Eq. (5.2) is from the dislocation theory of plasticity. When the viscous flow model of dislocations [22] is employed, the average dislocation velocity υ is expressed as υ = A(τ − τi )m ,

(5.5)

where A is the average velocity at unit effective stress, τ is the applied shear stress, τ i is the internal shear stress, and m is the dislocation velocity-stress exponent. Equation (5.2) is written using Eqs. (5.4) and (5.5) as ε˙ p = −Kρ(τ − τi )m ,

(5.6)

where K is a constant [23]. Then, hydrogen effects in stress relaxation are related to the density of mobile dislocations, the magnitude of internal stress, and m. Hydrogen enhances stress relaxation. Stress relaxation of a zone-refined pure iron in the uniform elongation region shows a substantial enhancement when cathodic

106 Fig. 5.3 Deformation parameters in Eq. (5.5) for coarse-grain pure iron at stress-relaxation tests from different initial strains ε0 with and without hydrogen charging. Hydrogen-charging current is 3.8 mA/cm2 (Lunarska [24])

5 Deformation Behaviors 1.0

0.7

10

1.0

[H] ppm 6

.98

2 0.02

0.06

0.10

0.14

0.18

ε0

hydrogen charging is applied [24]. Figure 5.3 [24] shows hydrogen effects on deformation parameters in Eq. (5.5) obtained by stress-relaxation experiments for coarsegrain pure iron at room temperature. Stress relaxation started at different initial tensile strains ε0 , and hydrogen charging was applied some 1.5–5 min after the start of stress relaxation, using cathodic electrolysis in poisoned 1 N H2 SO4 at a current density of 20 to 170 A/m2 . Figure 5.3 indicates that hydrogen reduces internal stress and the dislocation velocity-stress exponent m in Eq. (5.5). Hydrogen fugacity in that experiment was substantially high, while the data collection was before the formation of blisters. A reduction in the current density or interruption of hydrogen charging again increased the load, and the restart of the cross-head movement accompanied a jump-like increase in the load. Similar hydrogen effects in stress relaxation were observed for many types of iron and steel. Figure 5.4 [10] shows the effects of hydrogen charging to enhance stress relaxation in decarburized rimmed and 17Cr steel. Cathodic polarization was applied during stress relaxation at a constant strain of 4%. The thickness of the specimen was 0.8 mm, but the enhancement was more prominent for thinner specimens [10], similarly to the flow stress on tensile straining. The magnitude of the charging current density is related to hydrogen fugacity that determines the solid solubility of hydrogen (Sect. 2.1.1). Oriani and Josephic showed a threshold in the input hydrogen fugacity, i.e., some critical hydrogencharging current density, to induce an abrupt increase in the relaxation rate [25]. The threshold fugacity was higher for a higher initial strain to start stress relaxation. On the other hand, at initial strain below a certain amount, a well-defined effect by hydrogen was not discernible on the slope of the relaxation curve. The experiments were conducted for AISI 1045 steel sheet 0.25 mm in thickness at room temperature, carefully controlling test temperatures. Oriani and Josephic used poisoned 0.1 N NaOH for electrolyte at very low current density, and the estimated threshold fugacity was several MPa. On the other hand, most preceding flow stress and stress-relaxation experiments employed hydrogen charging under substantially high fugacity. Oriani

5.3 Stress Relaxation and Creep

107

Stress (MPa)

17Cr Steel

Current Density Hydrogen charging

Mild Steel

Constant Strain (4%)

Strain (%)

Time (min)

Fig. 5.4 Stress-relaxation curves of mild steel and 17Cr steel specimens started at constant strain of 4%. Cathodic electrolysis was applied in the course of stress relaxation (Asano et al. [10]. Reprinted with permission from Japan Inst. Metals)

and Josephic discussed the mechanism from the viewpoint of the hydrogen-assisted nucleation and growth of microvoids due to decohesion of atomic bonds. An enhancement in stress relaxation appears not only on hydrogen charging during stress relaxation but also by precharged hydrogen. Figure 5.5 [26] shows stress-relaxation curves of 0.37%C–0.6%Si–1.0%Mo–0.5%Cr–0.54 V martensitic steel tempered at 550 °C (823 K) and 650 °C (923 K). Secondary hardening due to the precipitation of fine vanadium carbides by tempering at 923 K, coupled with advanced recovery of martensite, gave the same tensile strength of 1470 MPa as that for specimens tempered at 823 K. Hydrogen precharging was conducted in a mild condition using cathodic electrolysis in a 3% NaCl + 3 g/l NH4 SCN solution at a current density of 5 A/m2 . The specimens were 2 mm thick, and stress relaxation at 28 ± 0.5 °C (301 ± 0.5 K) started by stopping tensile straining at 60% of the ultimate tensile strength. Enhancement of stress relaxation by hydrogen was observed for both tempering temperatures, but tempering at 923 K substantially reduced the extent of relaxation. High tempering temperatures and homogeneous distributions of vanadium carbides stabilize martensite microstructures. The stable and homogeneous structures suppress strain localization and rearrangement, reducing additional plastic strain at stress relaxation. Stress relaxation that occurs on stopping the stress rise to keep a constant displacement is similar to a decrease in the flow stress on tensile straining by switching on hydrogen charging, both representing breakdown of dynamic equilibrium. The breakdown is associated with microplasticity. Hydrogen enhancement of stress relaxation

108

5 Deformation Behaviors

Fig. 5.5 Effects of hydrogen precharging on stress-relaxation curves of Mo–V martensitic steel specimens tempered at 550 (823 K) and 650 °C (923 K). The initial stress is 0.6 of the tensile strength, and the test temperature is 28 ± 0.5 °C. (Nagumo et al. [26])

implies a concern of hydrogen with the origin of microplasticity, presumably a change in internal stress fields. A noteworthy fact concerning the relevance of stress relaxation to hydrogen embrittlement was that tempering of the Mo-V steel at 923 K improved the resistance to delayed fracture compared with tempering at 823 K [26]. The relevance of stress-relaxation rates to the susceptibilities to delayed fracture is likely a general feature for steel of similar strength levels or chemical compositions. Early studies revealed a high resistance to delayed fracture and a very small stress relaxation in an 18Ni maraging steel [27]. A correlation between stress-relaxation rate and the time to fracture in delayed fracture tests also existed for low-carbon martensitic steels [28]. The relevance of stress relaxation in Fig. 5.5 to hydrogen embrittlement for the Mo-V martensitic steel is described in Sect. 6.4.2 about Fig. 6.28 and in Sect. 8.1.2 about Fig. 8.5.

5.3.2 Creep Creep is time-dependent plasticity under constant load or stress and is particularly important for the high-temperature engineering life of materials. At elevated temperatures, grain-boundary sliding or diffusion of vacancies is the primary origin of creep failure. Creep strain is normally minimal at room temperature, but delayed fracture under constant applied stress is a phenomenon accompanying creep. Various mechanisms likely operate according to types of materials, applied stress, and temperatures

5.3 Stress Relaxation and Creep

109

Strain

Fig. 5.6 Schematic illustration of three stages in creep curve

I

II

III

Log time [29]. Internal stress and obstacles against slip oppose the dislocation motion induced by external stress. However, thermal energy activates dislocations or other elements equilibrated under applied stress, causing microplasticity. The general form of the creep curve is schematically shown in Fig. 5.6, and it depends on temperature and applied stress. Three stages generally compose the creep curve: the transient creep stage of decelerating flow, the steady-state creep of a constant minimum rate, and, eventually at high temperatures, the accelerating flow stage that ends in fracture. The exhaustion theory of transient creep is that each element is thermally activated only once by characteristic activation stress, contributing to plastic strain [29]. The creep rate in the transient and steady-state stages is expressed as ε˙ = At −n ,

(5.7)

where A and n are constants and 0 < n < 1. Creep is a thermally activated process, and the steady-state creep rate strongly increases with temperature. The creep rate over a small range of stress is expressed in terms of the activation energy of dislocation movement in the form of  U − bσ , ε˙ = K exp − RT 

(5.8)

where K, U, and b are constants. Cottrell derived a refined form of the activation energy, considering dislocation movement passing through closely spaced obstacles, like dislocation forests [30]. However, studies in the following about hydrogen effects were before this consideration. Hydrogen effects on the density, mobility, and barriers to the movement of mobile dislocations appear on creep behaviors, while experiments on this matter are not

110

5 Deformation Behaviors

many. Creep rates are higher for higher hydrogen concentrations, similarly to the stress-relaxation test shown in Fig. 5.4. During creep deformation of a single-crystal specimen of pure iron at 200 K, the creep rate was immune to a sudden application of cathodic potential when the potential was low. An increase in the applied potential accelerated the creep rate, initially gradually, then rapidly, and finally to a nearly steady state [18]. In the experiments by Park et al., the thickness of the specimens was 0.8 mm, and the applied stress was 60% of the yield stress. Hydrogen effects were more prominent at higher current densities and stress levels, but the acceleration decreased with increasing temperature and was insignificant at room temperature. Turn-off the potential reduced the creep rate in a few minutes to the initial value before cathodic charging. Such temperature dependence of the accelerated creep rate is similar to softening of the flow stress shown in Fig. 5.1. The threshold fugacity for accelerating creep rate was also found by Oriani and Josephic with spheroidized AISI 1040 steel [31] by a similar method as used for stress relaxation [25]. The wire specimen was 0.12 mm in diameter, and hydrogen charging was by cathodic electrolysis in poisoned 0.1 N NaOH aqueous solution at room temperature. The creep rate at room temperature increased abruptly on applying cathodic potential above a critical value. The increase then decelerated following the form of ε − ε0 = k ln(t − t0 ).

(5.9)

Shut off the charging current immediately and markedly raised the creep rate to a maximum, followed by a decrease. Oriani and Josephic inferred the function of hydrogen similar to that in stress relaxation [25], i.e., the reduction in internal stress due to the nucleation and growth of microvoids induced by a hydrogen-reduced cohesive strength, but no supporting observations. The contribution of vacancies to creep becomes significant with elevating temperatures. If hydrogen increases the density of vacancies, as described in Sect. 3.2.3.1, hydrogen must increase creep rate. The creep rate at 736–1200 K of a Pd wire of 0.1 mm in diameter was about six times higher in a 0.1 MPa H2 atmosphere than in an Ar atmosphere of the same pressure [32]. Hydrogen reduced the creep activation energy from 38.6 ± 1.9 kJ/mol in Ar gas to 30.0 ± 1.5 kJ/mol in H2 gas. The mechanism of the observed creep was ascribed to grain-boundary diffusion of Pd atoms, while the hydrogen effect on the diffusion of Pd atoms was out of the discussion.

5.3.3 Implications of Surface Effects The effects of hydrogen on stress relaxation and creep have been discussed mostly regarding hydrogen interactions with moving dislocations and surface damage induced by a high hydrogen fugacity. Hydrogen is introduced into metals by cathodic polarization, but the creep rate also increases by anodic polarization. Figure 5.7 [33] compares the creep curves of a thin copper wire for (a) anodic and (b) cathodic

5.3 Stress Relaxation and Creep

111

Fig. 5.7 Effects of polarization on creep curves of Cu wire at room temperature. The diameter of wires is 0.27 mm, and the applied stress is 90 MPa. (a) Anodic polarization and (b) cathodic polarization (Revie et al. [33])

polarizations. The average grain size was about 20 μm, and the diameter of the wire was 0.27 mm. The electrolyte was an aqueous acetate buffer solution of pH 3.7 at 298 ± 0.5 K (25 ± 0.5 °C), and the current density was 9A/m2 . Both cathodic and anodic polarizations increased the creep rate. Anodic polarization gradually increased the creep rate, and shutting off the current decreased the rate to a level similar to before the polarization application. On the other hand, cathodic polarization also increased the creep rate to the same order as anodic polarization. Still, the increase in creep rate was abrupt on the application of polarization. The increase in the creep rate by both anodic and cathodic polarizations implies that some factors other than hydrogen affect the creep rate associated with chemical reactions on the specimen surface. On anodic polarization, the estimated thinning of the wire was not significant. Revie and Uhlig [33] ascribed the observed lag in the creep response to a diffusional process of vacancies created very near the metal surface associated with the metal dissolution, and Jones later systematically discussed

112

5 Deformation Behaviors

concerning stress corrosion cracking [34]. Divacancies diffusing from the surface were assumed to interact with sessile dislocations causing climb under applied stress. On the other hand, cathodic polarization causes an abrupt increase in creep rate, a very small current density of 0.1A/m2 resulting in a marked increase in creep rate compared with anodic polarization. Revie and Uhlig ascribed the effect to the reduction of surface energy. Generated hydrogen by cathodic electrolysis adsorbs on the specimen surface, preceding the entry into the bulk. The Gibbs adsorption isotherm gives the change in the surface energy, dγ , of metals caused by a change of the chemical potential, dμ, of an adsorbed phase. For the adsorption at temperature T and pressure p, dγ = −Γdμ = −ΓkB T ln p,

(5.10)

where Γ is the number of molecules adsorbed per unit area and k B is the Boltzmann constant [35]. For the Langmuir adsorption, i.e., monolayer adsorption, of dissociated atoms of diatomic molecules, γ is expressed as   γ = γ0 − 2Γs kB T ln 1 + ( Ap)1/2 ,

(5.11)

where γ 0 is the surface energy without adsorption, Γ s is the saturation value of Γ , and A is a constant. Petch calculated the reduction of γ of α-iron caused by hydrogen adsorption on the crack surface at room temperature. Details of the calculation are described in Sect. 9.2, and the results are shown in Fig. 5.8 [35]. Reduction in surface energy facilitates the formation of new surfaces, and the idea is viable as a mechanism of hydrogen embrittlement. The magnitude of γ 0 is about 2 J/m2 , and the fractional reduction of γ shown in Fig. 5.8 is substantial even for very low hydrogen concentrations. Revie and Uhlig postulated that the reduction in the surface energy facilitated slip step formations on the metal surface [36]. The ease of the slip step formation is feasible in grains facing the surface, and the idea is consistent with the higher acceleration of creep rate for larger grain-size specimens. The idea is also compatible with the fact that the application of cathodic polarization causes a sudden response of creep rate. If the reduction in the surface energy due to adsorbed hydrogen affected the creep rate, it also should play a role in stress relaxation. Changing stress states at the surface should alter the balance of internal stress states, inducing extra plastic strain. From this notion, the additional plasticity is not a consequence of some direct interactions between hydrogen and dislocations within the bulk phase. In this context, the abrupt drop of the flow stress associated with cathodic polarization on tensile straining, shown in Fig. 5.1, might be ascribed to a decrease in surface energy. However, Fig. 5.5 demonstrates the effects of internal, not externally introduced, hydrogen on stress relaxation. It implies that surface effects, if any, are not the sole

5.4 Direct Observation of Dislocation Activity

113

Fig. 5.8 Decrease in the surface energy of iron by adsorption of hydrogen (Petch [35])

origin of hydrogen effects on creep and stress relaxation. Another viable mechanism is interactions between hydrogen and strain-induced vacancies. Vacancy formation associated with cathodic electrolysis or dissociation of water molecules at the surface of pure aluminum was observed by Birnbaum et al. [36]. Small-angle X-ray scattering and measurements of lattice parameters showed the formation of hydrogen-vacancy complexes clustered into platelets lying on the {111} planes. Candidate origins of vacancies are interactions of moving dislocations and possible products on the surface in the case of anodic polarization.

5.4 Direct Observation of Dislocation Activity The decrease in flow stress in Fig. 5.1 and the enhanced stress relaxation in Figs. 5.4 and 5.5 led to the idea that hydrogen enhances plasticity. Strong support for the notion has been obtained using in situ environmental cell transmission electron microscopy (TEM). The first observation was for iron foils stretched to a constant displacement in an equipped environmental cell, initially in a vacuum and successively in hydrogen gas [37]. Increasing the hydrogen gas pressure up to 35 kPa increased the velocity of screw dislocations, and removing the gas promptly decreased dislocation velocity to the initial value in a vacuum. Similar results were observed for various metals and alloys of bcc, fcc, and hcp structures [38]. For high-purity aluminum, introducing hydrogen increased the length of screw components of dislocations at the intersection of two slip planes and decreased the length of mostly edge components [39]. It was deduced then that dislocation pinning

114

5 Deformation Behaviors

by hydrogen stabilized edge segments of dislocations, reducing the tendency to cross-slipping [39]. For a nickel, detailed observations exhibited hydrogen effects to increase the dislocation velocity and the generation rate of both isolated and tangled dislocations [40]. The increase in dislocation velocity was observed for dislocations lying in tangles and emanating from crack tips, and the origin was ascribed to a volumetric rather than a surface phenomenon. However, an alteration of surface states may alter internal dislocation structures to establish a new stress balance in the specimen, even when hydrogen is absent. The observations may not rule out surface effects on the apparent dislocation activities. Enhanced strain localization is another feature of hydrogen effects. In situ observations revealed the crack propagation associated with the emission of dislocations from the crack tips in iron foil [41]. The generation of dislocations in the vicinity of dislocation cell walls was also observed ahead of the crack tip. Initially formed and arrested cracks in a vacuum restarted when hydrogen gas was introduced into the environmental cell, even at a stress lower than in a vacuum. Deformation was highly localized near the crack tip and resulted in the formation of small voids. The observations have served as an experimental basis for the hydrogen-enhanced localized plasticity (HELP) mechanism of hydrogen embrittlement described in the following Sects. 5.5 and 10.2. Hydrogen fugacity in the environment cell was much lower than the threshold fugacity at stress relaxation for carbon steel [25]. Concentrations of solute hydrogen estimated from Sieverts’ law are very low compared with other alloying elements or impurities that alter the deformation behaviors of steels. Accordingly, direct interactions of hydrogen with moving dislocations are hardly viable to enhance dislocation mobility. On the other hand, most dislocation arrays observed by TEM are initially pinned at the surface of the foil specimen, suppressing their movements. It is feasible that a substantial decrease in the surface energy caused by hydrogen adsorption, as shown in Fig. 5.8, releases pinning and alters the mechanical balance to move dislocations.

5.5 Elastic and Atomistic Calculations 5.5.1 Elastic Shielding of Stress Centers The elastic interaction energy between a hydrogen atom and an edge dislocation, originating in the volumetric effect, is described in Sect. 3.1.2. Hydrogen-enhanced dislocation mobility revealed by in situ TEM is quite general for fcc, bcc, and hcp crystal structures and also for both edge and screw types of dislocations. In addition to some qualitative explanations of experimental observations described in Sect. 5.2.3, quantitative estimation in a frame of elasticity has been made about reducing barriers for dislocation motion.

5.5 Elastic and Atomistic Calculations

115

The mobility of dislocations is affected by elastic interactions between dislocations and also between dislocations and other stress centers, such as solute atoms and precipitates. Hydrogen atmospheres form in the dilatational fields to make the energy of the system minimum. Sofronis and Birnbaum calculated hydrogen effects on the dislocation mobility, considering both the first-order dilatational interaction energy, expressed by Eq. (3.8) for an edge dislocation, and a second-order interaction energy that arises from the change in the elastic moduli caused by hydrogen in solid solution [38, 42]. Calculations were made for various configurations and types of elastic centers. Figure 5.9 [38, 42] is a schematic illustration of the coordinates of interacting two edge dislocations of the same sign and hydrogen atmosphere. The shear stress acting at the core of dislocation #2 located at the center is the sum of shear stresses due to the hydrogen atmosphere and neighboring dislocation #1. The hydrogen atmosphere in the area dS exerts the shear stress dτ H . Regarding the hydrogen volumetric effect, the net shear stress, τ H , acting at dislocation #2 due to the hydrogen atmosphere of the local concentration C(r, ϕ) is VH μ τH = − 2π(1 − ν) NA

 0

2π



R

r2

C(r, ϕ)

sin 2ϕ dr dϕ, r

(5.12)

where μ is the shear modulus, V H is the partial molar volume of hydrogen, N A is Avogadro’s number, r 2 is the inner cut-off radius of dislocation #2, and R is the outer cut-off radius of the atmosphere centered at dislocation #2. C(r, ϕ) is the hydrogen distribution in equilibrium with an applied stress field and stress fields arising from dislocations #1 and #2. On the other hand, the shear stress τ D resolved along the slip Fig. 5.9 Schematic model for the shear stress acting at the core of dislocation #2 by the hydrogen dilatation lines of an infinitesimal area dS at the position (r, ϕ) (Birnbaum et al. [38])

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5 Deformation Behaviors

plane and exerted by dislocation #1 is τD = −

cos ω cos 2ω b1 , 2π(1 − ν) l

(5.13)

where b1 is the Burgers vector of dislocation #1. The net shear stress exerting at the core of dislocation #2 is equal to τ D + τ H . Figure 5.10 [38, 42] plots calculated normalized shear stresses, τ H /μ, τ D /μ, and (τ D + τ H )/μ, versus normalized distance, l/b, and nominal hydrogen concentrations of H/M = 0.1 and 0.01 for bcc niobium at 300 K. Figure 5.10 indicates that the hydrogen atmosphere reduces the repulsive interaction between parallel edge dislocations of the same sign at a close distance. Two dislocations of opposite signs also give very similar results. Calculated elastic energies of edge dislocations with and without hydrogen atmospheres are shown in Fig. 5.11 [39] for aluminum as a function of nominal hydrogen concentration. The energies are expressed as the energy per atomic distance along the dislocations. In both Figs. 5.10 and 5.11, substantially high hydrogen concentrations over 0.01 are necessary to exhibit the shielding effects of hydrogen. Ferreira et al. postulated that the formation of hydrogen atmosphere around edge components of dislocations decreased the system’s energy and disturbed cross-slipping [39]. However, low hydrogen gas pressure in the environmental cell is unlikely to realize such a high hydrogen concentration.

τ/µ

Hydrogen free material (τD) Total shear stress (τD + τH)

Shear stress due to hydrogen atmosphere

l/b Fig. 5.10 Normalized shear stress due to hydrogen, τ H /μ, and due to dislocation #1, τ D /μ, and net shear stress, (τ D + τ H )/μ, at the core of dislocation #2 at 200 K and nominal hydrogen concentrations of H/M = 0.1, 0.01 in Nb (Sofronis et al. [42])

Fig. 5.11 Calculated elastic energies of edge dislocations with and without hydrogen atmospheres as a function of hydrogen concentrations. The energies are given as energy per atomic distance along the dislocation. (Ferreira et al. [39])

Energy, W (eV/slab of thickness a)

5.5 Elastic and Atomistic Calculations

117

15 Wdislocation 10 Wdislocation+hydrogen 5 Whydrogen 0

-5 10-5

10-4 10-3 10-2 10-1 Hydrogen Concentration (H/M)

100

For screw dislocations, direct interactions with hydrogen are very weak because of a cubic symmetry of the deformation field around a hydrogen atom. Sofronis and Birnbaum showed that hydrogen shielding also operates in elastic interactions between dislocations and a carbon atom. Screw dislocations interact with carbon atoms. Then, the stress acting on screw dislocations as well as edge dislocations are affected by hydrogen resulting from interactions between hydrogen and carbon atoms [38, 42]. Sofronis and Birnbaum calculated the interaction energy between a dislocation and a carbon atom in the hydrogen atmosphere. A finite element method calculation was conducted, taking into account the modulus changes of the carbon atom by hydrogen atmosphere using data for niobium [43], E = E 0 (1 + 0.34c), ν = ν0 − 0.025c, μ = μ0

1 + 0.34c . 1 − 0.0177c

(5.13)

The results are complicated; either an increase or decrease in the interaction energy, depending on the locations and tetragonal axes of the carbon atom. The modulus effect is a weak second-order interaction operating in a short range. Hydrogen effects were prominent when the carbon atom locates very close, within one Burgers vector, to the dislocation core. Also, the calculations were for the case of a very high nominal hydrogen concentration of H/M = 0.1. On the other hand, hydrogen softening is not feasible for the movement of edge dislocations. Atomistic modeling for the edge dislocation mobility and pileups showed hydrogen effects against the shielding of elastic fields [44]. Large-scale molecular dynamics simulations were conducted by applying shear stress to a cell composed of bcc iron and three edge dislocations with/without hydrogen precharging. The Cottrell atmosphere of hydrogen forms around moving dislocations, and hydrogen does not affect the pileup structures. The results imply that the drag of hydrogen reduces the mobility of edge dislocation and that the hydrogen atmosphere provides no measurable shielding of dislocation interactions.

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5 Deformation Behaviors

5.5.2 Mobility of Screw Dislocations—Atomistic Calculations First-principles calculations of the hydrogen binding energy with the screw dislocation core are described in Sect. 3.1.2. The nucleation of the kink pair and its expansion control the movement of a screw dislocation. Wen et al. simulated the effects of hydrogen on the nucleation and the sideward movement energies of kink pairs in bcc iron [45]. Assuming that a kink nucleates on 1/2[111] screw dislocation at a hydrogen atom, the hydrogen binding energies were calculated for various sites of hydrogen in the core. The activation energy of kinking was expressed as the maximum of the increased energy of the dislocation during kinking. When a kink pair meets hydrogen during expansion, the sideward motion of the kink pair is impeded by hydrogen. The kinking process was determined to take the minimum energy path during expanding along the dislocation meeting and overcoming another hydrogen atom. Softening by hydrogen, i.e., a reduction in the activation energy, appeared in the sideward movement rather than in the nucleation of a kink pair when the hydrogen state changed from a weaker trapped site to a stronger one. The maximum reduction by hydrogen was about 20% of the overall increase, about 100 kJ/mol, in the dislocation energy during the kinking process. However, softening was not always the case in the kinking process. Hardening was expected when the transition was from a stronger to a weaker trapped site. When hydrogen binding energies were the same before and after kinking, hydrogen effects did not appear in kinking. The sideward motion of a kink pair is impeded when the kink pair meets hydrogen, thus inducing hardening. Itakura et al. conducted a density functional theory (DFT) calculation of the kinkpair nucleation enthalpy H k in bcc iron, using a line tension model of a curved dislocation with/without hydrogen [46]. Two types of the core configuration, stable and unstable, were assumed for a screw dislocation, and hydrogen atoms were placed at various interstitial T-sites near the core. The movement of a screw dislocation tolerates alternation of the two core configurations with the saddle point of the migration path close to the unstable configuration. The enthalpy of a curved dislocation incorporates the position energy of the core, the Peierls barrier, the contributions of external stress, and the interaction energy between the dislocation line and hydrogen atoms. A reduction in H k by hydrogen enhances the kink nucleation rate. The calculated H k was a function of applied stress, decreasing from 700 kJ/mol to zero as shear stress up to 1000 MPa was applied [46]. The reduction of H k by hydrogen was about 11 kJ/mol for all applied stress levels. The kink nucleation rate determined the velocity of a screw dislocation. For softening to occur, sufficient hydrogen trapping must occur at moving kinks. On the other hand, hydrogen trapping at a kink disturbs the kink movement. Itakura et al. imposed four conditions for hydrogen softening to occur [46]: (1) the upper limit of temperature, T U , for a sufficient hydrogen concentration, (2) the lower limit of the applied stress, σ L , to overcome kink trapping by hydrogen, (3) an upper limit of the applied stress, σ U1 , above which dislocation velocity is too

5.5 Elastic and Atomistic Calculations

119

Softening Region

Ndb = 2μm

Ndb = 0.2 μm

Yield Stress

Fig. 5.12 Region in the temperature-stress diagram where an increase in the screw dislocation velocity by solute hydrogen is possible. N d Dislocation length in unit of b. Calculation for 0.1 at. ppm of hydrogen and two dislocation lengths of 2.0 and 0.2 μm (Itakura et al. [46])

fast, and (4) an upper limit of the applied stress, σ U2 , above which the increasing velocity of a kink cancels kink trapping by hydrogen. Figure 5.12 shows a region in the temperature-stress diagram where the screw dislocation velocity increases by hydrogen in bcc iron for the bulk hydrogen concentration which is 0.1 at. ppm [46]. Values of σ U2 were calculated for two typical dislocation lengths denoted as N d in the unit of the Burgers vector b. The temperature ranges are almost consistent with observed flow stress behaviors in Sect. 5.2, while exact hydrogen concentrations are not definite. Section 3.2 describes the generation of vacancies associated with dragging jogs on screw dislocations and its enhancement by hydrogen. The velocity of jog under applied stress is a function of the sum of the formation and the migration energies of vacancies. Matsumoto et al. noticed that hydrogen effects on the two energies almost cancel, and the velocity of jogs is not affected by the presence of hydrogen [47]. Hydrogen effects on jog dragging increase the density of created vacancies by suppressing the diffusion of vacancies. Teheranchi et al. remarked on an indirect function of hydrogen on the flow stress in nickel, i.e., hydrogen effects on dislocation–solute interactions, instead of the double-kink nucleation mechanism [48]. The field of solute atoms interacts with dislocations, and hydrogen modifies the misfit strain tensor of the solute. Teheranchi et al. addressed the glide of an edge dislocation through randomly distributed solutes in a nickel matrix. Molecular dynamics simulations were conducted to estimate the flow stress for two systems with identical spatial distributions of either solutes or solute–hydrogen complexes. Simulations using vacancies as the solutes showed reduced (softening) glide stress when hydrogen is bound to vacancies.

120

5 Deformation Behaviors

However, calculations were for high vacancy and vacancy-hydrogen complex concentrations of the order of %. On the other hand, for carbon and sulfur atoms as solutes, their complexes with hydrogen have larger misfit strains, indicative of hydrogen-induced hardening rather than softening.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26.

27. 28. 29. 30. 31. 32. 33. 34. 35. 36.

H.A. Wriedt, R.A. Oriani, Scr. Metall. 8, 203–208 (1974) N.E. Paton, O. Buck, J.C. Williams, Scr. Metall. 9, 687–691 (1975) E. Lunarska, A. Zielinski, M. Smialowski, Acta Metall. 25, 305–308 (1977) S. Matsuyama, in Report of Studies on the Mechanism of Delayed Fracture (Iron and Steel Institute Japan, Tokyo, 1975), pp. 113–124 A. Goumelon, Mem. Sci. Rev. Mét. 72, 475–489 (1975) A. Kimura, H. Matsui, H. Kimura, Hydrogen in metals. Suppl. Trans. JIM 21, 541–544 (1980) M. Cornet, S. Talbot-Besnard, Hydrogen in metals. Suppl. Trans. JIM 21, 545–548 (1980) Y. Tobe, W.R. Tyson, Scr. Metall. 11, 849–852 (1977) I.M. Bernstein, Scr. Metall. 8, 343–350 (1974) S. Asano, Y. Nishino, M. Otsuka, J. Jpn. Inst. Metals 43, 241–248 (1979) S. Moriya, H. Matsui, H. Kimura, Mater. Sci. Eng. 40, 217–225 (1979) H. Matsui, H. Kimura, S. Moriya, Mater. Sci. Eng. 40, 207–216 (1979) H. Kimura, H. Matsui, A. Kimura, Hydrogen in metals. Suppl. Trans. JIM 21, 533–540 (1980) H. Matsui, H. Kimura, A. Kimura, Mater. Sci. Eng. 40, 227–234 (1979) H. Wada, S. Sakamoto, Hydrogen in metals. Suppl. Trans. JIM 21, 553–556 (1980) R.A. Oriani, P.H. Josephic, Metall. Trans. A 11A, 1809–1820 (1980) E. Lunarska, V. Novak, N. Zarubova, S. Kadeckova, Scr. Metall. 17, 705–710 (1983) C.G. Park, K.S. Shin, J. Nakagawa, M. Meshii, Scr. Metall. 14, 279–284 (1980) C.D. Beachem, Metall. Trans. 3, 437–451 (1972) E. Furubayashi, J. Phys. Soc. Jpn 27, 130–140 (1969) A.S. Keh, Phil. Mag. 12, 9–30 (1965) W.G. Johnston, J.J. Gilman, J. Appl. Phys. 30, 129–144 (1959) I. Gupta, J.C.M. Li, Metall. Trans. 1, 2323–2330 (1970) E. Lunarska, Scr. Metall. 11, 283–287 (1977) R.A. Oriani, P.H. Josephic, Acta Metall. 27, 997–1005 (1979) M. Nagumo, T. Tamaoki, T. Sugawara, in Hydrogen Effects on Materials Behavior and Corrosion Deformation Interactions, ed. by N.R. Moody, A.W. Thompson, R.E. Ricker, C.W. Was, K.H. Jones (TMS, Warrendale PA, 2003), pp. 999–1008 T. Fujita, T. Sakai, in Report of Studies on the Mechanism of Delayed Fracture (Iron and Steel Institute Japan, Tokyo, 1975), pp. 189–199 M. Nagumo, Y. Monden, in Report of Studies on the Mechanism of Delayed Fracture (Iron Steel Institute Japan, Tokyo, 1975), pp. 149–164 A.H. Cottrell, Dislocations and Plastic Flow in Crystals, Chap. 16 (Oxford University Press, London, 1956), pp. 195–215 A.H. Cottrell, Phil. Mag. Lett. 82, 65–70 (2002) R.A. Oriani, P.H. Josephic, Acta Metall. 29, 669–674 (1981) Z.R. Xu, R.B. McLellan, Acta Mater. 46, 4543–4547 (1998) R.W. Revie, H.H. Uhlig, Acta Metall. 22, 619–627 (1974) D.A. Jones, Metall. Trans. A 16A, 1133–1141 (1985) N.J. Petch, Phil. Mag. 1, 331–337 (1956) H.K. Birnbaum, C. Buckley, F. Zeides, E. Sirois, P. Rozenak, S. Spooner, J.S. Lin, J. Alloys Compounds 253–254, 260–264 (1997)

References 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47.

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T. Tabata, H.K. Birnbaum, Scr. Metall. 17, 947–950 (1983) H.K. Birnbaum, P. Sofronis, Mater. Sci. Eng. A176, 191–202 (1994) P.J. Ferreira, I.M. Robertson, H.K. Birnbaum, Acta Mater. 47, 2991–2998 (1999) I.M. Robertson, H.K. Birnbaum, Acta Metall. 34, 353–366 (1986) T. Tabata, H.K. Birnbaum, Scr. Metall. 18, 231–236 (1984) P. Sofronis, H.K. Birnbaum, J. Mech. Phys. Solids 43, 49–90 (1995) F.M. Mozzolai, H.K. Birnbaum, J. Phys. F: Met. Phys. 15, 507–523 (1985) J. Song, W.A. Curtin, Acta Mater. 68, 61–69 (2014) M. Wen, S. Fukuyama, K. Yokogawa, Acta Mater. 51, 1767–1773 (2003) M. Itakura, H. Kaburaki, M. Yamaguchi, T. Okita, Acta Mater. 61, 6857–6867 (2013) R. Matsumoto, N. Nishiguchi, S. Taketomi, N. Miyazaki, J. Soc. Mater. Sci. Jpn. 63, 182–187 (2014) 48. A. Tehranchi, B. Yin, W.A. Curtin, Phil. Mag. 97, 400–418 (2017)

Chapter 6

Macroscopic Manifestations of Hydrogen Embrittlement

Hydrogen embrittlement appears as cracking or premature fracture during service or mechanical testing, and environmental and testing conditions are crucial to the evolution. Blistering is induced under high hydrogen fugacity even without external stress, but degradation or eventual failure of structural steel components usually emerges under applied stress in mild environments. The function of hydrogen in the degradation is coupled with applied stress and plastic strain. This chapter presents primarily phenomenological manifestations of hydrogen effects in various mechanical tests of steels.

6.1 Tensile Tests 6.1.1 Effects of Test Conditions In tensile tests using bulky specimens, hydrogen degradation appears as premature fracture after or eventually before necking, the seemingly elastic region close to the yield stress, according to materials, hydrogen concentrations, and stress conditions. The degradation is expressed in terms of the fracture stress, the elongation to fracture, and the reduction in area.

6.1.1.1

Hydrogen Concentration

Two methods, concurrent with or prior to testing, are used to introduce hydrogen into specimens, and the resultant degradation is not the same according to the method. Figure 6.1 [1] shows stress–strain curves of the same steel hydrogen precharged to different concentrations. Varied hydrogen concentrations did not affect the flow stress, but an earlier fracture occurred in higher hydrogen concentrations. The steel (0.84C–0.19Si–0.76Mn in %) was a lower bainitic bar 3 mm in diameter, 1517 MPa in © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 M. Nagumo, Fundamentals of Hydrogen Embrittlement, https://doi.org/10.1007/978-981-99-0992-6_6

123

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6 Macroscopic Manifestations of Hydrogen Embrittlement

3h

2000

1h

0h

6h

Stress (MPa)

1500

1000

18h

24h

500

0 0

5

10

15

Strain, ε (%)

Fig. 6.1 Tensile stress–strain curve of a high-strength lower-bainitic steel with/without hydrogen precharging by immersion in 20% NH4 SCN solution at 323 K for various periods. Test at room temperature at a strain rate of 5 × 10–7 /s (Takai et al. [1]. Reprinted with permission from The Iron and Steel Institute Japan)

tensile strength. Hydrogen precharging was immersing specimens in a 20% aqueous solution of NH4 SCN at 323 K for various periods. The tensile tests were at room temperature with a strain rate of 5 × 10–7 /s. The hydrogen concentration increased with the immersion time to saturate at about 3 mass ppm after 10 h. Thermal desorption analysis (TDA) profiles of hydrogen exhibited a single desorption-rate peak at around 393 K, suggesting that hydrogen is weakly trapped in lattice defects as described in Sect. 2.1.2. In fact, hydrogen almost totally diffused out at room temperature in 800 h. Trapped states of hydrogen in materials alter the dependence of degradation on the hydrogen concentration. Strong and weak hydrogen trapping sites were prepared in the steel of the same compositions as Fig. 6.1 by isothermal transformation at 823 K to eutectoid structure, followed by cold-drawing to 85% reduction in area [1]. TDA profiles of hydrogen, precharged in the same way as for Fig. 6.1, exhibited two peaks at around 393 K (Peak#1 ) and 823 K (Peak#2 ), similar to Fig. 2.8. Specimens that contain only Peak#2 hydrogen were prepared by annealing the cold-drawn and hydrogen-charged specimens at 473 K. Hydrogen composing Peak#2 is strongly trapped and non-diffusive even at 473 K. Figure 6.2(a) shows the relative reduction of area at tensile tests of specimens containing both Peak#1 and Peak#2 and only Peak#2 [2]. The reference specimens were without hydrogen precharging, and Fig. 6.2(a) shows that hydrogen composing Peak#2 is immune to the degradation, implying that the total hydrogen content does not serve as a parameter for the degradation of tensile properties. Figure 6.2(b) shows the increase in tracer hydrogen C H , i.e., hydrogen introduced as a tracer of lattice defects, described in Sect. 3.1.1.3 concerning Fig. 3.2. The hydrogen effect enhancing the strain-induced generation of defects is expressed by

1.22

125

5

Peak 2#2H (a) Peak

(b)

4

1.00 0.88 0.66 #1+Peak#2 Peak Peak 1H

0.44

ΔCH (wt ppm)

RA Ratio (with H / without H)

6.1 Tensile Tests

3

#1+Peak 1 H #2 PeakPeak

2 1

#2 2 H Peak Peak

0

0.22

0

1 2 3 Hydrogen content (wt ppm)

-1

1 0 2 3 Hydrogen content (wt ppm)

Fig. 6.2 (a) Relative reduction of area (RA) and (b) ΔC H as a function of the strain rate at 323 K of specimens containing (Peak#1 + Peak#2 ) and only Peak#2 . Peak#1 and Peak#2 hydrogen are 1.9 and 2.6 mass ppm, respectively (Doshida et al. [2])

ΔC H , defined as the difference in tracer-hydrogen between specimens strained to 0.08 with and without hydrogen. ΔC H was almost null in specimens showing only Peak#2 hydrogen. It again implies that hydrogen composing Peak#2 does not enhance the strain-induced generation of lattice defects.

6.1.1.2

Temperature and Strain Rate

Strain-rate and testing temperature dependencies characterize the susceptibility to hydrogen embrittlement of steel in tensile tests. Figure 6.3 [3] schematically illustrates the dependencies of fracture strain in terms of the reduction in area at fracture for mild steel. The degradation is the most prominent at around room temperature and with decreasing strain rates. A common understanding of the origin is the buildup rate of local hydrogen concentration through diffusion. However, studies on the origin using TDA gave information on the states of hydrogen in materials [2]. As shown in Fig. 2.8 and the preceding section, hydrogen introduced into colddrawn eutectoid steel bars exhibited two thermal desorption-rate peaks, Peak#1 and Peak#2 . Tensile test results for the two series of specimens, one containing both Peak#1 and Peak#2 and the other containing only Peak#2 , are shown in Fig. 6.4(a) for various strain rates [2]. The ordinate denotes the ratio of the reduction in area at tensile tests of steels with and without hydrogen precharging. Hydrogen degradation and a strong strain-rate dependence of tensile ductility appeared for specimens containing Peak#1 hydrogen, while specimens containing only Peak#2 were almost immune. The amounts of lattice defects newly created during tensile straining were evaluated in terms of the amount of tracer-hydrogen introduced after tensile straining. Similar to Figs. 6.2(b), 6.4(b) [2] shows ΔC H for [Peak#1 + Peak#2 ] and only

126

6 Macroscopic Manifestations of Hydrogen Embrittlement

(a) Uncharged

(b) Charged

Fig. 6.3 Schematic diagram for effects of strain rate and temperature on tensile properties of mild steel with and without hydrogen (Bernstein [3]. Reprinted with permission from TMS)

1.2

5

2 ]H [Peak Peak #2

(a)

(b) 4

0.8

0.6 [ Peak

#1 + Peak Peak 1 H#2 ]

Δ C H (mass ppm)

Relative Reduction in Area (with H/-without H)

1.0

0.4

0.2 -6 10

3

#1 + Peak #2 ] [ PeakPeak 1H

2 1

2 ]H [Peak Peak #2

0

10 -5

10 -4 10 -3 Strain Rate(s

10 -2 -1 )

10 -1

-1 10 -6

10 -5

10 -4 10 -3 10 -2 Strain Rate(s -1 )

10 -1

Fig. 6.4 Strain-rate dependencies of (a) relative reduction in area at tensile tests for specimens containing [Peak#1 + Peak#2 ] hydrogen and only [Peak#2 ] hydrogen, (b) difference of Peak#1 hydrogen, ΔC H , between specimens strained to 0.08 with and without hydrogen for [Peak#1 + Peak#2 ] and [Peak#2 ] series (Doshida et al. [2])

[Peak#2 ] specimens at different strain rates. The ΔC H for the [Peak#1 + Peak#2 ] series increased at lower strain rates, but it was immune to strain rates for the [Peak#2 ] series. The results correspond well to the degradation of tensile ductility shown in Fig. 6.4(a). Hydrogen effects are relevant to the enhanced creation of strain-induced defects composing Peak#1 , and the strain-rate dependence of degradation is associated with the amount of strain-induced defects. The strain-rate dependence is also shown in Figs. 7.23 and 7.24 in Sect. 7.4.2 for the effects of cyclic prestressing.

6.1 Tensile Tests

127

Similar experiments were conducted for the temperature dependence of tensile ductility. The hydrogen-enhanced loss of ductility appeared significantly with increasing test temperatures from 223 to 348 K for specimens containing Peak#1 hydrogen, while the ductility of specimens containing only Peak#2 was almost immune to hydrogen. The temperature range in which the increase in ΔC H appeared for the [Peak#1 + Peak#2 ] series was coincident with that for the loss of ductility. The vacancy-type entity of lattice defects relevant to the strain-induced increase in Peak#1 hydrogen is described with Figs. 3.10–3.12 in Sect. 3.2.3.2 about low-temperature thermal desorption spectroscopy. Positron annihilation spectroscopy was further successfully applied to discriminate lattice defects involved in the strain-rate effect [4, 5]. Positron lifetime in tensile-strained pure iron exhibited a long lifetime component exceeding 250 ps when hydrogen was precharged. The component corresponded to vacancy clusters, and its relative intensity increased with decreasing strain rates in accord with the behavior of ΔC H . It is a complementary and more direct support for the notion that the strain-rate dependence of the susceptibility to hydrogen embrittlement is closely related to the strain-induced creation of vacancies and their clusters.

6.1.2 Damage Generation During Straining Discussion on the function of hydrogen in embrittlement has addressed mostly the crack initiation and growth in the late stages of deformation. However, hydrogen in the final deformation stage is not necessarily required for the embrittlement to appear, as demonstrated for iron and Inconel 625 alloy [6]. The experiments were organized to interpose unloading and reloading during tensile tests of hydrogen-precharged specimens, as schematically shown in Fig. 6.5 [6]. Unloading was applied during straining at about half or close to the fracture strain for iron or Inconel 625 alloy, respectively, and degassing at 303 K or annealing at 573 K was conducted at the unloaded stage. Figure 6.6 [6] shows tensile curves of Inconel 625 subjected to the unloading and subsequent reloading, shown in Fig. 6.5. Hydrogen precharging, (b), substantially degraded tensile properties, and the interposed unloading did not affect the degradation of the hydrogen-charged specimen when reloaded immediately. (c) Removing hydrogen at the unloaded stage remained a substantial degradation despite the absence of hydrogen in the later stage. (d) On the other hand, annealing at 473 K completely recovered degradation. The result demonstrates that embrittlement is due to the strain-induced creation of vacancies enhanced by hydrogen preceding the crack initiation and growth, i.e., the HESIV mechanism described in Sect. 3.2.3.2. The effect of annealing at 473 K also rules out the degrading function of hydrogen via activating dislocations. A matter of concern in tensile testing is the onset of necking, i.e., plastic instability during straining. Figure 6.7(a) [7] is an example of tensile stress–strain curves of Type 304 and Type 316L austenitic stainless steel at room temperature with and without

128

6 Macroscopic Manifestations of Hydrogen Embrittlement

(b)

(c), (d)

Stress

(a)

Held at 30ºC or 200ºC

Strain

Strain Hydrogen Precharge

Hydrogen Precharge

Strain

Fig. 6.5 Procedures of interposed unloading and reloading during tensile test. (a) Immediate reloading after unloading without hydrogen precharging. (b) Hydrogen precharged and immediate reloading after unloading. (c) Hydrogen precharged and aged at 30 °C (303 K) or (d) at 200 °C (473 K) after unloading (Takai et al. [6])

60 (d) Aged at 200ºC and reloaded 50

Stress (MPa)

Fig. 6.6 Stress–strain curves of Inconel 625 at tensile tests with interposed unloading shown in Fig. 6.5 (Takai et al. [6])

(a) Without hydrogen

40 30

(c) Aged at 30ºC and reloaded

20 (b) Hydrogen precharged, immediate reloading after unloading

10 0

0

0.1

0.2

0.3 Strain

0.4

0.5

hydrogen precharging. Hydrogen was uniformly precharged in 10 MPa hydrogen gas at 673 K to about 35 mass ppm. Hydrogen degradation appeared in Type 304 steel, and the onset of fracture was apparently discontinuous in the uniform elongation stage. It was like the onset of brittle fracture triggered by the nucleation of an incipient crack. However, a careful examination of the stress–strain curve revealed a rather continuous load drop, as shown in Fig. 6.7(b). Since the strain rate was as low as 8.3 × 10–4 /s, an elongation of 0.5% spent about 1 min. The finding suggests that hydrogen promoted the onset of plastic instability. Still, the diffusion of hydrogen is not likely

6.2 Fracture Mechanics Tests

129

660

900 800 Flow Stress ,MPa

700

( b) SUS 304

600 SUS 316L

500 400

10MPaH Vacuum

300 200

2

Flow Stress ,MPa

(a) 650

SUS 304

640

630

100 620

0 0

10 20 30 40 50 60 70 Elon gation Elongation ,% (%)

21.5

22.0

22.5

Elon gation , (% Elongation %)

Fig. 6.7 (a) Stress–strain curves of Type 304 and Type 316L stainless steels with/without hydrogen precharging. (b) A magnified view of the curve near the load drop of hydrogen-charged Type 304 (Hatano et al. [7])

the cause of the instability since diffusion of hydrogen in austenitic stainless steels is almost negligible during the test at room temperature. The mechanism of the early onset of plastic instability is not definite, but the decrease in stress-carrying capacity due to increasing lattice disorder is feasible. Related descriptions of the event are in Sect. 7.3.3 about plastic instability and in Sect. 8.3.4 (b) about strain localization.

6.2 Fracture Mechanics Tests The fracture toughness of materials is evaluated by various test methods using notched or precracked specimens. Charpy impact tests are not appropriate for assessing hydrogen embrittlement because of involved high strain rates. Fracture toughness is expressed in terms of various quantities such as stress intensity factor (K), crack-opening displacement (COD), and J-integral [8, 9]. The macroscopic crack initiates at the notch root or the precrack tip. The initiation and slow growth rates of cracks are schematically shown in Fig. 6.8 as a function of applied K. Below a threshold stress intensity K TH , crack growth is negligible, and K TH is usually denoted as K ISCC for stress corrosion cracking under plane strain conditions. Crack growth rates generally exhibit three stages. The growth rate in Stage II is much lower than in Stage I or insensitive to K. Stage III corresponds to the final fracture when K reaches the fracture toughness K c of the material. K increases with the crack growth under sustained-load testing at constant applied stress. On the other hand, in constant displacement loading using wedge-opening load (WOL) compact tension (CT) specimen, K decreases with the crack growth. Another threshold stress intensity is K th

130

6 Macroscopic Manifestations of Hydrogen Embrittlement

Fig. 6.8 Schematic diagram of three stages of slow crack growth rates with increasing stress intensity

Log da/dt

III

II

I

K

TH

Stress Intensity K

for crack arrest, the value at which the crack growth ceases. Fracture mechanics tests usually employ bulky specimens, and the inhomogeneous distribution of hydrogen makes difficult the exact estimation of the hydrogen concentration at active sites for fracture in the specimen.

6.2.1 Crack Initiation 6.2.1.1

Stress Intensity Factor Approach

The initiation and growth of a crack are detected using fatigue-precracked WOL, CT, and double cantilever beam (DCB) specimens under controlled environments [10–14]. Data of K TH in hydrogen gas were compiled by Moody and Robinson, as shown in Fig. 6.9 [15] for AISI steel of different yield strengths. The K TH values strongly depend on the yield strength and decrease to some limiting values with elevated hydrogen gas pressure. An observed relationship between K TH and PH2 at room temperature for AISI 4340 steel of 1240 MPa in yield strength was [10]. K TH = 151 − 60 log PH2 (15 < PH2 < 115),

(6.1)

where the unit of PH2 was 6.89 kPa (= 10–3 ksi) and the unit of K TH was 1.1 MPa · m1/2 (= 1ksi · in1/2 ). However, a lower limit existed for K TH at high hydrogen gas pressures above 690 kPa. The pressure dependence of K TH is strongly dependent on the yield stress of steel, and the dependence is also sensitive to the K TH ’s magnitude.

6.2 Fracture Mechanics Tests

131

100

586-779 MPa 1240 MPa

KTH (MPa m1/2)

80

1070 MPa

60 1330-1350 MPa

40

1238 MPa 869-1055 MPa

1720 MPa 20

0 10-5

10-4

1 10 10-1 10-3 10-2 Hydrogen Pressure (MPa)

102

103

Fig. 6.9 Effects of hydrogen pressure on the threshold stress intensity K TH for crack initiation for AISI 4340 steel of various yield strengths (in MPa) (Moody et al. [15])

K TH increases with rising temperature [10, 15]. Low K TH values at room temperature are similar to Fig. 6.3 for tensile ductility. The dependence differs by steel and the magnitudes of K TH . An Arrhenius relationship that indicates a thermally activated process for the same steel as used for Eq. (6.1) in 551 kPa hydrogen was [10], ) ( 1471 K TH = 3631 exp − T 298 < T (K ) < 480),

(6.2)

where the unit of K TH was 1.1 MPa · m1/2 . K TH decreases with the increasing strength of steel at a given hydrogen gas pressure. The yield strengths of the steel, shown in Fig. 6.9, were controlled through microstructural alterations by varying tempering temperatures. Microplasticity at the crack front should play a role in the degradation, but the intrinsic factor or microscopic process that controls such dependencies is not simple. Takeda and McMahon determined K TH or K ISCC values in modified WOL tests from the stationary load value that was reached after decreasing with time from a load drop on step loading [16]. In measurements for a 5% Ni HY 130 steel in hydrogen gas, Takeda et al. noticed that a subtle crack initiation occurred along the periphery of plastic hinge or slip lines well below the detectable K TH on loading [16]. Takeda et al. discussed concerns of impurity segregation in grain boundaries, and related descriptions concerning impurity effects are in Sects. 7.2.4 and 8.1.4 (a).

132

6.2.1.2

6 Macroscopic Manifestations of Hydrogen Embrittlement

J-Integral Approach

The validity of the stress intensity factor as a parameter of the stress and strain fields in front of the crack has limitations when crack-tip plasticity extends. COD and J-integral are then employed to properly evaluate fracture toughness for medium strength steels. The J-integral is a path-independent integral along an arbitrary counterclockwise path ⎡ around the crack tip, and it is defined as ∫ ( J=

⎡

) ∂ ui wdy − Ti ds , ∂x

(6.3)

where w is the strain energy density, T i is the i-th component of the traction vector, ui is the i-th component of the displacement vector, and ds is the length increment along the contour ⎡. J-integral is a measure of the energy dissipated per unit length of crack tip for per unit distance of the crack advance. J-integral is experimentally obtained from the specimen geometries and the load versus load-point displacement curve area. The J-integral value at the onset of stable crack growth, J TC , is determined as the intersection of the crack blunting line with the J versus Δa curve. J TC is denoted as J IC for pure mode I loading, as shown in Fig. 6.10 [17]. In many practical situations, multiple loading modes superpose, and mode III loading causes localized shear ahead of the crack tip. An empirical correlation was proposed to relate the mixed-mode fracture toughness with the process zone size [18]. Hydrogen effects on mixed mode I/III fracture toughness were examined for highpurity Ni–Cr–Mo–V steel of tempered lower bainitic structure and 855 MPa tensile strength [17]. Hydrogen was precharged in a 13.8 MPa hydrogen gas environment at 373 K to a hydrogen concentration of 2 at. ppm, equivalent to a hydrogen fugacity of 1.26 GPa at room temperature. In order to adjust the shear stress component, Fig. 6.10 Typical mode I J-resistant curve for a pure mode I test (Gordon et al. [17])

JI.exc 0J

JIC Blunting Line Exclusion Lines

0

0.15

1.5 Crack Extension Δa (mm)

6.2 Fracture Mechanics Tests

133

Fig. 6.11 A plot of J TC versus tilting angle ϕ showing J TC decreasing with increasing mode III loading (Gordon et al. [17])

CT specimens with a slant notch of varied angle ϕ were used. Figure 6.11 [17] shows that the increasing mode III component, i.e., increasing ϕ, decreases J TC in both hydrogen-charged and uncharged conditions and that hydrogen additionally enhances the degradation by about 30%. The fracture surface exhibited smaller and more uniform dimples associated with increasing the mode III loading component. The findings imply that plasticity plays a role in crack initiation and that hydrogen is incorporated in the degradation through plasticity. The mechanistic explanation of the finding is described in Sect. 10.4 concerning the autocatalytic void formation model for the mechanism of HE. Experimental determination of the crack initiation from the precrack is often not precise in medium-strength steel. A method for detecting the onset of stable crack growth from the precrack tip was devised [19] by recording the progress of cracktip opening displacement δ, according to the theory by Needleman and Tvergaard [20] described in Sect. 10.1.2.1. The onset of the stable crack growth expects a discontinuous increase in δ, accompanying a jog to appear on the δ versus J-integral curve. However, the jog will be too small to be directly detected. Alternatively, the gradient of the curve is more sensitive to the appearance of a jog, as schematically shown in Fig. 6.12. The method was applied to a three-point bending test of notched specimens of low-carbon steel of 450 MPa tensile strength. The result is shown in Fig. 6.13(a) [21], in which the yield strength σ y normalizes J-integral. The maximum on the δ/(J/σ y ) versus J/σ y curve corresponds to the evolution of a jog on the δ versus J/σ y curve. A simultaneous measurement of electric resistance across the ligament in front of the precrack confirmed the crack initiation, as also shown in the figure. The crack initiation points detected by the two methods were entirely consistent. The result

6 Macroscopic Manifestations of Hydrogen Embrittlement

δ

134

“Jog”

J / σy Fig. 6.12 Schematic illustration of the appearance of a “jog” on crack opening displacement δ versus J-integral normalized by yield stress

well reproduced a previous result for low-carbon low-alloyed steel of 600 MPa in tensile strength [19].

(a)

Initiation Initiation

δ/ (J/σ y s) y ) δ/(J/σ

5.5 0.435

55 4.5 0.43 0.43

44 3.5

0.425

88 0.39 0.39

2.5

0.3 0.3

0.4 0.5 0.6 0.4 0.5 0.6 J/σy (mm)

0.7 0.7

77 66 55 44

0.36 0.36

33 Initiation Initiation

33 0.42 0.42 0.2 0.2

99

0.33 0.33 0.2 0.2

Potential Difference (μV)

66

10 10

(b)

6.5

Potential Difference (μV)

0.44 0.44

0.42 0.42

77

δ/(J/σ y )

0.445

22 1

0.3 0.4 0.5 0.3 0.4 0.5 J/σy (mm)

0.6 0.6

0.7 0.7

Fig. 6.13 Ratio of crack opening displacement, δ, to J/σ y versus increasing J/σ y at a three-point bending test of notched specimen of a low-carbon steel. Concurrently observed electric potential drop across the notch is also shown. (a) Without and (b) with hydrogen precharging (Shimomura et al. [21])

6.2 Fracture Mechanics Tests

135

Subsequently, the above method was applied to hydrogen effects on crack initiation. The same steel used for Fig. 6.13(a) was hydrogen precharged to 0.82 mass ppm under a relatively mild fugacity, using cathodic electrolysis in an aqueous solution of 3% NaCl + 3 g/l NH4 SCN at a current density of 5 A/m2 for 24 h. A promoted crack initiation by hydrogen was revealed using the electric resistance method, as shown in Fig. 6.13(b), but δ/(J/σ y ) increased continuously with J/σ y without showing a maximum. It implies that the opening of the precrack proceeds gradually without a large step-wise advance. The theory by Needleman and Tvergaard [20], in Sect. 10.1.2.1, assumed that a discontinuous advance of the crack at a critical amount of void volume fraction is caused by the loss of stress-carrying capacity in the area adjacent to the crack. The observed gradual growth suggests that hydrogen, coupled with strain-induced defects, progressively reduces the stress-carrying capacity.

6.2.2 Crack Growth 6.2.2.1

Growth Rate—Gaseous Hydrogen Environment

The crack growth rate is directly measured [12, 13] or is calculated from the time record of the compliance of the specimen [10, 14]. Crack growth kinetics varies with the strength level, hydrogen concentration, and temperature. Crack growth rate is important for kinetics of hydrogen embrittlement, and it has been examined mostly for Stage II in the three stages shown in Fig. 6.8. The steady crack growth rate at Stage II is little affected by the magnitude of stress intensity and is likely rate-controlled by some factors other than the mechanical driving force. The temperature dependence of the crack growth rate gives information on the controlling process. Temperature dependencies of the growth rate of AISI 4130 steel in 98 kPa hydrogen gas and at applied stress of 39 MPa m1/2 are opposite in sign according to temperature regions as shown in Fig. 6.14 [22]. Activation energies obtained from each Arrhenius relationship were 16 and − 23 kJ/mol in Region 3 and Region 1, respectively. Similar opposite temperature dependence of Stage II crack growth rate was observed in 133 kPa dry hydrogen gas for AISI 4340 steel of 2082 MPa in tensile strength [12]. The activation energy of the Stage II crack growth in Region 3 was 14.7 kJ/mol, close to 16 kJ/mol for AISI 4130 steel. The crack growth in dry hydrogen gas proceeds with the adsorption and following migration of hydrogen on the specimen surface. Williams and Nelson ascribed the rate-controlling process of the crack growth to the adsorption of hydrogen on the steel surface, taking into account the fractional coverage of initial adsorption sites [22]. Simmons et al. noticed that fractographic features at tests in hydrogen gas and water are similar and deduced that surface reactions of water with steel controlled the crack growth rate in water [12]. The temperature dependence of Stage II crack growth rate varies by microstructures. For experiments with 18Ni maraging steel, tensile strength levels were controlled to 1330 MPa and 1720 MPa by tempering at 473 K and 523 K, respectively

136

6 Macroscopic Manifestations of Hydrogen Embrittlement

Fig. 6.14 Temperature dependence of the crack growth rate for AISI 4130 steel in low-pressure hydrogen gas (Williams et al. [22])

[23]. The temperature dependence of Stage II crack growth rate in dry hydrogen was similar to Fig. 6.14, but the slope in Region 1 was very steep. The transition from Region 1 to Region 3 in 133 kPa hydrogen gas occurred at about 293 K and 253 K for steels tempered at 523 K and 473 K, respectively. The crack growth rate magnitudes at the transition temperature were also substantially different between the two steels, about 5 × 10–5 m/s and 5 × 10–6 m/s for tempering at 523 √ K and at 473 K, respectively. The crack growth rate increased proportionately to PH2 in Region 3 with the activation energy of 18.4 kJ/mol, irrespective of tempering temperatures and hydrogen gas pressures. Gangloff and Wei suggested that some reactions in a near-surface region operated associated with hydrogen transport by diffusion, but the process controlling Region 1 was not definite [23]. Vehoff and Rothe found that the crack-tip opening angle (CTOA) α is constant during the stable crack growth at tensile loading of notched Fe-2.6%Si single crystals in low-pressure hydrogen gas [24]. The value of α characterizes ductility accompanying crack growth. The fracture surface showed a fine mixture of plastic shearing off and cleavage-like facets on a scale of 0.1 μm or less. The value of α was a function of temperature, hydrogen pressure or activities, and crack growth rate. The temperature dependence of α in the intermediate temperature range, 293 K < T < 390 K, showed an Arrhenius-type relation with an apparent activation energy of 49 kJ/mol. Vehoff and Rothe deduced that isolated microcracks initiated along the crack front. Related to embrittlement, Vehoff and Rothe also deduced the fractional hydrogen coverage of special sites, right at the tip of a stressed crack, with the binding energy of 49 kJ/mol [24].

6.2 Fracture Mechanics Tests

137

Low cycle fatigue of nickel single crystals showed similar results in electrolytes at different cathodic potentials. The fracture mode was a mixture of alternate slip and local brittle fracture [25]. The apparent binding energy obtained from the temperature dependence of CTOA was 32 kJ/mol.

6.2.2.2

Crack Growth Rate—Internal Hydrogen

The crack growth in gaseous hydrogen likely involves surface reactions, but internal hydrogen effects have also been considered. Three stages of the crack growth rate of the type, shown in Fig. 6.8 appeared at sustained-loading tests of hydrogen precharged AISI 4340 steel [13, 26]. Hydrogen precharging was by cathodic electrolysis in a poisoned 5% H2 SO4 aqueous solution at a current density of 20 A/m2 , and hydrogen was enclosed within the specimens by cadmium plating [26]. The crack growth in hydrogen-precharged specimens exhibited an incubation time and a transient stage before establishing the steady-state Stage II. The growth rate at room temperature was at least one order of magnitude faster for specimens of 1620 MPa yield strength tempered at 503 K than for 1340 MPa specimens tempered at 723 K. Stage II crack growth rates also depended on temperature with Arrhenius relations. A theoretical model for the crack growth rate assumed the build-up of local hydrogen concentration to a critical value in the crack tip region by diffusion, triggering fracture there and inducing the crack advance [26]. Using numerical values of parameters obtained from the literature, experiments, and adjusting as a variable, the calculated crack growth rates fitted pretty well with the observed temperature dependence for 503 K tempering. The estimated binding energies of hydrogen with the critical trap sites for the crack initiation were 75 kJ/mol and 27 kJ/mol for 503 K and 723 K tempering, respectively. Fractographic features were mixtures of inter-granular (IG) and quasi-cleavage (QC) for specimens tempered at 503 K. For tempering at 723 K, alternate IG and MVC regions were assigned to intermittent slow and fast crack growth. Details of fractographic features are described in Sect. 7.2.4. In the model proposed by Gerberich et al. [26], crucial assumptions are (1) the fracture stress decreasing in proportion to hydrogen concentration and (2) high local hydrogen concentrations due to both the dilatational stress field and trap-binding effects. The plastic constraint was also considered for computing the triaxial stress at the critical site. The critical trap sites to cause sequential fracture were assigned from fractographic observations to martensite lath boundaries intersecting the prior austenite grain boundaries for 503 K tempering and to oxysulfides located at the edge of plastic zone for tempering at 723 K. However, the critical hydrogen concentrations that the model estimated at the trap sites were very high, more than 106 times of hydrogen in solution. The crack growth is further described in Sect. 8.1.1 about changes of fractographic features and Sect. 9.3.2 about the mechanism.

138

6.2.2.3

6 Macroscopic Manifestations of Hydrogen Embrittlement

Crack Growth Resistance

The J-integral is a measure of energy dissipation associated with crack advance, and the crack growth resistance curve (R-curve) is the plot of J value versus crack extension (Δa) in slow stable crack growth. The R-curve reflects internal changes causing the energy dissipation during the crack advance. A previous study for low-carbon ferrite–pearlite steel demonstrated a noticeable decline in the R-curve by increased strain-induced lattice defects, presumably vacancies [27]. In the experiment, lattice defects were detected using thermal desorption analysis (TDA) of hydrogen introduced as a tracer of lattice defects, described in Sect. 3.1.1.3. A simulation of the R-curve using a constitutive relation for porous material and a finite element method (FEM) calculation showed that an enhanced void generation reduces the crack growth resistance [28]. The simulation method was applied to the effect of hydrogen on the Rcurve. Figure 6.15 [29] compares R-curves of notched specimens of low-carbon ferrite–pearlite steel subjected to three-point bending tests with and without hydrogen precharging. Hydrogen charging was conducted in a mild condition by cathodic electrolysis in a 3% NaCl + 3 g/l NH4 SCN aqueous solution at a current density of 5 A/m2 for 24 h. A substantial decrease in the crack growth resistance appeared in hydrogencharged specimens. The Δ and ▲ marks in the figure denote specimens without and with hydrogen precharging, respectively, and J-integral values are calculated from the stress and strain fields near the crack. In the simulation, the volume fractions of the void nucleating particle, f N , were adjusted from experimentally determined 2% for the hydrogen-free material to 3.5% for the hydrogen-charged material, to make a good fit to the observed R-curves. f N for the hydrogen-free specimen was for a specimen given plastic strain just before the maximum stress. Accordingly, the decrease in the J-integral by hydrogen was ascribed to an increase in nucleation void 450 450

Uncharged Non-Charged Volume Fraction of Void void volume fraction=2% Nucleation Particles: 2%

400 400

350 350 ( N/mm) J-integral, J -integral (N/mm)

Fig. 6.15 R-curves of low-carbon ferrite–pearlite steel with and without hydrogen precharging. ◯, ●: Observed values, Δ, ▲: Calculated values using a finite element method (Nagumo et al. [29])

300 300 250 250 200 200

150 150 100 100

H-Uncharged Hydrogen-Charged Volume Fraction of Void void volume fraction=3.5% Nucleation Particles: 3.5%

50 50

0 0 00

20 20

40 40

60 60

80 100 100 120 140 160 180 200 80 120 140 160 180 200

Stable Crack (μm) ⊿a(μm) Stable CrackLength Length,Δa

6.3 Fatigue

139

densities. Details of the modeling method for the R-curve in Fig. 6.15 are described in Sect. 10.1.2.3. Effects of hydrogen on R-curve were also shown for disk-shaped compact tension specimens of 21Cr–6Ni–9Mn austenitic stainless steel [30]. Hydrogen was thermally precharged to 210–230 mass ppm in high-pressure hydrogen gas. The fracture initiation toughness J Q was defined as the J value at the intersection of the 0.2 mm offset blunting line with the R-curve. Alternatively, initial damage at the precracktip was detected as a subtle deviation from the linearity of the COD versus crack length measurement using the direct current potential difference according to ASTM E1737. The deviation point was denoted as J i and J Q according to the choice of the initial blunting line. Hydrogen reduced J i and J Q by more than 80% of the values for hydrogen-free specimens. Crack growth resistance denoted by dJ/da also decreased nearly 50% by hydrogen. Nibur et al. carefully examined deformation microstructures exhibiting enhanced strain localization and deduced that any mechanism that hydrogen directly lowers fracture resistance was not feasible [30]. Surface morphologies of strain localization are described in Sec. 7.4.1.1. The R-curve is strongly dependent on the microstructures of steels. For ferrite– pearlite steels, carbides precipitated along grain boundaries act as barriers against slip extension across grain boundaries and affect R-curves prominently [27]. The functions of the slip constraint in R-curve are described in Sect. 10.1.2.3, concerning the strain-induced creation of vacancies.

6.3 Fatigue Fatigue failure is the most common failure of metallic structural components in practical services. Not only in high-pressure hydrogen gas environments, but hydrogen also comes from humid or corrosive environments, during cathodic protection of off-shore structures, or at electroplating. Hydrogen produced by corrosion reactions on the metal surface is often a cause of corrosion fatigue failure. Fatigue properties of materials are commonly expressed in terms of fatigue life and fatigue limit, determined by plotting the stress amplitude versus the number of cycles to failure (S–N curve). The fatigue limit Δσ c and the threshold stress intensity range for no detectable crack growth ΔK th are design parameters for the safety against fatigue failure [31]. Fatigue failure proceeds through the crack nucleation and growth. Measurements of fatigue-crack growth in laboratories are conducted commonly using notched specimens. Fatigue tests consume a substantial time for one run, and hydrogen contents in specimens are often not constant during a test-run due to the entry and loss of hydrogen and/or internal changes of materials. Fatigue failure is affected by many factors; their effects are not similar among different expressions of fatigue properties. Gerberich reviewed early works for hydrogen effects on metal fatigue concerning different approaches such as total life, crack threshold, and growth [32].

140

6 Macroscopic Manifestations of Hydrogen Embrittlement

6.3.1 Fatigue Limit Hydrogen generally reduces fatigue life and fatigue limit. Figure 6.16 [33] plots tension–compression fatigue test data of two lots of surface-hardened 0.36C–Cr– Mo martensitic steel with/without hydrogen. Hydrogen was initially charged by immersing specimens in a 20% NH4 SCN aqueous solution at 323 K, and hydrogen contents were controlled to 10, 0.8, and 0.3 mass ppm by partial degassing at room temperature. Fatigue specimens contained a small hole of 100 μm in diameter and depth on the specimen surface as the crack starter. Fatigue tests were conducted at a stress ratio R (= σ min /σ max ) of −1 and with different frequencies up to 1000 Hz. Hydrogen was recharged to specimens every 8 × 106 fatigue cycles to keep the same content during the test. The control of hydrogen content was by partial degassing, and the reductions in fatigue life and fatigue limit by hydrogen were reversible against the entry of hydrogen. A small amount, ~ 0.3 mass ppm, of hydrogen existed in asheat-treated specimens, and thermal desorption analysis (TDA) showed a small peak at 573 K, indicating a strongly trapped non-diffusive nature of residual hydrogen as described in Sect. 2.1.2. On the other hand, artificially charged hydrogen diffused out at room temperature, and the thermal desorption ceased by 573 K. The observations imply that diffusive hydrogen causes degradation. Murakami et al. revealed the fatigue-crack initiation from non-metallic inclusions [33]. Non-metallic inclusions are viable trap sites of non-diffusive hydrogen, but non-diffusive hydrogen is generally immune to degradation. Alternatively, diffusive hydrogen might interact with non-metallic inclusions

Stress Amplitude, σ (MPa)

1000

500

0

103

104 106 107 105 108 Number of Cycles to Failure, Nf

109

Fig. 6.16 Effects of hydrogen on S–N diagram of two lots of SCN 435 steel. Open marks: as-heattreated (0.3 ppm H), solid marks: H-charged. Initial hydrogen contents are controlled by partially degassing at room temperature after hydrogen charging: ● (10 ppm), ∎ (100 h after hydrogen charging, 0.8 ppm), ˛ (4300 h after hydrogen charging, 0.3 ppm) (Murakami et al. [33])

6.3 Fatigue

non-charged pre-charged

Stress Amplitude σ (MPa)

Fig. 6.17 S–N diagrams at rotational bending fatigue for a Si–Cr martensitic steel with and without hydrogen precharging. The arrows indicate no failure (Nagumo et al. [34])

141

650

600

550

500 104

106 105 107 Number of Cycles to Failure

and/or with plastic deformation around inclusions, but changes of trapped states during fatigue cycles were not examined. Hydrogen effects of decreasing fatigue life and fatigue limit at rotational bending tests are shown in Fig. 6.17 [34] for un-notched round bar specimens. The steel was a high-strength Si–Cr martensitic steel hydrogen-precharged under a fairly mild condition by cathodic electrolysis in a 3% NaCl + 3gl−1 NH4 SCN aqueous solution at a current density of 7.5 A/m2 . By analogy with the hydrogen effects on tensile tests, described in Sect. 6.1.2, lattice defects produced during fatigue were detected by introducing hydrogen as the tracer of defects into fatigued specimens after removing precharged hydrogen at room temperature. TDA of tracer-hydrogen exhibited a single peak at about 393 K, indicating weakly trapped states. The amounts of the tracer-hydrogen in fatigue-fractured specimens at two applied stress levels are shown in Fig. 6.18 [34]. The stress amplitude of 580 MPa was close to the fatigue limit. The amounts of the tracer-hydrogen were more significant in hydrogen-precharged specimens than in uncharged ones despite shorter fatigue cycles for hydrogen-precharged specimens. The results suggest that the promoted failure by hydrogen is due to the enhanced creation of defects during fatigue cycles. Vacancy-type nature of defects created during fatigue cycles is described in Sect. 7.4.1.2. In a high pressure, 115 MPa hydrogen gas environment, the fatigue limits of both martensitic (671 and 824 MPa in the proof and tensile strength, respectively) and ferrite–pearlite (360 and 537 MPa in the proof and tensile strength, respectively) steels showed almost no detrimental hydrogen effects [35, 36]. The fatigue tests were tension–compression at 1 Hz and a stress ratio of −1, using smooth or surfacenotched specimens. The stress amplitude is low near the fatigue limit, limiting the activation of dislocations. Near the fatigue limit of the martensitic steel, short fatigue

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6 Macroscopic Manifestations of Hydrogen Embrittlement

Hydrogen Content (wt ppm)

3.5 3.0

non-charged pre-charged

2.5 2.0 1.5 1.0 0.5 0.0

580MPa 610MPa Applied Stress Amplitude

Fig. 6.18 Amounts of tracer-hydrogen in Si–Cr steel specimens fatigue-fractured at two applied stress amplitudes with and without hydrogen precharging. Fatigue cycles applied to the non-charged and precharged specimens were respectively 6 × 106 and 5.5 × 106 at the stress amplitude of 580 MPa, and 2 × 105 and 8 × 104 at the stress amplitude of 610 MPa (Nagumo et al. [34])

cracks existed at the ends of the surface notch in both air and hydrogen atmospheres. Ogawa et al. confirmed that the short fatigue cracks were non-propagating, i.e., the fatigue limit was a non-propagation limit of small cracks [36].

6.3.2 Crack Initiation and Growth-Rate Near Threshold The kinetics of the fatigue crack growth commonly uses the stress intensity range ΔK as a parameter. ΔK is defined as ΔK = K max − K min ,

(6.4)

where K max and K min are the maximum and the minimum stress intensity factor per cycle. ΔK at which the crack growth initiates is defined as the threshold stress intensity range, ΔK th . Accurate detection of the crack initiation and then of ΔK th is difficult. Reported hydrogen effects on ΔK th differ, increased or decreased, by steel types and environments [37]. The growth of a fatigue crack starting from the surface notch is schematically shown in Fig. 6.19 [31] against fatigue cycles for two applied stresses. The crack growth rate is computed from the observed crack length record. However, precise crack growth rate measurements are problematic in a regime as low as 1 × 10–9 m/cycle, and the computed growth rate does not necessarily mean the step-bystep-crack advance. In this case, a measured crack growth rate denotes the number of cycles needed for the crack to advance a certain distance feasibly in a step. Environments often complicate the morphology of the notch root, and effects of corrosion or oxidation overlap hydrogen embrittlement.

6.3 Fatigue

143

Crack Length, a

Fig. 6.19 Schematic illustration of applied stress dependence of fatigue crack growth (Hertzberg [31])

aj σ1

σ2 ai σ2 > σ1

Fatigue Cycles, n

Environmental effects on fatigue crack growth of high-strength steels are complicated according to ΔK levels and stress ratios. Accelerated fatigue crack growth in hydrogen gas compared to that in the air was reported for 2.25Cr–1Mo steel at two growth rate regimes, i.e., at near threshold levels and at higher growth rates, typically > 10–8 m/cycle above a critical K max value [38]. The hydrogen effect in the latter regime appeared at frequencies below a critical value (e.g., 5 Hz at the stress ratio of 0.05), associated with a fracture mode change to predominately intergranular cracking, consistent as a general strain-rate effect in hydrogen embrittlement. On the other hand, near the threshold levels below 10–9 m/cycle, the accelerated growth rate in dry hydrogen compared to moist air appeared only at low load ratios [38]. Suresh et al. ascribed the influence of the environment on the nearthreshold fatigue crack growth to the oxide-induced crack closure mechanism. An earlier contact between the fracture surfaces during the closure portion raises the closure load and reduces ΔK eff as, ΔK eff = K max − K cl ,

(6.5)

where K cl is the stress intensity at which the crack surface contact occurs. The reduced ΔK eff decelerates crack growth rates at low load ratios. The deceleration of the crack growth due to the crack closure is prominent when the crack opening is small at low ΔK levels and low stress ratios in corrosive environments. The magnitude of the mechanical wedging action is a function of the thickness and location of the debris [39]. Suresh et al. noted that pulsating crack-tip opening displacements were of a size comparable to fracture surface roughness and the thickness of corrosion debris within the crack [38]. The initiation and the early-stage growth of fatigue crack, especially in the range of very small ΔK under corrosive environments, have been extensively studied [32, 40]. Fatigue crack growth rates of high-strength steel under the same applied stress intensity increased in 3% NaCl aqueous solution and water compared to those in air.

144

6 Macroscopic Manifestations of Hydrogen Embrittlement

The increase was much higher for short than long cracks [32]. An expression of short crack effects is to use ΔK eff by adding an effective crack length l0 to the actual crack length l [40, 41], i.e., √ ΔK eff = A Δσ π (l + l0 ),

(6.6)

where A is the elastic stress concentration factor, and Δσ is the applied nominal stress range. The magnitude of ΔK eff is larger than the apparent ΔK, and the contribution of l0 to ΔK eff is significant when l is small. Environmental effects are ascribed to large l 0 in the presence of a corrosive environment. However, the physical meaning of l 0 is not definite, while an intrinsic defect size such as a microfracture process zone size has been proposed. Hydrogen enhancement of the fatigue crack growth rate at the near-threshold region was deduced by Esaklul et al., separating crack closure effects [42]. The steel was AISI 4340 of 1800 MPa in the tensile strength, and hydrogen was precharged under a pretty high fugacity by cathodic electrolysis in poisoned 5% H2 SO4 at a current density of 20 A/m2 followed by cadmium plating. Fatigue tests were conducted using compact tension (CT) specimens at R = 0.1 and 30 Hz. Log da/dN versus nominal ΔK showed a hydrogen enhancement of the crack growth rates at ΔK above 7 MPa-m1/2 or in da/dN above 5 × 10–9 m/cycle. However, in the lower ΔK range, crack growth rates were almost identical for hydrogen-charged and uncharged specimens. Fractographic features showed oxide buildup and geometrical asperities for hydrogen-charged specimens, and the load versus the crack-openingdisplacement curves exhibited closure of the crack surface. Then, the nominal ΔK was converted to ΔK eff in Eq. (6.5), using the estimated contact area and contact point on the observed fracture surface. Then, the modified plot of log da/dN against ΔK eff revealed hydrogen-enhanced crack growth rates even in the ΔK eff range below 5 MPa-m1/2 or in da/dN below 1 × 10–9 m/cycle.

6.3.3 Stage II Crack Growth in Steel 6.3.3.1

Effects of Microstructures

The dependence of the fatigue crack growth (FCG) rate on increasing ΔK is schematically similar to Fig. 5.6 in creep and Fig. 6.8 in fracture mechanics tests. The FCG rate in Stage II is commonly expressed by Paris’ law as, da = A ΔK m , dN

(6.7)

where A and m are constants that vary with material, environment, and testing conditions [31, 37]. Paris’ law is originally an empirical relation, and the measured m-values are 3–4 for various metallic materials.

6.3 Fatigue

145

An early study showed increased crack growth rates with increasing hydrogen gas pressure [43]. Figure 6.20 shows FCG of high-strength 0.4C–Ni–Cr–Mo martensitic steel (SNCM 435 in Japanese Standard) subjected to three types of heat-treatment to different microstructures and tensile strengths, i.e., annealed at 1123 K (991 MPa), asquenched (1344 MPa), and quenched-tempered (1274 MPa). The specimens were a double cantilever beam (DCB) type. Fatigue tests were in hydrogen gas environments of 1.1 and 4.0 MPa at the stress ratio R = 0.1 and a sinusoidal test frequency of 5 Hz. The growth rates at a given ΔK were in the order of the tensile strength. The transition from Stage I to Stage II was not discernible, and m-values applying Paris’ law in hydrogen environments were substantially higher than conventional values of 3–4, as observed in Ar. The m-value was also higher for the tempered martensite than for the annealed or as-quenched ones, as shown in Table 6.1 [43]. 10-4 10-5

Quenched

SNCM435 Annealed

da/dN, m/cycle

10-6 10-7 QuenchedTempered

10-8 ●: 0.6 MPa Ar Δ: 1.1 MPa H2 □: 4.0 MPa H2

10-9

5 10 20

100 200

2

ΔK, MPa·m1/2

5 10 20 50

ΔK, MPa·m1/2

3

10 20

100 200

ΔK, MPa·m1/2

Fig. 6.20 Fatigue crack growth rates in high-pressure Ar and H2 of high-strength martensitic steel subjected to three different heat treatments. The stress ratio is 0.1, and the test frequency is 5 Hz (Fukuyama et al. [43]. Reprinted with permission from The Soc. Mater. Sci., Japan)

Table 6.1 Fatigue crack growth parameter m in Eq. (6.7) for 0.4C–Ni–Cr-Mo steels in Ar and hydrogen environments Steel

Annealed

Quenched (TS:1344 MPa)

Quenched-Tempered (TS: 1274 MPa)

Atmosphere Ar

1.1 MPa 4 MPa Ar H2 H2

1.1 MPa 4 MPa Ar H2 H2

1.1 MPa 4 MPa H2 H2

m

4.2

6

KQ (MPa m1/2 )

163 111

6.3

4.1

6.5

7.1

4.7

12.1

15.6

99

59

23

17

72

27

21

Fukuyama et al. [43]. Reprinted with permission from The Society of Materials Science, Japan

146

6 Macroscopic Manifestations of Hydrogen Embrittlement

In experiments by Fukuyama et al., the threshold ΔK th was not definite, but hydrogen substantially accelerated FCG for the as-quenched specimens even at low ΔK near the threshold, suggesting a decrease in ΔK th . On the other hand, the FCG rates of annealed or tempered specimens were almost immune to hydrogen in the small ΔK range. The reason for the difference between the two steels is not definite, but the stability of dislocation configurations might be a feasible one. Closure effects due to oxides or debris are not likely since all the tests were conducted in dry environments. The susceptibility to hydrogen embrittlement in terms of fracture toughness K Q is included in Table 6.1, and the reductions by hydrogen, in terms of the ratio to the fracture toughness in Ar gas, were of similar levels for the two heat treatments. Precise measurements of FCG in high-pressure hydrogen gas environments have been extensively conducted in recent years. Ogawa et al. measured the FCG rate for pure iron in 0.2–90 MPa hydrogen gas [44]. Figure 6.21 compares the FCG curves with those in the air and 0.7 MPa nitrogen gas. The constant load-amplitude (= ΔP constant) fatigue tests were conducted using CT-type specimens at the load ratio R (= Pmin /Pmax ) of 0.1 and a test frequency of 1 Hz. In the air and 0.7 MPa nitrogen, the FCG curves were linear with m-values of nearly 3.0. On the other hand, the FCG rate in hydrogen gas increased during Stage II to about 30 times higher than in air or nitrogen gas. The onset of hydrogen acceleration, or the transition, occurred in the intermediate ΔK range, and the higher hydrogen gas pressure promoted the start of acceleration. A noticeable fact was that the onset of acceleration was during Stage II, i.e., after a significant stable crack growth, in a relatively low-pressure hydrogen gas. It suggests that substantial activation of plasticity is the precursor for hydrogen acceleration. It is Fig. 6.21 Fatigue crack growth rates of pure iron in laboratory air and high-pressure nitrogen and hydrogen (Ogawa et al. [44])

6.3 Fatigue

147

also to be noticed that hydrogen gas pressure hardly affected the later FCG rate after acceleration. During the transitional acceleration stage before attaining a new steady crack growth, the fraction of intergranular (IG) fracture morphology decreased, as shown in Fig. 7.10 in Sect. 7.2.6. Similar transitions by hydrogen in Stage II FCG rate appeared for ferrite–pearlite [45, 46], and martensitic [47] steels. In ferrite–pearlite steel, increasing carbon contents, i.e., the pearlite volume fraction, raised ΔK to start the transition [46]. After reaching the higher Stage II (m ~ 3.63), tentatively termed as Stage II’, the FCG rates in 0.7 MPa hydrogen were about 15, 13, and 5 times the values in air, for 0.16, 0.25, and 0.55% C steels, respectively. Pearlite mitigates hydrogen-assisted fatigue crack acceleration. Hydrogen acceleration of FCG is much remarkable in martensitic steel. Figure 6.22 shows FCG curves for 0.4C–Cr–Mo martensitic steels prepared to different tensile strengths of 1025, 921, and 811 MPa by varying tempering temperatures [47]. The fatigue tests using CT specimens were conducted in air or 90 MPa hydrogen gas at the stress ratio R of 0.1 and test frequencies of 5 or 1 Hz. Acceleration of the FCG rates in 90–115 MPa hydrogen sharply appeared when the steel’s tensile strength exceeded 900 MPa, particularly at low test frequencies or strain rates. The FCG rates at ΔK of 30 MPa·m1/2 in a ΔK- constant fatigue test were 100–2000 times the values in the air. Another notable feature in Fig. 6.22, compared to Fig. 6.21 for pure iron, is a wide transition range of ΔK and an uncertain finish to Stage II’. Large m-values obtained in Fig. 6.20 might correspond to the transition from Stage II to Stage II’. Concerning substantially different FCG rates near Stage II’ among the three steels, differences in the original martensite microstructures are to be noticed. The FCG rate in Stage II’ in the hydrogen environment is the higher for higher strength or lower tempering temperature.

JIS SCM 440 Stress ratio; 0.1 Temperature: RT

90 MPa H2 f =1 Hz

da/dN, m/cycle

Fig. 6.22 Fatigue crack growth rates in laboratory air and high-pressure hydrogen gas of high-strength steel prepared to different tensile strength by tempering temperatures (Setoyama et al. [47])

●: T550 (1025 MPa) ▲:T600 (921 MPa) ■: T650 (811 MPa)

Stress intensity factor range, ΔK(MPa·m1/2)

148

6.3.3.2

6 Macroscopic Manifestations of Hydrogen Embrittlement

Effects of Test Conditions

Hydrogen embrittlement is generally more prominent in higher hydrogen concentrations, and temperature and strain rate play in the extent of degradation, as described in Sect. 6.1.1 on tensile tests. In fatigue tests under hydrogen gas environments, the effects of hydrogen also depend on testing conditions. (a) Temperature In the FCG test of ferrite–pearlite steel in 0.7 MPa hydrogen gas, Yamabe et al. showed the start of the FCG rate acceleration to delay with increasing temperature from room temperature to 363 K and 423 K [45]. The attained steady Stage II’ growth rates also decreased associated with the temperature rise. A similar dependence of the start of the FCG rate transition was exhibited for pure iron, raising the temperature from 298 to 373 K, and 423 K in 0.7, 10, and 90 MPa hydrogen gas [48]. Such results likely correspond to the case of tensile tests shown in Fig. 6.3. Effects of temperature on Stage II’ growth, after reaching a new steady state, were not sure in pure iron. Acceleration by hydrogen did not occur at ΔK less than 14 MPa·m1/2 at 423 K in pure iron, even in 90 MPa hydrogen gas which expected a high hydrogen concentration. On the other hand, in low-carbon ferrite–pearlite steel, acceleration of the FCG rate occurred even at 423 K in 0.7 and 10 MPa hydrogen gas environments [49]. (b) Test frequency A strong dependence of FCG on the test frequency was demonstrated for high hardness SAE 52100 bearing steel (Vickers hardness number 569) [50]. The wedgeopening-load (WOL) specimens were hydrogen-precharged in 100 MPa hydrogen gas at 358 K (~ 1.5 ppm). The fatigue test was under a constant load range at the load ratio R = 0.1, and test frequencies were 0.2, 2, and 20 Hz. The FCG rates steeply increased at ΔK of about 6 MPa·m1/2 , inclining to the initial Stage II growth line. The test frequencies hardly affected the steep increase, but the FCG rates in the newly attained Stage II’ were remarkably higher with decreasing strain rates. Any difference in the m-values by test frequencies was not sure. FCG tests in high-pressure hydrogen gas also exhibited the dependence of the FCG rate on test frequency. Sun et al. cyclically changed the test frequency during the fatigue test of 15–5 PH martensitic stainless steel in 0.9 MPa hydrogen gas [51]. A decrease in the frequency from 20 to 0.2 Hz during a certain number of fatigue cycles induced a significant enhancement of the FCG rates. After the crack propagated over a predefined distance at 0.2 Hz, returning the frequency to 20 Hz decreased the crack growth rate, recovering the values under 0.9 MPa at a frequency of 20 Hz. The enhanced FCG rate by the lower frequency was associated with intergranular fracture (IG) surface. For ferrite–pearlite steel, a substantial acceleration occurred on decreasing the test frequencies as low as 0.01 Hz in 90 MPa hydrogen gas [46]. For martensitic steels of different strengths, 811, 921, and 1025 MPa in tensile strength, a wide range of the test frequencies from 1 to 0.001 Hz exhibited strong dependencies of the FCG rate on frequencies [47]. In that case, a step-wise frequency change was

6.3 Fatigue

149

conducted at ΔK of 30 MPa·m1/2 . At 0.001 Hz, the FCG rate was as much as 2500 times the value in the air for the 921 MPa steel. On the other hand, for the 811 MPa steel, hydrogen acceleration was about 20–30 times in the air, almost immune to the frequency change. The fracture surface of steel of 921 and 1025 MPa in tensile strength contained a few tens % of IG surface. However, the fraction of the IG surface was almost unaffected by the test frequency, suggesting that the fraction of the IG surface was not necessarily the essential origin of the acceleration. Lower frequencies need a longer time per cycle, extending hydrogen entry at the crack tip. (c) Environmental impurity effect As described in Sect. 6.3.2 oxide-induced crack closure is a factor to be considered in the near-threshold regime for enhanced crack growth rates in hydrogen gas. Somerday et al. examined the inhibiting function of oxygen in the onset of hydrogen acceleration in Stage II FCG [52]. The constant load-amplitude fatigue tests were conducted using CT specimens of API X52 steel at the stress ratio R of 0.1 or 0.5 and a test frequency of 10 Hz. The environments were 21 MPa pure hydrogen or (H2 + O2 ) mixture of up to 1000 vol. ppm O2 . Hydrogen-accelerated fatigue crack growth was activated when exceeding both threshold levels of the inert environment crack growth rate and K max . The ΔK at the onset of accelerated crack growth systematically increased as oxygen enriches in hydrogen gas. Either a lower load cycle frequency or a higher R ratio delayed the onset of hydrogen-accelerated crack growth to higher ΔK levels. About the function of oxygen, Somerday et al. assumed that the crack tip coverage by oxygen, disturbing hydrogen entry into the matrix, is overcome when the rate of new crack tip surface creation reaches a critical level. Once this condition is attained, hydrogen uptake at the crack tip is enhanced and hydrogen-accelerated fatigue crack growth can proceed [52]. Accordingly, a balance between oxygen transport to the crack tip and the creation rate of the new crack surface determines the onset of hydrogen acceleration of FCG. The steady stage II’ FCG rates after acceleration were reasonably irrelevant to oxygen contents, suggesting hydrogen–matrix interactions are unaffected. (d) Internal hydrogen In the experiment on an environmental effect cited above [52], the hydrogen supply from the environment is a crucial process for the FCG rate. Ogawa et al. compared FCG of a hydrogen-precharged Ni-base superalloy 718 (internal hydrogen) with that in high-pressure hydrogen gas [53]. The alloy was a face-centered cubic (FCC) structure, precipitation-hardened with γ ' (Ni3 (AlTi)) and γ '' ’ (Ni3 Nb). Hydrogen precharging was likely uniform by exposing specimens to 100 MPa hydrogen gas at 543 K for 600–800 h. Fatigue tests using CT specimens were under a constant load range at the load ratio R = 0.1 and a test frequency of 1 Hz. The hydrogen gas pressure for tests of uncharged specimens was 95 MPa. Figure 6.23 shows FCG curves under external and internal hydrogen conditions [53]. Under the external hydrogen condition, the FCG rate was 3–6 times faster than that in air, with the same m-value of nearly 3 in Paris’ law. On the other hand, the FCG

150

6 Macroscopic Manifestations of Hydrogen Embrittlement

Fig. 6.23 Fatigue crack growth rates of Alloy 718 in high-pressure hydrogen gas (External H) compared with hydrogen-precharged (Internal H) one (Ogawa et al. [53])

rate under the internal hydrogen condition steeply increased with increasing ΔK, far exceeding values under the external hydrogen condition. Separately conducted measurements of the frequency dependence of FCG exhibited a monotonic increase in the FCG rates with decreasing test frequencies at ΔK of 50 MPa·m1/2 under both external and internal hydrogen conditions. However, in all frequencies, no hydrogen acceleration appeared at a low ΔK of 30 MPa·m1/2 under the internal hydrogen condition. Fractographic features exhibited intergranular and quasi-cleavage surfaces under the external hydrogen condition, while fine planar facets appeared under the internal hydrogen condition. Fractographic features characterizing hydrogen embrittlement are described in Sect. 7.2.5. The origin of the difference between external and internal hydrogen is not definite. However, be noticed is that tolerations of hydrogen effects in a cyclically stressed volume element in front of the advancing crack are more frequent under the internal hydrogen condition than the external one.

6.3.4 Fatigue in Austenitic Stainless Steel Austenitic stainless steel is characterized by low hydrogen diffusivities and occasional phase instabilities. Murakami et al. measured the FCG from a surface notch on Type 304 and 316L stainless steels containing 24–90 mass ppm hydrogen [54]. The specimens were round bars of 7 mm in diameter, and hydrogen was precharged at

6.3 Fatigue

151

Fig. 6.24 Slip deformation behaviors near fatigue crack front in Type 304. (a) Uncharged, N = 13,200, (b) hydrogen-charged to 47.2 mass ppm, N = 18.4000 (Murakami et al. [54])

~ 553 K in high-pressure hydrogen. A small hole, 100 μm in both depth and diameter, was drilled on the surface after hydrogen charging as the starter of a fatigue crack. A tension–compression fatigue test with a constant-stress amplitude of 280 MPa was conducted at 1 Hz and a stress ratio of −1, and the advancing crack length was measured on the surface using a replica method. Hydrogen generally promotes crack initiation and growth in fatigue, but an unexpected “decrease” was found in the FCG rates in both types of stainless steel. The decrease was significant for Type 304 with high hydrogen concentrations of ≥ 70 mass ppm. The surface relief around the crack is due to plastic deformation, and hydrogen precharging much reduced the relief, as shown in Fig. 6.24 [54]. Murakami et al. deduced that, at a high hydrogen concentration, material surrounding a crack blocked the extension of the plastic zone at the crack tip. Internal hydrogen builds up a dilatational stress field, and hydrogen desorption associated with the crack extension, when it occurs, will release the stress field, reducing plastic deformation around the extending crack. Hydrogen degradation in 45 MPa hydrogen gas was negligible or very small for Type 316L stainless steel in tensile tests, the stress-fatigue life diagram at tension– compression tests, and the FCG tests [55]. Type 316L was immune also to fatigue tests using cyclic pressurization of tubular specimens by 88 MPa hydrogen gas [56]. The cycle time was 20 s per cycle. On the other hand, similar tests showed a substantial decrease in the fatigue life for Type 304 and precipitation-hardened A286 steels. Microscopic observations revealed crack paths along the interfaces of α’ martensite in Type 304 and Ni3 Ti in A286. Hydrogen effects on microstructural alterations during fatigue tests are prominent in Type 304 [57]. Characteristics of hydrogen embrittlement of austenitic steel are in Sect. 8.3.

152

6 Macroscopic Manifestations of Hydrogen Embrittlement

6.3.5 High-Cycle Fatigue Near Threshold Fatigue crack growth behaviors near the threshold stress intensity range are of practical importance for structural components under long-term service. The threshold ΔK th is ΔK below which the crack growth rate becomes diminishingly small. ΔK th was not definite in ultrasonic tension–compression fatigue tests of mild steel, Type 304 stainless steel, and copper in a 3.5% NaCl aqueous solution, while a clear threshold existed in non-corrosive silicon oil [58]. The fracture morphology of samples given fatigue cycles in a corrosive environment changed from ductile transgranular to intergranular fracture. The involvement of a minimal amount of hydrogen in extremely high-cycle fatigue limits was presented by Murakami et al. [59] for surface-hardened Cr– Mo steel quenched and tempered in a reductive atmosphere (QT) or in a vacuum (VQ). Hydrogen entered into specimens during the fabrication process to concentrations of 0.7–0.9 and 0.01 mass ppm for QT and VQ, respectively. Fatigue tests were tension–compression at R = −1 with cyclic frequency of 20–80 Hz. For extremely high-cycle fatigue in the regime of N > 107 , the S–N plots showed a substantial scatter, but fatigue lives and the fatigue limit were lower for QT than VQ. Murakami et al. pointed out the importance of non-metallic inclusions for ΔK th [59]. Subsurface non-metallic inclusions located at centers of fish-eye were crack initiation sites, associated with an optically dark area (ODA) characterized by rough and irregular surface morphology. ODA in QT was about twice as large as that of non-metallic inclusions and was larger than ODA in VQ. Secondary ion mass spectroscopy detected hydrogen at near non-metallic inclusions in QT but not in VQ. Murakami et al. deduced that hydrogen assists the formation of ODA and determines fatigue lives at low stress levels near the fatigue limit [59]. At an extremely slow crack growth stage of 1 × 10–10 m/cycle, a detectable crack advance needed more than thousands of cycles. Effects of some structural damages might be expected.

6.3.6 Models of Fatigue Crack Extension Paris’ law in Eq. 6.7 for the FCG was originally derived for the fatigue-life prediction in designing metallic construction. Hydrogen acceleration of FCG rate appears in coefficient A in Eq. 6.7, with an exponent m-value common to many metals, but transition or occasionally large m-values appear, as described in preceding sections. To understand the function of hydrogen in fatigue, microscopic origins of such parameters are indispensable knowledge. However, the issue is not yet conclusive. Details of the discussion made so far are beyond the scope of this book, and brief outlines of the main ideas are as follows.

6.3 Fatigue

6.3.6.1

153

Criteria for the Crack Advance

Paris’ law is originally an empirical one to give the best fit with m = 4 [60, 61], and its theoretical derivations followed concerning criteria for the fatigue crack advance. Preceding Paris’ law, Head proposed a stress-controlled advance for a relatively short rack [62]. Head considered three types of neighboring volume elements in the crack front, tolerating work hardening, plastic constraint, and shear, differing by their sites. The widths of the respective elements are determined by the force balance under a boundary condition. Assuming that the crack advance occurs when work hardening exceeds the fracture stress of the material, Head derived the crack growth rate proportional to K 2 . In the small-scale yielding condition, the crack opening displacement (COD) δ more correctly expresses stress fields ahead of the crack. Donahue et al. assumed the crack growth rate to increase proportionately to the difference from a critical value, as [63] da = A(δ − δth ). dN

(6.8)

Since δ=

4K 2 , π σy E

(6.9)

Equation (6.8) written in terms of K is. ) 4A ( 2 da K − K th2 , = dN π σy E

(6.10)

where A is a material constant, σ y is the yield stress, and E is Young’s modulus. Weertman considered the displacement D of two atomic planes forming the upper and lower surface of a crack and assumed its critical value D* as the condition of the crack advance [64]. Weertman also assumed cyclic variations of D in fatigue tests are additive and that the critical D* is the sum of D at each cycle. Summing of cyclic D implicitly presumes accumulation of plastic work at each cycle. Weertman calculated accumulated plastic work W p over the plastic zone. On the crack advance, W p converts to the newly created surface energy. Giving proper expressions for the plastic zone size, Weertman derived the crack growth rate in the form of Paris’ law, da = C(ΔK )4 . dN

(6.11)

The coefficient C is inversely proportional to the surface energy γ , i.e., C increases with decreasing γ .

154

6.3.6.2

6 Macroscopic Manifestations of Hydrogen Embrittlement

Models in Respect of Damage Accumulation

Criteria of crack advance, such as ΔK th or δ th , are helpful as a design parameter for structures, but the criteria per se are not the microscopic mechanism. An approach to understanding the crack advance in fatigue is to consider the microscopic process in front of a crack leading to advance. In fatigue tests, a monotonic increase in the potential energy due to rising load is not expected, and Lee and Liebowitz remarked on internal alteration associated with plastic deformation in the crack front [65]. The energy originating in plasticity is generally irreversible on unloading, but a partial recovery occurs associated with released interactions of lattice defects with applied stress. Bodner et al. assumed that the non-reversible work W p stored in the plastic area around the crack tip is critical in the crack advance and proposed as [66], da = dN

(

da dWp

)(

) dWp . dN

(6.12)

The idea implies that the elastic strain energy and accumulated lattice defects contribute to the crack advance. Kingbeil assumed that dW p /da in fatigue is the same as the critical potential energy release rate or the fracture toughness Gc in monotonic loading [67], i.e., dWp dΠ = ≡ Gc. da da

(6.13)

During fatigue crack advance, the change in the total potential energy per cycle dΠ /dN must balance the plastic work per cycle dW p /dN, i.e., dWp dWp da dΠ = = . dN dN da dN

(6.14)

Accordingly, from Eqs. 6.12–6.14, 1 dWp da = . dN G c dN

(6.14)

Kingbeil numerically calculated dW /dN for various metals using a finite element method and agreed well with experimental FCG curves [67]. For a titanium alloy, the calculated result was dW = 3.735 × 10−8 (ΔK )4.002 ( J/m). dN

(6.15)

On the right-hand side of Eq. 6.14, dW p /da is determined by the material’s constitutive relation, while Gc concerns the degradation of materials.

6.4 Delayed Fracture

155

The calculation of plastic energy by Kingbeil was over the entire plastic zone length. However, the plastic zone length is usually much larger than the width of one striation, which corresponds to the crack advance per cycle. A further issue is the fracture of elements within the plastic zone, and Duran et al. proposed a sequential fracture model in the plastic zone [68]. Damage generated by cyclic stressing accumulates in each volume element in the plastic zone, and its magnitude differs by the distance of the element from the crack tip. During the crack advance over the entire plastic zone, an element initially located neighboring the extent of the plastic zone tolerates cyclic damage accumulation, gradually increasing as the crack front approaches. Accumulated damage in the element when the element faces the crack tip likely attains a critical level for the crack advance. Mechanistic models of FCG, including hydrogen effects, have not been presented. From Eq. 6.14, hydrogen effects are not likely due to the constitutive relation, like yield stress or work-hardening rate, according to findings presented in Sect. 6.1. Hydrogen feasibly operates in processes that concern degradation of the energy release rate, Gc . Damage accumulation is a viable process in fatigue. Extensive studies on fatigue in high-pressure environments are now in progress, and precise nanoscopic observations, as described in Sect. 7.3.2, will elucidate the mechanism of hydrogen effects in fatigue failure.

6.4 Delayed Fracture 6.4.1 Characterization Eventual failure during service is a crucial problem for structural components. Molecular hydrogen precipitation is a well-established cause of delayed cracking, and modern industrial technologies, such as steel refining and welding technologies, have minimized the problem. On the other hand, delayed failure of tendons in prestressed concrete or high-strength steel fasteners under sustained loading occurs even in mildly corrosive environments. The mechanisms of these two types of delayed fracture are different, and this chapter focuses on the latter. The time until failure often extends to many years. The time dependence of failure is like fatigue failure, and “static fatigue” is an alternative terminology for sustainedloading delayed fracture. The occurrence of failure depends on the environment, and delayed fracture belongs to environmental degradation of materials. Accordingly, corrosion on the surface of materials is deeply concerned with, and delayed fracture under corrosive environments is sometimes regarded as stress corrosion cracking (SCC). Hydrogen is a byproduct of corrosion reactions on the surface. When SCC dominates, corrosion pits or crevice corrosion produced by anodic dissolution on the metal surface leads to failure. On the other hand, in laboratory tests, the cathodic polarization of the specimen in liquid environments promotes failure, proving the dominant role of hydrogen in failure.

156

6 Macroscopic Manifestations of Hydrogen Embrittlement

A long exposure time to fracture in engineering services inevitably necessitates some devices to accelerate failure in laboratory tests. As described in the following Sect. 6.4.2, the meaning or validity of an accelerating method is a critical issue. In laboratory tests, delayed fracture characteristics are expressed by applied stress versus time to fracture diagram similar to the S–N curve in fatigue tests. The delayed fracture diagram varies by test temperature, environment or hydrogen concentration, and specimen geometry. Figure 6.25 by Johnson et al. [69] might be the first diagram obtained by laboratory tests under constant-stress tensile loading. The specimens of AISI 4340 steel of 1600 MPa in tensile strength were circumferentially notched bars, and hydrogen was precharged under a fairly high fugacity by cathodic electrolysis in a 4% H2 SO4 aqueous solution at a current density of 30 A/m2 . Hydrogen was enclosed in specimens by cadmium-electroplating, and the specimens were then baked at 423 K to homogenize the distribution of hydrogen. Partial degassing took place during baking, but hydrogen concentrations were not measured. Instead, baking time at 423 K was the parameter of hydrogen concentration. In the experiments, as-received specimens contained about 1.5 mass ppm of hydrogen, exceeding electrolytically introduced hydrogen. The as-received hydrogen was non-diffusive and immune to embrittlement. It implies that apparent hydrogen concentrations do not always serve as a measure for causing degradation. Figure 6.25 exhibits the incubation time to the final failure, suggesting the initiation of an incipient crack substantially prior to the final fracture. The initiation and discontinuous growth were detected using electric resistance techniques [69, 70]. Decreasing hydrogen concentration retarded the onset of the crack initiation, but the onset was almost independent of the applied stress for a given hydrogen concentration [71]. The incubation period covers most of the time to fracture at low hydrogen concentrations. Nominal Notch Strength = 300 kpsi (=2.1GPa) 300

Applied Stress (1000 psi)

Fig. 6.25 Delayed fracture diagram of AISI 4340 steel. Hydrogen-charged specimens are Cd-plated and baked at 423 K (150 °C) for various periods (Johnson et al. [69])

uncharged 24h baked

250 18h 200 12h 150 7h 3h

100

0.5h 50 -2 10

10-1

1 10 Fracture Time (h)

102

103

6.4 Delayed Fracture

157

Assuming a diffusion-controlled process in the incubation period, Steigerwald et al. obtained the activation energy of 38 kJ/mol from an Arrhenius relationship for the logarithm of the ratio of the incubation time to the absolute temperature [71]. The value is fairly higher than the reported activation energies of hydrogen diffusion in iron and steel, and some other controlling processes are not ruled out. A noteworthy result was that the true fracture stress, i.e., applied stress divided by the uncracked area measured on the fracture surface, was constant over a wide range of applied stress and hydrogen concentration. It suggests that hydrogen does not affect the fracture stress in the central portion of specimens. It was likely that hydrogen operated in some other kinetics during the incubation period, not necessarily decreasing the fracture stress at the final crack propagation stage. Events during the incubation period of delayed fracture tests were detected using the acoustic emission (AE) technique for high-strength steel of 1300 MPa in tensile strength [72]. The delayed fracture tests used V-notched specimens subjected to a constant load cantilever bending in 0.1 N HCl solution. Acoustic emissions occurred in the incubation period prior to the onset of the crack initiation, detected by a concurrently conducted electric resistance measurement. The number of AE signals increased with time, and Fig. 6.26 compares waveforms in the incubation period and the crack growth stage [72]. The waveform in the incubation period was packet-like, similar to that associated with plastic deformation, while that in the crack growth stage was irregular with higher amplitudes. Activation of dislocations and hydrogen diffusion is certainly a process that proceeds during incubation. Fracture mechanics test under sustained loading is a type of delayed fracture test. The threshold stress intensity for the crack initiation K TH , described in Sect. 6.2.1 for fracture mechanics tests, corresponds to the lower limit of the applied stress below which delayed fracture does not occur. However, notches are not always required in specimens to induce delayed fracture. The correspondence between practical and laboratory test results is a matter that needs careful examination.

Fig. 6.26 Wave forms of acoustic emission generated during delayed fracture tests of high-strength martensitic steel. (a) Incubation time, (b) during crack extension (Nagumo [72])

158

6 Macroscopic Manifestations of Hydrogen Embrittlement

6.4.2 Effects of Materials Factors The susceptibility to delayed fracture of steel is generally higher for higher strength levels. Figure 6.27 [73] compiles threshold stresses of various commercial steel subjected to delayed fracture tests in water for 100 h. The threshold stress turns to a decrease in steel of the tensile strength higher than 1200 MPa, which corresponds to the strength level of high-strength fasteners that exhibit delayed fracture in service under atmospheric environments. The evolution of delayed fracture on raising the strength of steel was a serious warning to industries aiming to use higher-strength steel. A noticeable result in Fig. 6.27 is that the critical tensile strength, above which the threshold stress turns to decrease, differs by steel type. Maraging steels are more resistant to degradation than low-alloyed steels, suggesting a design principle for hydrogen-resistant steel. Testing temperature also substantially affects the time to fracture. For sustained tensile-load delayed fracture tests in water for martensitic steel of 1510 MPa in tensile strength, elevating water temperature from 298 to 353 K reduced the time to fracture to more than one order of magnitude [73]. Strengthening steel by, e.g., alloy design or heat treatment is associated with microstructural changes that alter the response to applied stress. Hydrogen interactions with strain-induced lattice defects are viable functions of hydrogen in the incubation period. Mechanistic behaviors in delayed fracture tests under sustained loading are the same as stress relaxation and creep that involve plastic deformation, described in Sect. 5.3. 18Ni maraging steel

Fig. 6.27 Threshold stresses at 100 h for delayed fracture of various high-strength steels in water (Yamamoto et al. [73]) Delayed fracture strength in water for 100h (GPa)

Piano wire Stress concentration factor α ≈ 10 In water

Tensile strength (GPa)

6.4 Delayed Fracture 1.0 □ 823 K ○ 923 K

0.8

Applied Stress Ratio, σ/σB)

Fig. 6.28 Delayed fracture diagrams for medium-carbon Mo-V martensitic steels tempered at 823 K (550 °C) and 923 K (650 °C). The arrow indicates unfailed specimens (Nagumo et al. [74])

159

0.6

0.4 0.2 0.0 0.1

1

10 100 Time to Fracture (h)

1000

Hydrogen-enhanced stress relaxation shown in Fig. 5.5 for a 0.37%C–0.6%Si– 1.0%Mo–0.5%Cr–0.54 V martensitic steel indicates the precipitation of fine VC to reduce both the stress-relaxation rate and its enhancement by hydrogen. Figure 6.28 shows delayed fracture test results of the same steel in Ref. [74]. Two tempering temperatures of 823 K and 923 K were employed to give the same tensile strength of 1470 MPa with and without VC precipitation. Sustained loading tests were conducted at room temperature using a smooth hydrogen-precharged specimen. Hydrogen charging was under a mild hydrogen fugacity by cathodic electrolysis in a 3% NaCl + 3gl −1 NH4 SCN solution at a current density of 5 A/m2 . Precipitation of fine VC brought about a substantial improvement in the time to fracture. The correspondence between the stress-relaxation rates and hydrogen effects implies the involvement of plasticity and associated hydrogen effects in delayed fracture.

6.4.3 Effects of External Factors Environmental conditions like applied stress, temperature, and humidity are not constant for structural components during engineering service. Alternating hydrogen entry due to daily humidity changes in the ambient atmosphere is demonstrated in Fig. 2.3 in Sect. 2.1.1. Delayed fracture is usually regarded as a fracture under static loading, but the effects of mechanical and electrochemical variations must be considered. (a) Stress variations The superposition of small amplitude stress oscillation on sustained loading promotes the macroscopic crack initiation and decreases the lower limit stress in delayed fracture tests [75]. The used material was a Ni–Cr–Mo steel of 1800 MPa in tensile strength, and sinusoidal oscillation of 15 or 400 cpm was superposed on U-notched static bending at various constant stresses. Promoted crack initiation by superposing

Fig. 6.29 Decrease in the lower limit stress by superposing cyclic variations of applied stress at sustained loading delayed fracture tests for various high-strength steels (Kido et al. [76]. Reprinted with permission from The Iron and Steel Institute Japan)

6 Macroscopic Manifestations of Hydrogen Embrittlement

○: σscc (σa = 0) ●: σscc (σa = 50 MPa)

2000

Lower Limit Stress (MPa)

160

SUS 420J2

1500

SNCM8 SKD61 18Ni Maraging Steel

1000

σt

500

In water

σ t = 100h

0

1500 500 1000 2000 0.2% Proof Stress, σy (MPa)

oscillating stress was prominent when dropped water at the U-notch. The degradation appeared for stress amplitude as low as 50 MPa at the constant stress of 1260 MPa, and the degradation was more prominent with higher stress amplitudes and oscillating frequencies. Results for various steels are shown in Fig. 6.29 [76] at an oscillating frequency of 15 cpm and a stress amplitude of 50 MPa. The superposed oscillating stress may induce interactive functions of hydrogen with dislocations, operating alternately in process in sustained-loading tests. For experiments in Fig. 6.29, the maximum applied stress increased on superposing the oscillatory stress. In order to separate the effects of the cyclic variation and the applied stress level, keeping the maximum stress constant during the test was conducted [77]. During sustained–load delayed fracture tests of martensitic steel, the applied load was cyclically reduced by up to 10% at a frequency of 5 or 10 cpm [77]. The steel was 1300 MPa in tensile strength, and smooth specimens of 5 or 7 mm in diameter were immersed in a 20% NH4 SCN aqueous solution at 323 K. Figure 6.30 [77] shows delayed fracture diagrams for various stress amplitudes. The promoted fracture was evident at a stress amplitude of 10%, while the mean stress was lower than the constant-stress level. A noteworthy finding was that the hydrogen concentration in specimens was uniquely determined by the immersion time in the solution, irrespective of constant or cyclic stressing. It implies that total hydrogen content is not the controlling factor for promoting fracture. The amount of lattice defects measured in terms of the amount of tracer-hydrogen introduced after the tests decreased when tested specimens were annealed at 473 K. The decrease was more significant for cyclic-stressed specimens than for sustained-loaded specimens. It indicates that cyclic activation of dislocations enhances the generation of vacancies during the incubation period. Further studies on the effects of cyclic prestressing on tensile tests and interactions between fatigue and delayed fracture are in Sect. 7.4.2 concerning damage accumulation in stress histories.

6.4 Delayed Fracture

1200

Applied Stress (MPa)

Fig. 6.30 Accelerated fracture by superposing cyclic stress variations at delayed fracture test of high-strength steel. The maximum stress is constant (Izutsu et al. [77])

161

1100 1000 900 800 700 600 10

Stress Amplitude ● 0% □ 2.5% Δ 5% ◊ 10%

100 Time to Fracture (h)

1000

(b) Environmental variations Another environmental factor to be examined is variations of hydrogen fugacity associated with weather changes. A method devised to examine the effects was to apply cyclic variations to hydrogen-charging current density [78]. Experiments used high-strength martensitic steel of 1390 MPa in tensile strength in sustained-loading tests under simultaneous hydrogen charging. The specimens were round bars of 5 mm in diameter, and mild cathodic electrolysis was conducted in a 3% NaCl + 3 g/l NH4 SCN aqueous solution. The applied tensile stress was 70% of the tensile strength, and the current density was cyclically varied from 0.1 to 100 cpm in a rectangular form keeping the maximum current density constant. The time to fracture as a function of the frequency of the cyclic current is shown in Fig. 6.31 [78], where the maximum current density was 7.5 A/m2 , and the relative amplitude of the current variations was 10%. Promoted failure by higher frequencies is evident. The frequency of the cyclic current does not affect the total charging time, and hydrogen contents in unstressed specimens were uniquely determined by the total amount of supplied electric charge, irrespective of cyclic variations of the current density [78]. Accordingly, hydrogen content is irrelevant to the frequency effects. Subsequent TDA analyses of trapped states of hydrogen revealed changes in TDA profiles with an elapsed time of the test. The TDA profile was a single broad peak centered at around 353 K, but the higher temperature side of the peak showed a more pronounced increase with time. Similar to the case of cyclic stress variation [77], alteration of TDA profiles with time appeared earlier for the cyclic current conditions than for the constant current test. The TDA results indicate the creation of trap sites of high binding energies. The low-temperature thermal desorption spectroscopy (LTDS), shown in Figs. 3.2 and 3.11, ascribed the origin of such TDA profiles to vacancy clustering. Effects of environmental variations are consistent with promoting vacancy clustering.

6 Macroscopic Manifestations of Hydrogen Embrittlement

Fig. 6.31 Effects of cyclic variation of hydrogen-charging current density on the time to fracture at delayed fracture tests of high-strength steel. The maximum current density, imax , is the same (Nagumo et al. [78])

100 90

▲ Average

80 Time to Fracture (h)

162

70 60 50 40 30 20 10

imax i max i min imin i min Constant 0.1 10 100 1000 1 Cyclic Current Frequency (cpm)

6.4.4 Laboratory Test Methods Laboratory test methods for structural materials intend to reproduce situations in engineering practice. However, in delayed fracture, only limited information is available on the occurrence of failure in engineering service, and a long time to fracture necessitates some devices to accelerate failure in laboratories. The methods should not impede the validity of the test. The primary purpose of mechanical tests is to evaluate the performance of materials in engineering practice. However, the term “evaluation” has two meanings; one is to assess the quality, and another is to find a numerical expression. In other words, the former is for qualification in safety and reliability, and the latter is to characterize materials. Some proposed “evaluation” methods are not necessarily definite in their purpose. (a) FIP test method A test method as a standard for prestressing steel bars for concrete was published by Fédération Internationale de la Précontraint [79]. A smooth steel bar under constant loading is immersed in a 20% aqueous solution of NH4 SCN at 323 K. The pH of the solution is 4–4.5. The title of the method was for stress corrosion cracking, and corrosion reactions were observed on the specimen surface. However, hydrogen entry of about 3 mass ppm was confirmed in high-strength martensitic steel after several hours of immersion. The time to failure is the measure of the susceptibility to cracking, but a substantial scatter of data necessitates statistical consideration. The method gives a relative measure for the quality of different steels. (b) Constant load tests using hydrogen-precharged specimens A quantity proposed as the measure of delayed fracture is the hydrogen concentration in the material. The idea is intuitively natural in cases where hydrogen plays a decisive role in fracture. Suzuki et al. measured the time to fracture under constant loading for hydrogen-precharged martensitic steel [80]. The initial hydrogen concentration was

6.4 Delayed Fracture

163

controlled by varying HCl concentrations in aqueous solutions to dip the specimens, and the time to fracture was longer by decreasing the initial hydrogen concentration. Suzuki et al. defined the initial hydrogen concentration that did not cause fracture until 100 h as the critical hydrogen concentration HC of the specimen at the applied stress. The hydrogen concentration was measured using thermal desorption analysis (TDA), which exhibited two desorption peaks. The higher temperature peak was likely an artifact in the experiment, and Suzuki et al. employed the lower temperature peak as meaningful diffusible hydrogen. Yamazaki and Takahashi refined the method [81]; (1) hydrogen precharging and enclosing using cathodic electrolysis in a 3% NaCl + 3 g/l NH4 SCN aqueous solution at 0.5–10 A/m2 followed by Cd plating, (2) the applied stress in delayed fracture at 0.9 of the ultimate tensile strength, confirming the failure of more than 99% of specimens within 50 h. Yamazaki et al. considered that failure in engineering service occurs when the amount of hydrogen from the environment, HE , exceeds HC . Since HE varies with materials and environments, the meaningful measure is the difference between HC and HE at use, not HC itself. Yamazaki et al. estimated HE using a laboratory cyclic corrosion test (CCT) without applying stress and compared the laboratory and statistical failure frequencies in atmospheric exposure for several high-strength steels. A pretty good correspondence to the statistical result was found for a parameter (HC –HE )/HC . The meaning of the parameter, rather than (HC –HE ), is not definite. The strength of each steel was different, and the orders of HC and the statistical failure frequency were the same as the orders of the strength, implying a simple dependence on the strength level in the case. Thus determined HC is a phenomenological quantity averaged over an entire specimen. Delayed fracture is sensitive to specimen geometries, like the notch sharpness. As a criterion of the local crack initiation, Takagi et al. proposed the local critical hydrogen concentration HC * , estimated at the maximum hydrostatic stress site in front of the crack [82]. Takagi et al. further considered the stress distribution in front of the crack and proposed to take the average in a certain high-stress area, similar to the idea of process zone in fracture mechanics, at the crack front [83]. Within the scope of laboratory tests, the local hydrogen concentration well corresponds to the time-to-fracture diagram in delayed fracture. Figure 6.32(a) shows the time to fracture under a constant load test of high-strength martensitic steel [84]. Two levels of the ultimate tensile strength σ B , 1450 and 1320 MPa, were prepared by varying tempering temperatures. The specimens were circumferentially notched round bars, and the notch-root radius was varied to give the stress concentration factors Kt of 2.1 and 4.9. Hydrogen precharging was by cathodic electrolysis in a 0.1 N NaOH aqueous solution at the current density of 0.3–10 A/m2 for 48 h, and following cadmium plating prevented hydrogen release. The constant load test was at 0.9 σ B at the notch-root section. In Fig. 6.32(a), the time to fracture increased with decreasing hydrogen content, and HC was lower for higher K t or the strength level. During constant loading, enclosed hydrogen accumulates at the site of the maximum hydrostatic stress. Wang et al. calculated the local hydrogen concentration by diffusion at the time of fracture [84]. Figure 6.32(b) plots the maximum local hydrogen concentration in Fig. 6.32(a)

6 Macroscopic Manifestations of Hydrogen Embrittlement

Fig. 6.32 (a) Constant load tests for the AISI 4135 steel at two strength levels and with two stress concentration factors. (b) Calculated peak values of the accumulated hydrogen concentration at the time of fracture or after loading for 6000 min for the specimens shown in (a) (Wang et al. [84])

(a) Hydrogen content, C0 (wt ppm)

164

Peak value of accumulated hydrogen concentration, C* (wt ppm)

(b)

for different initial hydrogen concentrations. The peak value of the accumulated hydrogen concentration at the time of fracture was almost constant, indicating that HC * is decisive for the occurrence of fracture in this case. The incubation time is the time spent for enough hydrogen to accumulate at the crack site.

6.4.5 Concept of the Critical Hydrogen Concentration 6.4.5.1

Limitation as Fracture Criterion

Above cited Wang’s results [84] demonstrated that HC * is the decisive measure of delayed fracture in their test method. HC * is not a material constant and varies with testing conditions. In their case that uses hydrogen-precharged specimens, internal hydrogen diffusion increased the local hydrogen concentration with time.

6.4 Delayed Fracture

165

Hydrogen Content (ppm)

0.3 Sapporo Niigata Kashima Tokyo Osaka

0.2

Amagasaki Wakatama KitaKyuushu Saga Okinawa

Tensile Strength: 1500 MPa U-bend Portion 0.1

0

0

10

20

30

40

50

Month Fig. 6.33 Hydrogen contents in U-bend loaded high-strength steel sheets of 1500 MPa in tensile strength after exposure at various sites in Japan (Kushida [85]. Reprinted with permission from The Iron and Steel Institute Japan)

The buildup of hydrogen concentration to a critical value is a widely adopted explanation of delayed fracture, but often without microscopic details of its function in fracture. Reported data of hydrogen concentration in structural components exposed to environments for the long term are few. The entry of hydrogen from atmospheric environments was investigated at various sites in Japan for four years, and Fig. 6.33 shows the results [85]. The specimens were U-shape bent 1500 MPa high-strength steel plate of 3 mm in thickness. Hydrogen contents were measured using TDA as the amounts of hydrogen desorbed up to 473 K, at which the desorption almost ceased. The increase in the hydrogen content in the initial six months was as expected, but further exposure decreased hydrogen content to a constant level. Data scattered substantially by the exposure sites, but systematic effects of local climates were not discernible. The facts are against the common notion of time-dependent hydrogen accumulation and imply that hydrogen contents are not always the decisive factor in causing delayed fracture under long atmospheric exposure. Hydrogen entry initially increasing and then turning to decrease in sustained loading was also observed in laboratory tests. Figure 6.34 shows the time dependence of hydrogen contents during immersion in a 20% NH4 SCN aqueous solution at 323 K for 0.33% C martensitic steel bars of 5 mm in diameter [86]. The order of the increase in hydrogen content among three conditions, i.e., (◯) unstressed, (▲) prestressed at 80% of the tensile strength, or (∎) under sustained-loading, corresponds to the order of strain-induced creation of lattice defects and its enhancement by hydrogen, described concerning Fig. 3.10 in Sect. 3.2.3.2.

(a) Tempered at 250ºC

Immersion Time (h)

Amount of Absorbed Hydrogen (ppm)

6 Macroscopic Manifestations of Hydrogen Embrittlement Amount of Absorbed Hydrogen (ppm)

166

(b) Tempered at 350ºC

Immersion Time (h)

Fig. 6.34 Amounts of absorbed hydrogen in medium-carbon tempered martensitic steels during immersion in 20% NH4 SCN aqueous solution at 323 K (50 °C). ◯: unloaded, ▲: prestressed to 80% of the tensile strength, ∎: concurrently loaded to 80% of the tensile strength. (a) Tempered at 523 K (250 °C), (b) tempered at 623 K (350 °C) (Nagumo et al. [86])

The initial increase in hydrogen content was not monotonic in the steel tempered at 623 K, as shown in Fig. 6.34(b). Hydrogen content turned to decrease with increasing loading time. The TDA profile of absorbed hydrogen for each condition exhibited a single broad peak between 323 and 473 K. A comparison of TDA profiles for the three conditions indicated that the higher temperature side of the TDA peak concerns the increased hydrogen contents. The evolution in the higher temperature side implies the formation of traps with high binding energies with hydrogen during immersion, as described in Sect. 2.1.2. The reason for the decrease in hydrogen content is not definite, but the exchange of external and internal hydrogen occurs to keep equilibrium, reflecting changes in trapping states. Alterations of strain-induced defects during delayed fracture tests have been discussed with respect clustering of vacancies [86].

6.4.5.2

Evaluation: Characterization or Assessment

Delayed fracture test methods developed in Refs. [81, 82, 84] were standardized by the International Organization for Standardization (ISO) [87]. The method is entitled “for evaluation of delayed fracture resistance”, but the document is limited in describing procedures to determine HC . When HC is the decisive factor for delayed fracture of a material, HC is a quantitative expression characterizing delayed fracture of the material. In this meaning, the procedures to determine HC are worthy as an evaluation method. However, the qualification of thus characterized material or assessing the material’s performance in engineering service is out of scope. A further simplified proposal was a conventional strain-rate technique (CSRT) for evaluating delayed fracture [88]. The underlying idea might be that HC or HC * under

References

167

stress is decisive generally and common in HE and must be identical in different loading methods. Accordingly, provided enough hydrogen comparable to HC * is present, the fracture condition obtained by a conventional strain-rate tensile test must be the same as those in a slow strain-rate tensile test or sustained-loading delayed fracture. The strain-rate and temperature effects on HE originates in the interaction between hydrogen and dislocation dynamics. The idea of CSRT lacks material aspects, such as microstructural alterations during straining and events that occur in the incubation period in delayed fracture. The CSRT is a proposal of a procedure to determine HC * , but its use for assessing the safety or reliability of material remains another subject. The comparison of HC and HE , proposed by Yamazaki et al. [81], was to assess the safety of steel in engineering service. However, proper assessments so far published for engineering services are few. As described in the preceding Sect. 6.4.5.1, hydrogen contents from the environment do not monotonically increase during the incubation time, against the presumption in laboratory tests. The concept of the critical hydrogen concentration is not always proper as the fracture criterion. When reliable empirical data for safe use are lacking, an alternative approach to assessing materials’ quality should be based on the materials’ intrinsic response to the operation of hydrogen causing embrittlement. The microscopic process that causes degradation of the material proceeds prior to the crack initiation, as described in Sects. 7.3 and 7.4. Based on these findings, Nagumo and Takai proposed a method to assess the intrinsic susceptibility to hydrogen embrittlement [89], described in Sect. 11.4.

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19. Y. Fujii, A. Kikuchi, M. Nagumo, Metall. Mater. Trans. A 27A, 469–471 (1996) 20. A. Needleman, Tvergaard, J. Mech. Phys. Solds, 35, 151–183 (1987) 21. Y. Shimomura, M. Nagumo, in Environment-Induced Cracking of Materials: Chemistry, Mechanics and Mechanisms, ed. by S.A. Shipilov, R.H. Jones, J.M. Olive, R.B. Rebak (Elsevier, Oxford, 2007), pp. 285–294 22. D.P. Williams, H.G. Nelson, Metall. Trans. 1, 63–68 (1970) 23. R.P. Gangloff, R.P. Wei, Metall. Trans. A 8A, 1043–1053 (1977) 24. H. Vehoff, W. Rothe, Acta Metall. 31, 1781–1793 (1983) 25. H. Vehoff, H.-K. Llameth, Acta Metall. 33, 955–962 (1985) 26. W.W. Gerberich, T. Livne, X.-F. Chen, M. Kaczorowski, Metall. Trans. A 19A, 1319–1334 (1988) 27. M. Nagumo, T. Yagi, H. Saitoh, Acta Mater. 48, 943–951 (2000) 28. H. Yoshida, M. Nagumo, ISIJ Int. 38, 196–202 (1998) 29. M. Nagumo, H. Yoshida, Y. Shimomura, T. Kadokura, Mater. Trans. 42, 132–137 (2001) 30. K.A. Nibur, B.P. Somerday, D.K. Balch, C. San Marchi, Acta Mater. 57, 3795–3809 (2009) 31. R.W. Hertzberg, Deformation and Fracture Mechanics of Engineering Materials 3rd Ed. (John Wiley & Sons, N. Y. 1989), pp. 457–515, 517–604 32. W.W. Gerberich, in Hydrogen Degradation of Ferrous Alloys, eds. by R.A. Oriani, J.P. Hirth, M. Smialowski (Noyes Pub., Park Ridge NJ, 1985), pp. 366–413 33. Y. Murakami, H. Matsunaga, Int. J. Fatigue 28, 1509–1520 (2006) 34. M. Nagumo, H. Shimura, T. Chaya, H. Hayashi, I. Ochiai, Mater. Sci. Eng. A348, 192–200 (2003) 35. H. Matsunaga, M. Yoshikawa, R. Kondo, J. Yamabe, S. Matsuoka, Int. J. Hydrogen Energy 40, 5739–5748 (2015) 36. Y. Ogawa, H. Matsunaga, J. Yamabe, M. Yoshikawa, S. Matsuoka, Int. J. Hydrogen Energy 43, 20133 e20142 h (2018) 37. N. Nanninga, A. Slifka, Y. Levy, C. White, J. Res. Nat. Inst. Stand. Technol. 115, 437–452 (2010) 38. S. Suresh, G.F. Zamiski, And R. O. Ritchie: Metall. Trans. A 12A, 1435–1443 (1981) 39. S. Suresh, R.O. Ritchie, Scr. Metall. 17, 575–580 (1983) 40. S.J. Hudak Jr., Trans. ASME J. Eng. Mater. Tech. 103, 26–35 (1981) 41. M.H. Haddad, N.E. Dowling, T.H. Topper, K.N. Smith, Int. J. Fracture. 16, 15–30 (1980) 42. K.A. Esaklul, A.G. Wright, W.W. Gerberich, Scr. Metall. 17, 1073–1078 (1983) 43. S. Fukuyama, K. Yokogawa, M. Araki, J. Soc. Mater. Sci. Jpn. 34, 709–714 (1985) 44. Y. Ogawa, D. Birenis, H. Matsunaga, O. Takakuwa, J. Yamabe, Ø. Prytz, A. Thøgersen, Mater. Sci. Eng, A 733, 316–328 (2018) 45. J. Yamabe, M. Yoshikawa, H. Matsunaga, S. Matsuoka, Int. J. Fatigue 102, 202–213 (2017) 46. Y. Ogawa, H. Nishida, M. Nakamura, V. Olden, A. Vinogradov, H. Matsunaga, Int. J. Fatigue 154, 106561 (2022) 47. A. Setoyama, Y. Ogawa, M. Nakamura, Y. Tanaka, T. Chen, M. Koyama, H. Matsunaga, Int. J. Fatigue. https://doi.org/10.1016/j.ijfatigue.2022.107039 48. Y. Ogawa, K. Umakoshi, M. Nakamura, O. Takakuwa, H. Matsunaga, Int. J. Fatigue 140, 105806 (2020) 49. S. Matsuoka, O. Takakuwa, S. Okazaki, M. Yoshikawa, J. Yamabe, H. Matsunaga, Scripta Mater. 154, 101–105 (2018) 50. J. Yamabe, T. Matsumoto, S. Matsuoka, Y. Murakami, Int. J. Fracture 177, 141–162 (2012) 51. Z. Sun, C. Moriconi, G. Benoit, D. Halm, G. Henaff, Metall. Mater. Trans. A 44A, 1320–1330 (2013) 52. B.P. Somerday, P. Sofronis, K.A. Nibur, C. San Marchi, R. Kirchheim, Acta Mater. 61, 6153– 6170 (2013) 53. Y. Ogawa, O. Takakuwa, S. Okazaki, Y. Funakoshi, S. Matsuoka, H. Matsunaga, Corros. Sci. 174, 108814 (2020) 54. Y. Murakami, T. Kanezaki, Y. Mine, Metall. Mater. Trans. A 41A, 2548–2562 (2010) 55. S. Ohmiya, H. Fujii, ASME Pressure Vessels and Piping Conf. 2007–26492

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Chapter 7

Microscopic Features Characterizing Hydrogen Embrittlement

Fracture associated with plasticity proceeds by the nucleation of cracks or voids and their growth. This combination is crucial in fracture, and its evolution differs by situations like materials and applied stress states. Hydrogen degradation of macroscopic mechanical properties must originate in hydrogen effects in the microscopic process of fracture. Microscopic features are expected to exhibit more concretely the hydrogen functions in promoting failure.

7.1 Crack Nucleation Sites Early works revealed striations on tensile-fractured surfaces of hydrogen-charged iron specimens [1]. Except for fatigue fractures, striated surfaces are not popular in fractographic features. Striations have been observed mostly for single-crystal and coarse-grain specimens. Figure 7.1 shows striations on the tensile-fracture surface of a hydrogen-charged 0.001% C iron single crystal [1]. The crack growth as a whole was in the [010] direction on a macroscopically (001) plane, but the actual growth of the crack front was in the direction. Striations parallel to the crack front coincided with traces of {112} slip planes. Examinations of fine details utilizing scanning tunneling microscopy (STM) and mating of opposite fracture surfaces revealed the formation of fine voids at intersections of striations, as shown schematically in the lower part of Fig. 7.1. Crystallographic relations are consistent with the void formation originating in interactions of dislocations that move on intersecting slip planes. Formerly, fine striations of about 1 µm spacing along {112} slip planes were reported to be associated with the slow crack growth macroscopically on {001} and in directions for Fe-3%Si single-crystal specimens [2]. Acoustic emission (AE) measurements detected discontinuous crack growth in sustained-loading tests for fatigue-prenotched disk-shaped miniature compact tension specimens, which were

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 M. Nagumo, Fundamentals of Hydrogen Embrittlement, https://doi.org/10.1007/978-981-99-0992-6_7

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Fig. 7.1 Striations on the tensile-fracture surface of a hydrogen-charged iron single-crystal specimen. The lower illustration is a schematic STM view showing a microcrack formed at the intersection of striations (Terasaki et al. [1])

Crack initiation due to hydrogen at slip bands or cell walls. Main Crack

gaseous hydrogen charged and subjected loading parallel to axis. The discontinuous steps were ascribed to intermittent cleavage fracture, but direct evidence for cleavage was not presented from crystallographic measurements. The internal surface of hydrogen-induced cracks formed within coarse-grain polycrystalline Fe-3%Si specimens also exhibited fine striations and associated plasticity [3]. Internal cracks were initiated at non-metallic inclusions and propagated macroscopically on {100} cleavage planes associated with striations of an average spacing of 300 nm. More fine striations with a spacing of around 30 nm and a height of 15 nm were also observed. Transmission electron microscopy (TEM) revealed planar slip with an interplanar spacing of 15–30 nm that corresponded to the separation of fine striations. Electron backscatter diffraction (EBSD) patterns from regions within internal cracks were diffuse and indicated a substantial crystalline distortion. The involvement of plasticity in hydrogen-induced crack growth was more explicitly observed for blisters in a bicrystal pure iron [4]. Hydrogen charging under a high hydrogen fugacity, i.e., by cathodic electrolysis in a 0.1 N H2 SO4 solution with 10 mg/l As2 O5 + 3 ml CS2 /l at a current density of 300 A/m2 , produced cracks without applying external stress. The cracks were parallel to variants of mostly {110} and partially to {112} instead of {001} in the case of Fe-3%Si specimens. Fracture surfaces, showing striations with planar segments and markings perpendicular to the advancing crack front, were common to Fe-3%Si specimens. Planar segments perpendicular to primary striations were also parallel to variants of slip planes. Striations noted in the above studies indicate a periodic crack advance, likely due to hydrogen diffusion, sequentially building up the hydrogen concentration at the crack front. The trace of the {112} slip plane along striations suggests the preparation of

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Fig. 7.2 Cross-sectional view of the area beneath the fracture surface of a coarse-grain iron specimen tensile-fractured under hydrogen charging. The surface striations correspond to internal slip bands, and etch pits are formed along slip bands (Nagumo et al. [5])

new cracks by activated dislocations. Direct evidence of the crack nucleation at sites of a high density of dislocations is shown in Fig. 7.2 [5]. More distinct and large striations were also observed. Figure 7.2 [5] shows a cross-section of a commercial pure iron specimen tensile fractured at room temperature under relatively mild hydrogen charging by cathodic electrolysis in a 3% NaCl aqueous solution at a current density of 100A/m2 . The specimens of 5 mm in diameter had a bamboo structure, and fracture occurred after the onset of necking. The fracture surface exhibits coarse striations extending to internal deformation structures. A cross-sectional observation in Fig. 7.3 [5] revealed that the striations were on the extension of deformation bands in which etch pits and microvoids formed. Trace analyses confirmed the coincidence of the lamellae in Fig. 7.3 with {110} and {112} slip planes. Deformation bands are regions where slip on the primary slip planes is hindered associated with the activation of secondary slip, thus causing there a high dislocation density and mutual interactions of dislocations [6]. A TEM observation near the fracture surface revealed dislocation cell structures with cell walls coincident with {112} traces [5]. Etch pits frequently observed in the deformation bands imply deterioration of crystallinity at the sites. Void nucleation is a natural consequence of intense strain localization, and the voids-link along deformation bands is a microvoid coalescence (MVC) process as general in ductile fracture. Void nucleation sites resulting from interactions of high-density dislocations are not limited to deformation bands. Grain boundaries and interfaces of secondary particles, acting as barriers for dislocation slip, are viable sites, as described in the following.

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Fig. 7.3 Etch pits and microvoids formed in deformation bands in a coarse-grain iron specimen tensile-fractured under hydrogen charging (Nagumo et al. [5])

7.2 Fractographic Features The fracture surface manifests the crack propagation path. Most of the energy dissipated in the crack propagation is due to plasticity, and its concern with the fracture surface is crucial to understand the mechanism of mechanistic degradation. Fracture surfaces of metallic materials are diverse depending on situations but are classified generally into a few elementary modes; cleavage, interface separation, and MVC. The fracture surface of hydrogen-degraded steel exhibits some characteristic features depending on microstructures, hydrogen concentration or fugacity, and stress states. Characteristic features in hydrogen embrittlement are to be examined along with the understanding of basic fracture modes.

7.2.1 Cleavage Cleavage fracture is typical of brittle fracture of body-centered-cubic steel and is characterized by the transgranular crack propagation along {100} planes associated with river markings. In hydrogen embrittlement of steel, cleavage fracture is exceptional and appears when an incipient crack forms by the precipitation of molecular hydrogen of a high fugacity that satisfies the Griffith condition for an unstable crack extension. Cleavage fracture was observed for Fe-3%Si single crystals which were severely hydrogen charged either by cathodic electrolysis in a 4 vol.% H2 SO4 + CS2 + As2 O3 solution at a current density of 160 A/m2 or by quenching from a hydrogen atmosphere of 0.125 MPa at 973 ~ 1473 K [7]. The specimens were not

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175

externally loaded, but arrays of decorated dislocations in the vicinity of cracks indicated plastic deformation associated with the discontinuous growth of cracks. On the other hand, under static loading under hydrogen charging, i.e., in sustained-loading delayed fracture tests, fracture surfaces exhibited many curved steps different from cleavage steps [8]. Cleavage fracture in hydrogen embrittlement was also observed on a tensile test of 0.014% C iron single crystal at room temperature under simultaneous hydrogen charging [1]. The tensile axis was along [001], and hydrogen charging was by cathodic electrolysis in poisoned 0.05N H2 SO4 at a current density of over 30A/m2 . In that case, cleavage fracture with river markings occurred after the advance of the crack of striation-like appearance. The occurrence of cleavage might not be hydrogen effects.

7.2.2 Dimple Patterns Dimple patterns typically characterize ductile fracture that proceeds with so-called microvoid coalescence (MVC). The size and shape of dimples are not uniform and are roughly classified into relatively large primary dimples and fine secondary ones. Second-phase particles, like non-metallic inclusions or precipitates, often locate in primary dimples, but fine secondary dimples are generally not associated with any particle. Activated dislocations are a most likely concern, and voids formed by the growth and coalescence of nanovoids resulting clustering of vacancies are a viable source of fine dimples. Dimple patterns appear on hydrogen-assisted fracture surfaces of steel when a substantial ductility remains in degradation. Two cases are to be noticed for hydrogen effects on dimple formation. An increase in dimple size by hydrogen precharging was reported for tensile fracture of spheroidized near-eutectoid steels [9]. In that case, the diameters and spacing of carbides were less than or comparable to dimple size. Hydrogen precharging was under a high fugacity using cathodic electrolysis in 1 N H2 SO4 poisoned by arsenic at a current density as large as 300A/m2 . High hydrogen fugacity of precipitated hydrogen should have caused decohesion of the interface between carbides and the surrounding matrix, promoting the void formation and the following growth. On the other hand, hydrogen generally reduces the size of secondary dimples. On a mixed mode I/III loading fracture toughness test of a high-purity Ni–Cr–Mo–V steel of lower bainitic structure of 855 MPa in tensile strength, hydrogen precharging at an equivalent hydrogen fugacity of 1.26 MPa at room temperature degraded the fracture toughness, associated with reduced dimple sizes compared with those of uncharged specimens [10]. The fracture surface at a three-point bending test of a mildly hydrogen-precharged low-carbon medium-strength steel plate exhibited patterns consisting of mostly primary and secondary dimples [11]. Hydrogen precharging enlarged primary dimples while reducing secondary dimples. The area fractions of dimples with different depth (h)/width (w) ratios are shown in Fig. 7.4 [11] for hydrogen precharged and uncharged specimens. Hydrogen precharging increased the area fraction of

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A real Fraction (%)

60 50 40 30 20 10 0

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 Depth/Width of Dimple

Fig. 7.4 Area fractions of dimples with different depth/width ratio on fracture surfaces of a low-carbon medium-strength steel subjected to a three-point bending test with/without hydrogen precharging. The open and filled bars indicate non-charged and hydrogen-charged specimens, respectively (Nagumo et al. [11])

shallow dimples (h/w < 0.5). It implies that hydrogen reduces the extent of plastic deformation to form dimples; thus, the energy dissipated during ductile crack propagation. Shallowing of dimples generally characterizes moderate hydrogen degradation of steel. Examples are low alloyed steel in a three-point bending test [12] and Type 304 austenitic stainless steel in a tensile test [13]. An observation that suggested intimacy between dimple patterns and interface separation was tensile test results for as-quenched low-carbon martensitic steel [14]. An orientation relationship of the fracture surface that exhibited dimple patterns was parallel to {011}M planes which are also parallel to block and lath boundaries of martensite [14]. In that case, microcracks along prior austenite grain boundaries were present in areas far from the fracture surface. Hydrogen precharging was not mild, conducted by cathodic electrolysis in 1 N H2 SO4 with As2 O3 at a current density of 100A/m2 .

7.2.3 Quasi-cleavage “Quasi-cleavage” is a term that broadly indicates fracture surfaces adequately flat with irregular markings but not specified to cleavage planes. Quasi-cleavage (QC) often appears in hydrogen embrittlement of steel, and the morphologies substantially differ by microstructures, specimen geometries, and hydrogen-charging conditions. The fracture surface of low carbon-tempered martensitic steel (0.06C-5.9Ni1.2Mn-0.7Cr-0.2Mo), subjected to three-point bending after hydrogen charging, exhibited irregular flaky patterns of about 10 µm in size [15]. The specimens were a fatigue-notched standard Charpy type, and hydrogen precharging was conducted by

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(a)

(b)

20μm

20μm

Fig. 7.5 Fracture surfaces of a low-carbon ferrite–pearlite steel subjected to three-point bending tests (a) without and (b) with hydrogen precharging. (a) dimple and (b) quasi-cleavage patterns. Hydrogen charging is conducted by cathodic electrolysis in 3% NaCl+ 3 g/lNH4 SCN at a current density of 5A/m2 (Shimomura et al. [16])

cathodic electrolysis under a fairly high fugacity in poisoned 1 N H2 SO4 at a current density of 103 A/m2 . Scanning electron micrograph (SEM) revealed fine, lath-like features that correspond in dimension to martensite laths. From the shape of etch pits on the surface, their formation was on not cleavage {110} surfaces. Transmission electron microscopy (TEM) also revealed that the fracture surface was along martensite lath boundaries almost over its entire length. The lath boundaries are sites of high dislocation density. The observations also revealed many fine secondary cracks immediately beneath the fracture surface and their initiation at irregularities in the lath boundary, such as boundary intersections, steps, or foreign particles. The intermediate range between ductile and brittle fracture is wide. QC locates in the intermediate range, and its morphology is diverse. QC surfaces like a premature dimple fracture often appear in hydrogen embrittled medium-strength steels and moderately embrittled high-strength steels. Figure 7.5 compares low-carbon ferrite–pearlite steel fracture surfaces subjected to three-point bending tests with and without hydrogen precharging [16]. The hydrogen charging was conducted under mild fugacity by cathodic electrolysis in 3% NaCl + 3 g/l NH4 SCN at a current density of 5A/m2 . After the onset of the stable crack, shown in Fig. 6.13, dimple patterns for the uncharged specimen changed to QC with irregular morphologies by hydrogen charging. Fine striations also appeared in the latter. Effects of hydrogen are reasonably ascribed to the cause of premature fracture before round-shape dimples form by substantial growth of voids. The reduced roughness of the fracture surface by hydrogen shown in Fig. 7.4 is consistent with the decrease in the crack growth resistance by hydrogen shown in Fig. 6.15 for low-carbon ferrite–pearlite steel of similar compositions.

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QC surface in Fig. 7.5(b) is an extension of dimple fracture, but QC surface as an extension of intergranular fracture shows a significantly different morphology, as shown in Fig. 7.10. The latter usually appears in hydrogenated martensitic or bainitic high-strength steel. The morphologies manifest deformation microstructure to form the crack surface, naturally varying with steel microstructures. Microstructural changes under the QC fracture surface were investigated using a focused ion beam (FIB) technique. Martin et al. examined the correspondence between fine topographic features and underlying microstructures of API X60 and X80 pipeline steel subjected to compact tension tests in high-pressure (5–100 MPa) hydrogen gas [17, 18]. The fracture surface exhibited different morphologies, and the surface with striations was referred to as QC. A topographic surface map showed that striations running approximately parallel to the crack direction were, in fact, ridges. At low magnifications, ridges on QC [17] and fine undulations on flat, featureless regions [19] correlated with intense and highly localized shear bands. In high magnifications, the undulation was composed of small ~50 nm rounded mounds with a high density of dislocation lines and loops immediately beneath the surface [18]. Similarly, the fracture surface of a medium-carbon high-strength martensitic steel, which was gaseous hydrogen charged and subjected to four-point bending tests, showed “flat” and “QC” features [19]. The maximum nominal bending stress decreased by hydrogen from 2415 to 501 MPa at room temperature. A high density of dislocations with localized slip bands was revealed beneath both “flat” and “QC” features, while the flat one was along prior austenite grain boundaries with destructed lath boundaries. Martin et al. postulated that either near-surface relaxation after fracture or the underlying dislocation structures formed undulations and mounds on the fracture surface [18]. However, Lynch objected that mounds were possibly small, shallow dimples resulting from nanovoid coalescence during the fracture process [20]. Neeraji et al. carefully examined the fracture surfaces of hydrogen-precharged X65 and X80 line-pipe steel [21]. Evolution of a high dislocation density beneath QC facets was consistent with the observations by Martin et al., but mottled contrasts on the fracture surface were confirmed to be nanoscale dimples, 5 ~ 20 nm wide and 1 ~ 5 nm deep, of “valley-on-valley” type by mating halves of conjugate fracture surfaces. The findings indicate that nanovoid nucleation and linking, rather than the interface decohesion due to dislocation pileup, have occurred preceding the final fracture. QC and striations that characterize fractographic features of hydrogen embrittlement of steel originate in intense strain localization at shear bands. Grain boundaries and interfaces of different phases, providing flat planes, are preferential sites for strain localization, i.e., QC, before substantial plastic deformation proceeds over the entire specimen. Shear localization promoting final fracture is described in Sects. 7.3.2 and 10.1.3 about the mechanism of hydrogen embrittlement.

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7.2.4 Intergranular Fracture In many cases, fracture surfaces of hydrogen-degraded high-strength martensitic steel exhibit morphologies that match prior austenite grains. The features have been assigned to intergranular (IG) crack propagation along prior austenite grain boundaries and have served as a basis for brittle fracture models of hydrogen embrittlement. The IG fracture is typical in the temper embrittlement of martensitic steel. As for hydrogen effects, step-cooling heat treatment of HY 130 (900 MPa in the yield stress) steel drastically reduced the threshold stress intensity K th for no failure in edge-notched cantilever bend tests conducted in poisoned 0.1 N H2 SO4 using precracked specimens [22]. In unembrittled specimens, a slow crack growth started, showing fractographic features with some IG mode. The features soon shifted to a mixture of cleavage and MVC, then to full cleavage in the fast fracture region. On the other hand, the specimens embrittled by the step-cooling exhibited IG fracture from the crack initiation site through the slow and fast growth regions. Hydrogen favors IG fracture, and related results concerning the effects of impurity segregation in prior austenite grain boundaries on hydrogen embrittlement are described in Sect. 8.1.4a. The impurity effects similar to temper embrittlement of martensitic steel led to the idea that IG fracture in hydrogen embrittlement is intergranular decohesion. However, the IG fracture surfaces are not quite smooth, and fine markings associated with plastic deformation are usually present. Gerberich et al. exhibited fracture surfaces mixed with IG, QC, and MVC regions for hydrogen-precharged AISI 4340 steel subjected to sustained-loading tests using compact tension specimens [23]. Hydrogen precharging was by cathodic electrolysis in poisoned 5% H2 SO4 at a current density of 20A/m2 . The main fractographic features of specimens tempered at 503 K were IG and QC, and the fraction of IG increased by elevating test temperatures from 253 to 390 K. On IG facets, “brittle” striations appeared perpendicularly to the local crack growth direction. The striations occasionally accompanied some small tear ridges, and the spacing of striations was nearly coincident with the average martensite lath spacing of 1 µm. A discussion on the crack growth behaviors at the test is described in Sect. 6.2.2.2. Gerberich et al. assumed that brittle striations were intermittent arrest lines of the advancing IG crack. The appearance of IG was less ductile than QC. However, the increase in the areal fraction of IG by elevating test temperatures was against an expected increase in ductility associated with the thermal activation of dislocations. A few oxysulfides observed on IG surfaces were not associated with ductile tears and were assigned to the origin of IG at elevated temperatures. On the other hand, fractographic features of tempering at 723 K showed intermittent slow and fast-growing regions, accompanying mixtures of IG and MVC ductile rupture regions. The fraction of IG versus MVC was nearly fifty-fifty at room temperature. Ductile fingers or ligaments alternated in IG regions with a distance of about 200 µm. A series of second-phase particles were present on IG facets along ductile tearing striations. It was deduced that IG fracture started from the particles in regions 100 to 200 µm in extent and then destabilized the ligaments to cause tear by MVC.

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Alteration of fracture morphologies associated with an extending crack concern the stress fields and microstructures in front of the crack. Related information suggesting plasticity concerns was reported by Kameda according to X-ray diffraction line broadening on IG fracture surfaces [24]. Fracture surfaces of compact tension (CT) test specimens of hydrogen-precharged 3.5% Ni martensitic steel specimens showed IG fracture. Doping of phosphor and coarsening of prior austenite grain size reduced the threshold stress intensity and increased the crack growth rate. Rough and striped grain facets on fracture surfaces of undoped specimens became smoother and featureless by phosphor doping and grain coarsening. However, the {110} X-ray line was broader for the smooth surfaces than the rough surfaces. It indicates a substantial residual strain beneath the fracture surface, while plasticity is seemingly less on the fracture surface. Different morphologies might have a common mechanism, as described in Chaps. 9–10. This aspect is stimulated by IG fracture not specific to steel and the presence of hydrogen. Fracture surfaces of ultra-high-strength 7075 aluminum alloys containing high Mg and Zn solutes were predominantly IG mode at fracture toughness tests, and a decrease in fracture toughness was accompanied by increasing amounts of IG fracture [25]. High magnifications of IG surfaces revealed very shallow dimples with fine particles (~0.1 µm). In situ observations of thin-foil specimens revealed void initiation at grain-boundary precipitates. It was postulated that constraints against deformation near grain boundaries induced the void initiation. The evolution of IG fracture depends on the compositions of steel. Figure 7.6 shows fracture surfaces of medium-carbon Mn–Cr–Mo martensitic steel at slow-elongation rate tensile tests under simultaneous hydrogen charging [26]. The compositions of the steels were similar except Mn contents of 0.5, 1.0, and 1.5%. The specimens were plates of 2 mm in thickness and 10 mm in width without a notch. Simultaneous hydrogen charging was conducted by cathodic electrolysis in a 3% NaCl aqueous solution containing 0.5 g/l NH4 SCN at a current density of 5A/m2 . The tensile properties of the three steels were similar when hydrogen was absent, but a significant degradation appeared in hydrogen-charged specimens with increasing Mn contents. Fractures under hydrogen charging were always initiated near the corner of the specimen, with IG fracture mode prevailing. Fine tear patterns were frequently observed on IG surfaces, but the surface was smoother for higher Mn contents. Chemical etching of the IG surface with saturated picral revealed tear markings along martensite lath boundaries. The average roughness of the fracture surface, measured using scanning laser microscopy, decreased with increasing Mn contents, as shown in Fig. 7.7 [26]. The roughness corresponds to the dissipated plastic energy on the crack growth. Lower roughness implies lower resistance to the crack advance, and the smooth IG surface can be a crack path with minimal energy dissipation. The origin of energy dissipation in IG fracture is a subsequent issue. Martin et al. precisely examined dislocation activities regarding the IG fracture surface on Ni [27]. The material was a commercially pure Ni bar of 4 mm in diameter, thermally hydrogen charged in high-pressure hydrogen gas to about 2000 at ppm. The fracture surface by tensile straining at a strain rate of 4 × 10–4 /s was fully

7.2 Fractographic Features

181

Average Roughness (μm)

Fig. 7.6 Tensile-fracture surfaces of medium-carbon martensitic steels under hydrogen charging. Manganese contents: (a) 0.5, (b) 1.0, and (c) 1.5% (Nagumo et al. [26])

Quasi-Cleavage

1

Intergranular with tear ridges Flat Intergranular

0

0.5 1.0 1.5 Manganese Content (mass %)

Fig. 7.7 Average roughness and patterns of fracture surfaces shown in Fig. 7.6 (Nagumo et al. [26])

intergranular, but high-resolution fractography exhibited slip traces about 1 µm apart. The microstructure immediately beneath the fracture surface consisted of a high density of dislocations, organized into cell structures on the order of 200 ~ 400 nm of the average cell size. High dislocation densities extended to 4 ~ 5 µm from the fracture surface. The existence of a grain boundary was not observed immediately beneath the surface, and the crack was supposed to propagate in, not adjacent to, the grain boundary. Similar results were also obtained for iron that contained 25.8 at. ppm hydrogen [28]. A seemingly flat IG fracture surface was highly distorted in a magnified sale.

182

7 Microscopic Features Characterizing Hydrogen Embrittlement

(a)

(b)

(c)

microcrack

Fig. 7.8 (a), (b) Backscattering electron images and (c) Electron backscattering diffraction orientation map of the tensile-fractured Fe-0.2%C martensitic steel (Shibata et al. [29])

Shibata et al. examined a cross-section of a tensile-fractured specimen of asquenched and hydrogen-precharged 0.2% C martensitic steel [29]. Figure 7.8(a) and (b) are backscattering electron (BSE) images of a microcrack present beneath the tensile-fracture surface, and Fig. 7.8(c) is the electron backscattering diffraction (EBSD) orientation map around the area (b). Several micro voids likely coalesced and propagated along {011} planes, slightly away from the prior austenite grain boundary.

7.2.5 Alteration of Fracture Morphology on Crack Extension Fractography is a powerful tool to characterize the fracture type, but fractographic features are not uniform over the entire crack path. The stress-intensity factor K or J-integral, which represents the extent of stress fields in front of a crack, alters with the crack extension. The evolution of local deterioration of material that leads to fracture must vary with the crack extension. In an early study, a pop-in crack introduced by wedge-loading of AISI 4340 steel specimens in 3.5% NaCl solution propagated under a freely corroding (stress corrosion cracking, SCC) or attached to Mg anode (hydrogen-assisted cracking, HAC)

7.2 Fractographic Features

183

condition [30]. The fracture surface showed transitions in a sequence of ductile dimple, QC, IG, and fast fracture. The test was under a constant displacement condition using a wedge-loading CT specimen, and the stress intensity (K) decreased during the crack extension. Beachem postulated that dissolved hydrogen-enhanced deformation and that K, the content of dissolved hydrogen cH , and the microstructure determined the crack path. The combination of K and cH at the crack tip varies with time. Beachem proposed a qualitative diagram of the critical combination of K and cH for each fracture mode [30]. According to the diagram, the fracture mode changes as MVC → QC → IG by either a decrease in K at a constant cH or a decrease in cH at a constant K. A change in K with the crack extension implies changes in the intensity and extent of the stress fields in front of the crack, affecting the activation of local plasticity. The diagram was experimental, and microscopic details of various fracture modes were not shown. A change in the fracture mode of cracks from QC to IG was also observed for high-strength AISI 4340 and ASTM A490 steels subjected to constant-stress delayed fracture tests [31]. The steel was 1970 and 1700 MPa in tensile strength, respectively, and specimens were round or V-notched bars. Simultaneous hydrogen charging was by cathodic electrolysis in 1 N H2 SO4 at a current density of 10–1000 A/m2 . The length of the QC region increased with decreasing notch sharpness and applied stress level. It was deduced that QC triggered IG and that the crucial process for starting delayed fracture was QC associated with plasticity even though the macroscopic fracture mode was brittle-like IG. A subject of concern is the role of plasticity. Alternatively, a highly disordered microstructure was revealed on the fracture surface of a hydrogen-charged iron [32]. Plate specimens of a 0.06%C ferritic steel of 310 MPa in tensile strength were tensile fractured under concurrent cathodic hydrogen charging in a 3% NaCl+ 3 g/l NH4 SCN aqueous solution at a current density of 10 A/m2 . The hydrogen-charging condition was fairly mild, and the elongation to fracture was still as high as 19% in the presence of hydrogen. The fracture surface and the subsurface area were examined by transmission electron microscopy (TEM) using a focused ion beam (FIB) technique for the sample preparation. The selected electron diffraction (SAD) from the fracture surface showed halo patterns, and the lattice image of the surface layer showed disordered distributions of atoms. The thickness of the layer was less than 1 µm, and the dislocation densities in neighboring areas were very high, forming cell structures. Similarly disordered, amorphous-like layers of about 50 nm in thickness were occasionally observed along dislocation cell walls at about 1 µm below the fracture surface. In the above experiments, many short cracks were present transverse to the tensile axis on the side surface of the fractured specimens. Similar to the subsurface area, a featureless zone existed in the crack front, as shown in Fig. 7.9 [32]. The SAD pattern in the insert showed halo rings similar to that at the subsurface, and the dark field image clearly showed the presence of amorphous-like structures in the crack front. The featureless zone of a few 100 nm in length was within the plastic zone. Amorphization just below the tensile-fracture surface was also reported for hydrogenated Type 316L steel [33].

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7 Microscopic Features Characterizing Hydrogen Embrittlement

(a)

(b)

d110

Fig. 7.9 (a) Featureless zone revealed by transmission electron microscopy in front of a small side crack formed on an iron specimen tensile-fractured under concurrent hydrogen charging. (b) The dark field image of the encircled area in (a) from a hallo ring in selected electron diffraction (Nagumo et al. [32])

Solid-state amorphization induced by heavy plastic deformation has been obtained by mechanical alloying. The mechanical property of amorphous metallic alloys is characterized by low strain-hardening that promotes strain localization and plastic instability. Hydrogen drastically reduces the ductility of amorphous metals accompanying volume expansion [34]. Heavily disordered microstructures shown in Fig. 7.9 are in accord with the high densities of vacancies described in Sect. 3.2.3.2 and are viable as the origin of reduced ductility. However, only limited observations have been reported on the amorphous phase formation at hydrogen embrittlement.

7.2.6 Fatigue Fracture The fatigue crack growth (FCG) curves of some steels are shown in Figs. 6.20–6.23. Hydrogen generally accelerates the FCG rate in Stage II to Stage II’ (the extended stage of Stage II after transient hydrogen acceleration), but the FCG rates at a stressintensity range ΔK differ by steel and test conditions. Birenis et al. and Ogawa et al. examined the fracture surfaces of pure iron specimens subjected to fatigue tests in laboratory air and high-pressure hydrogen [35, 36]. Fatigue tests for fractographic examinations used a constant load amplitude (ΔP constant). Figure 7.10 by Ogawa et al. [36, 37] compares fracture surfaces of pure iron in the air, (a) and (c), and 0.7 MPa hydrogen, (b) and (d), at ΔK of 12 MPa·m1/2 . ΔK of 12 MPa·m1/2 was in Stage II in Fig. 6.21, before the onset of hydrogen acceleration in 0.7 MPa hydrogen. The FCG rates there were the same in the air and 0.7 MPa hydrogen, as shown in Fig. 6.21, but the fracture surfaces were substantially different. The surfaces are classified as QC. (Notice a broad range of the term “QC”, referring to Fig. 7.5.) A high magnification shown in Fig. 7.10(c) in air exhibits QC covered with narrow ductile striations of the spacing more than one order of magnitude larger than

7.2 Fractographic Features

(a)

185

(b)

5 μm

(c)

(d)

Fig. 7.10 Fatigue fracture surface of pure iron (a), (c) in air and (b), (d) in 0.7 MPa H2 (Ogawa et al. [36, 37])

the apparent da/dN. On the other hand, Fig. 7.10(b) in 0.7 MPa hydrogen exhibits the fracture surface consisting of IG-like shallow facets mixed with ductile tear patterns and striations. The inset in Fig. 7.10(b) shows fine striations on an IG-like facet. A high magnification in Fig. 7.10(d) shows a part of irregular flaky units without distinct striations. The hydrogen acceleration of the FCG rate was associated with change in the fractographic morphologies. An interesting result was that the area fractions of IG facets on the fracture surfaces were a function of ΔK values in the transition range, as shown in Fig. 7.11 [36]. The area fraction of IG decreases during the transition from Stage II to Stage II’ and falls to almost zero at the late Stage II’ in 0.7 and 20 MPa hydrogen. Accordingly, IG fracture per se is not the cause of a high FCG rate. For pure iron, the FCG rates in Stage II’ were almost the same in 0.7 and 90 MPa hydrogen, and fracture surfaces of fairly flat and fine striations of irregular directions were similar. On the other hand, for martensitic steel, the FCG rates in Stage II’ in 90 MPa hydrogen differed by the strength, or the tempering temperature, of each steel, as shown in Fig. 6.22. At ΔK of 23 ~ 35 MPa·m1/2 , fracture surfaces were QC as a

7 Microscopic Features Characterizing Hydrogen Embrittlement

Fig. 7.11 Area fraction of IG fracture surface of pure iron in high-pressure H2 as a function of ΔK (Ogawa et al. [36])

Areal Fraction of IG fracture surface (%)

186

60 50

ΔP constant test R =0.1, f =1Hz

50 %

40 34%

30 19%

20

Δ KT in 0.7 MPa H2

Δ KT in 20 MPa H2

10 0

10

12 14 ΔK, (MPa·m1/2)

16

18

whole, but IG-like facets or cracks were present [38]. The area fraction of IG fracture surface at a constant-load amplitude test was about 0, 20, and 40%, respectively, for steel of 811, 921, and 1025 MPa of the tensile strength. High magnification of the IG-like facet was covered with fine slip-like patterns. The relation between FCG rates and fractographic features is not conclusive and is a matter for further examination.

7.3 Strain Localization Strain localization is crucial in the void initiation and growth in plasticity-related fracture. Hydrogen effects on strain localization are vital for understanding the function of hydrogen in promoting fracture.

7.3.1 Surface Morphology Fractographic features such as shallow dimples and QC in hydrogen embrittlement suggest that hydrogen suppresses the extension of plastic deformation on crack propagation. Hydrogen-enhanced strain localization has been reported mostly with slip morphology. Straightening, coarsening, and increasing the height of slip steps in the presence of hydrogen are general features on the fracture surfaces and side surfaces of tensile-fractured austenitic stainless steel foil specimens [39, 40]. On the other hand, the depression of surface reliefs around the advancing fatigue crack is shown in Fig. 6.24 for a bulky specimen of hydrogen-precharged Type 304 stainless steel [41]. Hydrogen was thermally precharged to about 90 mass ppm in high-pressure hydrogen, and the fatigue test was tension compression at a stress ratio

7.3 Strain Localization

187

of −0.1 at the test frequency of 1.0 Hz. A small hole was drilled on the surface of specimens as the crack starter. The surface relief results from dislocation slip on different slip systems to accommodate stress relief on the crack advance. The effect of hydrogen reasonably confines the extent of the plastic region involved in the crack advance. For austenitic stainless steel, the primary factor that promotes the planarity of slip is stacking fault energy. In fcc metals and alloys, the stacking fault energy plays a crucial role in plastic deformation associated with the ease of cross-slipping. Hydrogen reduces stacking fault energy, and reported reductions are from 18 ~ 15 mJ/m2 to 12 mJ/m2 by 12 mass ppm of hydrogen and from 34.2 mJ/m2 to 27.7 mJ/m2 under 5.3 kPa of hydrogen gas for a Type 304 austenitic steel [42] and a Type 310S austenitic steel [43], respectively. The effects of alloying elements on stacking fault energy in austenitic stainless steel were calculated by a first-principles calculation [44]. However, other types of steel also showed enhanced slip localization by hydrogen. Localized deformation around the advancing fatigue crack similar to Type 304 was observed for a high-strength Cr–Mo martensitic steel subjected to tension compression fatigue tests [45]. Specimens were hydrogen charged by immersion in 20% NH4 SCN aqueous solution at 313 K. Compared to hydrogen-uncharged specimens, the fatigue crack growth was straighter, with slip bands more concentrated near the crack front. Effects of hydrogen on the morphology of slip bands were examined precisely for a 0.45% C steel with ferrite and pearlite structures subjected to rotational bending fatigue tests at 45 Hz using shallow-notched specimens hydrogen-precharged by immersion in 20% NH4 SCN aqueous solution at 313 K [46]. Slip band morphologies at the notch root, observed using a laser microscope for replicas of microstructures, were classified into three types, as illustrated schematically in Fig. 7.12 [46]. The fraction of ferrite grains of Type C with discrete localized slip bands was 49% in hydrogen-charged specimens after 6 × 105 fatigue cycles at 230 MPa, while Type C was not present in uncharged specimens. Also, about 20% of the crack initiation sites were along slip bands in hydrogen-charged specimens, while almost all were at grain boundaries in uncharged ones. The results demonstrated hydrogen-enhanced slip localization and the crack nucleation therein. Degassing by aging hydrogencharged specimens at room temperature for 270 h substantially reduced the fraction of Type C grains after fatigue tests. Intense slip bands act as crack initiation sites, as revealed in Fig. 7.2. Surface cracks at U-notch bend tests of spheroidized AISI 1090 steel specimens appeared at intense surface rumpling induced by slip bands [47]. The appearance was essentially the same between hydrogen-charged and uncharged specimens, but strain about a factor of two lower than uncharged ones brought about a similar surface roughness level or cracking in hydrogen-charged specimens [47]. A similar U-notch bend test was conducted for quenched-tempered AISI 4340 steel of 1.35 GPa in tensile strength with and without hydrogen precharging under a high hydrogen fugacity estimated to be 1GPa [48]. Hydrogen charging markedly reduced strain to fracture, and cracks nucleated internally in a mode I manner. The crack extension to the surface was along the characteristic slip path. Simultaneous hydrogen charging, instead of precharging,

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7 Microscopic Features Characterizing Hydrogen Embrittlement

Axial Direction 15 μm

Type A

Ferrite Grain

Type B

Slip Band

Type C Slip Localization

Fig. 7.12 Schematic illustrations of three types of slip bands at the notch root on 0.45% carbon ferrite–pearlite steel specimens subjected to rotational bending fatigue (Uyama et al. [46]. Reprinted with permission from John Wiley & Sons)

markedly promoted the crack nucleation reducing the plastic strain for the nucleation to zero.

7.3.2 Internal Structures On examining the tensile-fracture surface of hydrogenated austenitic stainless steel, Ulmer et al. took notice of the continuity of steps on the fracture surface to internal slip bands and the crack formation along active slip bands [39], similar to Fig. 7.2 for pure iron. It suggests the extent of the region that concerns crack extension. Since hydrogen diffusivity in austenite is very low, the crack formation is hardly ascribed to the precipitation of molecular hydrogen during the test. High-voltage electron microscopy (HVEM) revealed enhanced strain localization in the subsurface of fatigue cracks in Fe-2.6%Si single crystalline specimens [49]. The fatigue test was a sinusoidal tensile loading in hydrogen or helium gas of 0.58 MPa at a stress ratio of 0.1 and a test frequency of 1 Hz. The crack propagation was along the (110) plane in the [001] direction. Tests in hydrogen and helium gases exhibited remarkably different slip morphologies and crack outlines on cross-sections of specimens. In hydrogen, the crack tip was sharp, and the distribution of slip bands concentrated within 5 µm from the crack was consistent with the surface relief observed for austenitic steel [41]. Also noteworthy is that the immediate vicinity of the crack was severely deformed, while the crack outline was “brittle-like” straight. Slip bands were intermittently emitted from the crack tip, corresponding to the macroscopic crack growth rate. The findings indicate that the crack advance is facilitated by highly localized strain at the crack tip prior to the extension of the plastic region that accompanies the macroscopic crack opening. However, which enhanced strain localization itself or the associated creation of defects or damage is the primary function of hydrogen in the crack advance is a matter to be examined further.

7.3 Strain Localization Fig. 7.13 GROD map, showing the rotation from the average crystal orientation, around fatigue crack in iron, in (a) air, (b) 0.7 MPa H2 , and (c) 20 MPa H2 . The arrowheads indicate the crack tip positions (Birenis et al. [35])

189

(a)

(b)

(c)

Birenis et al. examined a mid-thickness cross-section along the crack path of pure iron specimens subjected to fatigue tests in laboratory air and high-pressure hydrogen [35]. As a measure of the magnitude of local strain, Birenis et al. employed the grain reference orientation deviation (GROD), i.e., the rotation angle of each grain from the average crystal orientation in electron backscattering diffraction (EBSD) analysis. Figure 7.13 shows GROD maps along the cracks propagated in air and hydrogen gas in ΔK-constant fatigue tests at ΔK of 17 MPa· m1/2 [36]. The crack runs from the upper to the lower side in the middle part of each map. The crack front is indicated by an arrow. Reduction in the width of the plastic zone, i.e., enhanced strain localization, by hydrogen is evident. The fracture morphology of specimens at ΔK of 17 MPa· m1/2 was generally QC according to Fig. 7.11, but the crack growth rates were in 90 MPa H2 > 0.7 MPa H2 > air. Hydrogen localizes plastic deformation in front of the crack, likely increasing the local density of damage. The involvement of plasticity in IG fracture, as a type of brittle fracture, is generally considered minor. However, in pure iron fatigue-fractured at ΔK of 10 MPa m1/2 under 20 MPa hydrogen, transmission electron microscopy (TEM) of the region just beneath the IG fracture surface revealed dislocation cell structures, as shown in Fig. 7.14 [36]. The cell size was fine, less than 1 µm, at closer sites to the fracture surface, and nanovoids were occasionally observed, indicated by yellow arrows, within or close to cell walls. Refined dislocation cell structures just beneath the fracture surface imply that hydrogen increases the energy density ahead of the crack tip. A high energy density and the associated deterioration of the material ahead of the crack tip must promote fracture at the crack tip. Which of the enhanced strain localization or the energy density is original is a vital issue for understanding the function of hydrogen to

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7 Microscopic Features Characterizing Hydrogen Embrittlement

Fig. 7.14 Transmission electron micrograph of an area beneath the fatigue-fracture surface of pure iron in 20 MPa H2. Yellow arrows indicate nanovoids (Ogawa et al. [36])

cause a premature fracture. Nanoscopic details of microstructures are requisite but not available at present. Hydrogen effects on developing deformation microstructures were precisely analyzed by Okada et al. with tensile tests of low-carbon steel of ferrite microstructures [50]. A 0.1C-2Mn (mass%) steel sheet austenitized at 1173 K followed by furnace cooling was hydrogen charged by cathodic electrolysis in a 3% NaCl+ 3 g l−1 NH4 SCN aqueous solution at a current density of 5 A/m2 . On slow strain-rate tensile test of 8.3 × 10–6 /s, some specimens were unloaded at strain of 3%, 11.5%, 20%, and 24%, corresponding to the end of the Lüders deformation, the middle point of work hardening, the ultimate tensile strength, and prior to final rupture, respectively. For specimens at each deformation stage, the dislocation morphologies were characterized using scanning transmission electron microscopy (STEM) at an acceleration voltage of 200 kV. At the initial stage of 3% strain, dislocations are linear while curved and tangled in the hydrogen-uncharged and hydrogen-charged specimens, respectively. At 20% strain, well-developed dislocation cell structures formed in both specimens without and with hydrogen charging. The cell is likely low energy dislocation structures, and the cell size tended to be smaller in the hydrogen-charged specimen than in the uncharged specimen. Figure 7.15 compares the statistical distributions of the cell size at 24% strain [50]. Further, STEM images with different diffraction vectors under two-beam conditions revealed the nature of dislocations. It was concluded that almost all of the straight dislocations in the uncharged specimen (ε = 3%) had a significant screw component. The fraction of the screw component increased in the later stage of deformation in hydrogen-charged specimens, as shown in Fig. 7.16, while a certain number of dislocations that form cell boundaries are excluded [50]. Okada et al. deduced that these straight dislocations would be the origin of the tangled dislocation

7.3 Strain Localization

191

H-charged, under QC Dislocation cell size ~ 0.36μm H-charged, 1 mm from cracktip Dislocation cell size ~ 0.51μm

Uncharged Dislocation cell size ~ 0.8μm

Dislocation cell size, (μm)

×1014 6

6

(a)

4

2

0 0

5

10 15 20 Nominal strain, (%))

25

Edge dislocation density, (m-2)

Screw dislocation density, (m-2)

Fig. 7.15 Size distributions of dislocation cell near the crack tip in low-carbon ferritic steel tensilestrained to 24% with/without H-charging (Okada et al. [50])

×1014

(b)

4

2

0 0

5

10 15 20 Nominal strain, (%))

25

Fig. 7.16 Fractions of (a) screw and (b) edge dislocation densities of the uncharged (solid lines) and hydrogen-charged (broken lines) low-carbon steel as a function of nominal strain (Okada et al. [50])

morphology in the hydrogen-charged specimen: If hydrogen increased screw dislocation mobility, frequent cutting of screw dislocations would result in the tangled dislocation morphology. Okada et al. also deduced that jog-dragging by screw dislocations formed many vacancies on the {011} slip planes. In another aspect, an increase in the fraction of screw components is the reverse of a reducing fraction of edge components, a process generating many vacancies as described in Sect. 3.2.1.2. The proposed mechanisms of HE are described in Chaps. 9 and 10. Methods to detect local strain distribution in materials are limited. Su et al. used in situ high-resolution X-ray tomography to observe internal strain and microvoids

192

7 Microscopic Features Characterizing Hydrogen Embrittlement

during tensile straining of Al–Zn–Mg–Cu aluminum alloys [51]. The synchrotron X-ray beam in Spring-8 was used at 20 keV, and the effective pixel size of the detector was 0.5 µm. The Al–Zn–Mg–Cu alloys of 0.6 mm in thickness contained about 7 mass ppm hydrogen introduced on electrodischarge machining of specimens. The alloys contained fine precipitates, η2 phase, and the internal strain was obtained from displacements of particles during straining. In the in situ tensile tests, the stress rise was intermittently stopped for an X-ray tomography scan, and the interruption caused stress relaxation while holding the displacement. On the fracture surface, QC cracks initiated near the surface of the specimen and gradually transformed into dimple fractures on propagation. The strain map revealed a highly heterogeneous strain in all the strain components, especially along the fracture surface in the strain localization region. Obliquely aligned shear bands were a form, and a high hydrostatic strain concentration indicated volume expansion. Transmission electron microscopy (TEM) in the strain localization region revealed nanovoids that induce volume expansion, distinguishing from precipitates and dislocation pileups. Su et al. calculated the volume expansion using the theoretically estimated vacancy concentration and compared it with the measured volume expansion [51]. The calculated values in the localized flow region were nearly half of the measured values.

7.3.3 Plastic Instability Plastic instability is the localization of plastic flow departing from a uniform deformation on stressing [52, 53]. Flow localization into a shear band appears as a void sheet linking [54]. Plastic instability evolves in uniaxial straining when the crosssection of a small portion of the specimen length reduces from that of the remainder, and the magnitude of the difference increases as straining proceeds. Plastic instability is a crucial process in ductile fracture, and its mechanistic significance for ductile fracture is described in Sect. 10.1.3. The appearance of rugged surface shear bands at U-notch bend tests of spheroidized AISI 1090 steel indicated the onset of flow localization or plastic instability [47]. Hydrogen promoted the evolution of surface rumpling and reduced the critical strain for the onset of plastic instability well before the profuse void formation in bulk. Internal small crack nucleation following surface rumpling was along characteristic slip traces, as shown in Fig. 7.17 [47]. Criteria for the onset of plastic instability are derived from material constitutive relations. The critical principal notch surface strain observed at the onset of plastic instability was in good agreement with the calculated values for a U-notched bend specimen [47]. However, for a U-notched bend test of hydrogen-charged AISI 4340 steel, the critical notch-root strain at the crack initiation was nearly constant for three different notch-root radii of specimens [48]. Constitutive relations, such as yield stress and work-hardening rate, are generally insignificant as hydrogen effects. Then, it was deduced that hydrogen promoted plastic instability and that a combination of hydrogen concentration and total stress

7.4 Damage Accumulation Precursory to Crack Nucleation Fig. 7.17 Schematic show of logarithmic spiral slip traces for circular notch root and the formation microcracks (Onyewuenyi et al. [47])

193

θ β

induced the crack nucleation within the plastic zone. The formation of a void sheet or its precursory crystalline disorder might be the cause of plastic instability. A crack initially formed in the central part of the specimen propagated step-wise following a “void sheet” path. Link-up of microcrack with a void situated at the tip of the microcrack by shear was reported for spheroidized AISI 1520 steel bar specimens subjected to axisymmetric tension after hydrogen precharging [54]. In that case, second-phase particles are not ruled out as the crack initiation sites, but hydrogen promotes plastic instability and favors crack nucleation and propagation. The onset of plastic instability is due to sequential void nucleation and coalescence process. Hydrogen effects of decreasing fracture toughness on the mixed mode I/III loading tests, shown in Fig. 6.11, and the stable crack initiation from the pre-crack, shown in Fig. 6.9, are likely due to promoting plastic instability described in Sects. 10.1.3 and 10.4.

7.4 Damage Accumulation Precursory to Crack Nucleation Hydrogen embrittlement attracts public attention when accidents in engineering service, such as delayed fracture of high-strength steel components or leak of sour oil/gas from pipes, happen. Most studies so far have remarked on the onset and growth of cracks. However, the degradation of materials in stages preceding the onset of fracture is crucial, and the effects of hydrogen on the creation of damage in materials are critical subjects. The term “damage” in engineering often addresses

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7 Microscopic Features Characterizing Hydrogen Embrittlement

flaws such as cracks or voids, but it is used widely in the present context, addressing crystalline deterioration far below the visual scale.

7.4.1 Damage Precursory to Crack Initiation 7.4.1.1

Microscopic Observations

An early study detected local lattice distortion as smearing of X-ray Kossel lines around hydrogen-induced cracks for pure iron single crystal [55]. Cathodic hydrogen charging at a current density of 300A/m2 without external stress produced internal cracks of 50–75 µm in size, accompanying lattice distortion localized within 100 µm from the cracks. However, distorted absorption conics (Kossel lines) were also observed in regions where cracking had not yet occurred. Broadening of X-ray diffraction line width, associated with hydrogen charging, was also observed for mild steel specimen cathodically hydrogen charged in poisoned 0.1 N H2 SO4 at a current density of 103 A/m2 , a high hydrogen fugacity [56]. The line broadening remained during exposure of specimens at room temperature but decreased about 25% at 473 K and almost disappeared at 673 K. Hydrogen trapped in elastic fields is ready to diffuse out at room temperature. However, its dissociation from strong traps like vacancies occurs at elevated temperatures, as described in Sect. 3.2.1. The aging behaviors implied that the line broadening was not due to elastic strain around hydrogen atoms but to plastic deformation induced on hydrogen charging. The aging behaviors are consistent with TDA results of Figs. 3.4(b) and 3.14, which imply the presence of vacancy-type defects created by plastic straining. Effects of hydrogen on inducing lattice distortion are prominent when plastic straining has been or is simultaneously applied to the specimen. The image quality (IQ) in EBSD analysis represents the crystallinity of the diffracting area, and dark contrast results from lattice distortion. Figure 7.18 [13] shows IQ maps of hydrogencharged Type 304 austenitic stainless steel given a tensile strain of 5% or 24%. The maps show lattice distortion with increasing strain more pronounced in regions close to grain boundaries than in bulk. The average strain separately obtained from Kernel average misorientation (KAM) maps, a measure of the orientation difference between neighboring areas, was reasonably lower for the specimen strained to 5% than that for 24%. However, a preferential strain localization appeared in hydrogen-charged Type 304 steel at a strain as low as 5% [13]. Annealing twins were often observed within grains, as indicated by arrows in Fig. 7.18, and twin boundaries tended to become blurred with increasing strain, implying distortion of areas near the interface of twin bands. Nibur et al. examined fractographic features and deformation microstructures of 21Cr-6Ni-9Mn austenitic stainless steel specimens subjected to a compact tension test after thermal hydrogen precharging [57]. The features somewhat differed by ferrite volume contents in the material, but shallow, non-equiaxed dimples and flat facets with limited plasticity characterized the effects of hydrogen precharging.

7.4 Damage Accumulation Precursory to Crack Nucleation Fig. 7.18 Image quality (IQ) maps of EBSD for hydrogen-charged Type 304 austenitic stainless steels tensile-strained to (a) 5% and (b) 24%. Arrows indicate annealing twin boundaries (Hatano et al. [13])

195

(a)

(b)

30µm

Examinations of cross-sections revealed the primary void nucleation at deformation band intersections, and concentrated microvoids were present along a continuous obstacle, such as another deformation band. Fine, elongated dimples covered relatively large facets. Microcracks were revealed along annealing twin boundaries at intersection points with deformation bands in the annealed material. The observations are consistent with the formation of small cracks at the intersection of slip bands shown in Fig. 7.1 for pure iron and the void nucleation in deformation bands shown in Figs 7.2 and 7.3 for ferritic steel. Fractographic features and deformation microstructures of austenitic stainless steels are further described in Sects. 8.3.3 and 8.3.4. Nibur et al. postulated that hydrogen-enhanced localized plasticity (HELP) causes strain discontinuities at obstacles and void nucleation. However, deterioration of crystallinity along twin boundaries shown in Fig. 7.18 for Type 304 steel is viable as the precursor of void nucleation. An issue is again which of the enhanced plasticity or the strain-induced generation of vacancies (HESIV) has hegemony for the function of hydrogen in promoting failure.

7.4.1.2

Detecting Lattice Defects

Lattice defects creation during rotational bending fatigue tests of hydrogenated highstrength Si–Cr steel is shown in Fig. 6.18, using TDA of hydrogen introduced as the tracer of defects. Samples of the tracer-hydrogen contents in Fig. 6.18 are portions close to the fracture surfaces. The fatigue-cycle dependence of the density of lattice

196

7 Microscopic Features Characterizing Hydrogen Embrittlement

defects was examined using the same test method for two martensitic steels, i.e., a high-strength Si–Cr steel bar designed for spring and a PC steel bar for prestressing tendon [58]. The amount of tracer-hydrogen increased in the latter half of fatigue lives for both steels, indicating damage accumulation prominently close to the final fracture. The amounts of tracer-hydrogen in fatigued specimens decreased by annealing at 473 K, indicating the vacancy-type nature of the lattice defects created before fracture. However, changes in the amount of tracer-hydrogen in the incubation stage were not simple, depending on the tested steel. Before an increase in the late stage of fatigue, the amount of tracer-hydrogen gradually decreased with fatigue cycles in PC steel, while the decrease was minimal in Si–Cr steel. The reason of the decrease and its dependence on steels is not definite, but reconfigurations or annihilation of dislocation structures during cyclic stressing were premised [58]. Similarly, lattice defects generated during delayed fracture tests were evaluated using tracer-hydrogen introduced into specimens subjected to fatigue cycles. Tracerhydrogen was introduced into specimens interrupting loading and degassing at 303 K for 168 h at the unloaded state. Figure 7.19 [59] shows the amounts of tracer-hydrogen introduced to fine-grain 0.32% C martensitic steel specimens subjected to sustained loading in 20% NH4 SCN aqueous solution at 323 K. The applied stress was 60% or 80% of the tensile strength, and both levels were apparently within the elastic range. In Fig. 7.19, the amount of tracer-hydrogen, i.e., hydrogen absorption capacity, initially decreased and then gradually increased with increasing loading time. In fractured specimens, the portions near the fracture surface showed substantially high tracer-hydrogen contents, as indicated by Δ and ▲ marks. The high values are due to concentrated strain near the fracture surface, likely associated with crack propagation, but the gradual increase before fracture is consistent with the strain-induced creation of vacancies and its concern with fracture. The initial decrease might be due to the reconfiguration of dislocations in martensite associated with hydrogen entry 5 Tracer-Hydrogen Content (ppm)

Fig. 7.19 Amounts of tracer-hydrogen introduced to martensitic steel bar specimens subjected to sustained loading at 0.6 or 0.8 of the tensile strength in 20% NH4 SCN aqueous solution at 323 K (50 °C). Δ and ▲ denote fractured specimens (Doshida et al. [59]. Reprinted with permission from The Iron and Steel Institute, Japan)

4

Near-fracture area

Near-fracture area

3

(0.8 σB)

(0.6 σB)

2 150 200 50 100 Elapsed Loading Time (h)

7.4 Damage Accumulation Precursory to Crack Nucleation

197

and loading. A similar initial decrease followed by a gradual increase in tracerhydrogen content was also observed for a rotational bending fatigue test of highstrength steel [58]. Alterations of TDA profiles with increasing sustained-loading time are consistent with the formation of vacancy clusters, as described in Sect. 2.2.1 concerning Fig. 2.5 and Sect. 3.2 concerning Figs. 3.5 and 3.11. Compositional dependence of hydrogen degradation in high-strength martensitic steel exhibiting IG fracture is presented in Figs. 7.6 and 7.7. The compositions of the steels were similar except Mn contents, and the slow-elongation rate tensile test was under simultaneous hydrogen charging [26]. A crucial issue concerning IG fracture is the involvement of plasticity in embrittlement. A useful tool to detect lattice defects is to utilize tracer-hydrogen, and the amount of absorbed tracer-hydrogen represents the densities of trap sites. Figure 7.20 [26] shows the amounts of hydrogen absorbed to saturation in specimens given various amounts of strain. The amounts for the three steels are almost the same when unstrained. On the other hand, a substantial increase by straining appeared more pronouncedly for higher manganese contents. As described in Figs. 3.2 and 3.10, TDA gives information about the nature of strain-induced defects. Figure 7.21 [26] shows TDA curves of tracer-hydrogen introduced into three states of the 1.5% Mn specimens, i.e., unstrained, strained to 2%, and annealed at 523 K for 1 h after straining. The increase in the amounts of tracer-hydrogen totally disappeared by annealing the strained specimen at temperatures as low as 523 K, indicating that lattice defects that interact with tracer-hydrogen are vacancies rather than dislocations. Thus, the origin of the effect of Mn contents is reasonably ascribed to the density of strain-induced vacancies. Precipitation of carbides along martensite boundaries was present, but quantitative differences in microstructures that specify the three steels were not definite. Related degradations of tensile properties are described in Sect. 8.1.4 concerning Fig. 8.11 Positron annihilation spectroscopy (PAS), described in Sect. 3.2.2, is a more direct method to detect damage, particularly vacancies with large free volumes. PAS Fig. 7.20 The amounts of hydrogen absorbed to saturation in specimens given various amounts of prestrain. The three martensitic steels with different Mn contents are used for Figs. 7.6 and 7.7 (Nagumo et al. [26])

Fig. 7.21 Thermal desorption profiles of tracer-hydrogen introduced to 1.5% Mn steel specimens, unstrained, prestrained to 2%, and annealed at 250 °C (523 K) for 1 h after straining (Nagumo et al. [26])

7 Microscopic Features Characterizing Hydrogen Embrittlement

50

Hydrogen desorption rate (10-3 ppm/min)

198

40

Strained Strained (2%) (2%)

30 Unstrained Non-deformed

20 Annealed Annealed at 250ºC after straining after straining

10 0

50

0

250

100 200 150 Temperature (ºC)

was applied to identify the type of lattice defects generated during tensile straining of hydrogenated Type 304 steel. Figure 7.22 [13] shows the mean positron lifetimes τ m of Type 304 and Type 316L steels given tensile strain with and without hydrogen charging to 30 mass ppm. Hydrogen charging enhanced the increase in τ m with increasing strain. The strain-induced increase in τ m implies the creation of lattice defects that have longer τ m than the bulk. Successive isochronal annealing of strained materials showed a monotonic reduction in τ m with increasing annealing temperatures [13]. The decrease in τ m by annealing continued to temperatures as high as 1000 K, but the enhanced increase in τ m by hydrogen disappeared by annealing at 573 K. 200

Mean Positron Lifetime,

Fig. 7.22 Mean positron lifetimes of strained austenitic stainless steels: ♦: SUS304, ◆: H-charged SUS304, Δ: SUS316L, × : H-charged SUS316L (Hatano et al. [13])

180 160 140 120 100 0

10

20

30 40 Strain (%)

50

60

70

7.4 Damage Accumulation Precursory to Crack Nucleation

199

The annihilation temperature corresponds to vacancy clusters, and the difference in hydrogen effects between Type 304 and Type 316L is reasonable to ascribe to the creation and clustering of strain-induced vacancies. The results are consistent with PAS measurements for iron [60]. However, the observed τ m is a weighted average of multiple lifetime components, as described in Sect. 3.2.2. The contributions of dislocations and vacancies to τ m for iron deformed with and without hydrogen precharging are tabulated in Table 3.5. Deformation microstructures are further described in Sect. 8.3.4.

7.4.2 Effects of Stress History—Damage Accumulation Hydrogen degradation manifests under various types of loading, and resultant mechanical properties are measures of degradation. Controlling factors of degradation differ by the type of loading, and the operating mechanism might not necessarily be identical. Structural components tolerate various stress histories during service. However, the damage produced in the early stages is carried over to the final fracture. In this section, some studies about the effects of stress histories on hydrogen degradation are presented. In Sect. 6.1, the viable role of vacancy-type lattice defects in hydrogen degradation is presented for tensile tests of iron, cold-drawn eutectoid steel, and Inconel 625 alloy. Cyclic variations of applied stress promote failure at sustained-loading delayed fracture tests of martensitic steel as described in Sect. 6.4.3a. The degradation by cyclic prestressing implies the accumulation of strain-induced damage when the plasticity induced by prestressing is minor. Then, the effects of cyclic prestressing with and without hydrogen on tensile tests were examined for martensitic steel of 1433 MPa in tensile strength concerning the creation of damage [60]. Initially, the applied stress was cyclically varied in the range of 0.7 ± 0.1 of the tensile strength under hydrogen charging by immersing specimens in 20% NH4 SCN solution at 323 K. The specimens with and without hydrogen charging were denoted as [σ + H] and [σ ], respectively. Degradation of tensile properties due to hydrogen was expressed in terms of the hydrogen embrittlement susceptibility (HES), defined as the ratio of the fracture strain of [σ + H] to that of [σ ] specimens at following tensile tests. Effects of cyclic prestressing on HES are shown in Fig. 7.23 [61] for increasing numbers of prestressing cycles at various strain rates. Cyclic prestressing enhances HES, i.e., hydrogen degradation, more pronouncedly by increasing the number of cycles and reducing the strain rates. Damage introduced by cyclic prestressing was then examined using hydrogen as the tracer. Tracer-hydrogen was introduced to saturation to cyclically prestressed specimens after exposing prestressed specimens at 323 K for 168 h to delete hydrogen present at the prestressing stage. External stress was not applied when introducing tracer-hydrogen under the same condition as the initial charging. The amounts of tracer-hydrogen increased with the number of stress cycles in both [σ ] and [σ + H] specimens. The difference between [σ + H]

Fig. 7.23 Hydrogen embrittlement susceptibility (HES) on tensile tests of martensitic steel specimens applied cyclic prestressing at various strain rates (Doshida et al. [61])

7 Microscopic Features Characterizing Hydrogen Embrittlement

Hydrogen Embrittlement Susceptibility, (HES)

200

Number of Cycles at Prestressing

and [σ ] specimens was denoted as ΔC H . It is a measure of the increased damage due to hydrogen. The amount of ΔC H represents hydrogen effects on the strain-induced creation of defects at cyclic prestressing. The magnitude of ΔC H increased with cyclic stressing more pronouncedly with lower strain rates, as shown in Fig. 7.24 [61]. The increase in ΔC H with decreasing strain rate is consistent with Fig. 6.4b in Sect. 6.1.1.2 for tensile tests. It indicates that cyclic stressing accumulates damage prior to the tensile tests. The tracer-hydrogen thermal desorption profiles showed a single peak centered at about 393 K, and ΔC H humped the higher-temperature side of the TDA peak, implying vacancy clusters as described in Sect. 3.2.3.2. An approximately linear correspondence exists between HES and ΔC H [60]. It supports the notion that the hydrogen-enhanced creation of damage causes degradation throughout the whole stage of plastic deformation. In Sect. 6.3.1, promoted fracture by hydrogen at rotational bending fatigue tests of high-strength Si–Cr steel is described, and the defect creation in the early stages of tests before the final fracture is shown in Fig. 6.18. Similarly, in delayed fracture, defects are accumulated in the incubation period, as shown in Fig. 7.19 for high-strength Si–Mn martensitic steel. The findings lead to the notion that stress histories play a crucial role in hydrogen degradation. An experiment that demonstrated the effects of prefatigue on following sustained loading delayed fracture tests is shown in Fig. 7.25 [62] for the Si–Cr martensitic steel used for Fig. 6.16. Stress cycling (prefatigued) was applied by rotational bending for cycles about a half (Treat-A) of or close (Treat-B) to the fatigue life at the applied stress amplitude level of 640 MPa [62]. The two types of specimens were successively subjected to sustained-loading delayed fracture tests in 20% NH4 SCN

Fig. 7.24 Hydrogen enhancement of the strain-induced increase in the hydrogen absorption capacity, ΔC H , on tensile tests of martensitic steel specimens after cyclic prestressing at various strain rates (Doshida et al. [61])

201

Δ CH (mass ppm)

7.4 Damage Accumulation Precursory to Crack Nucleation

Number of Cycles at Prestressing

aqueous solution at 323 K. Specimens without prefatigue (Treat-N) were also tested for comparison. The fracture of specimens given prefatigue for cycles close to the fatigue life, Treat-B, occurred substantially earlier. However, annealing the fatigued specimens at a temperature as low as 473 K for 1 h reduced the degradation caused by prefatigue. The results indicate that damage accumulated during prefatigue plays a function in failure common to that created during sustained loading and that damage introduced by prefatigue is mostly vacancies without forming flaws such as voids and cracks. Inversely, damage accumulated in sustained loading deteriorated tensile properties following the sustained loading [62]. Specimens of 5 mm in diameter of high-strength martensitic steel, 1433 MPa in tensile strength, were initially sustained-loaded at a constant stress of 80% of the tensile strength, apparently within the elastic range, for 96 h in 20% NH4 SCN aqueous solution at 323 K. After the sustained loading, hydrogen was completely removed at 303 K for 168 h, and then, some specimens were annealed at 473 K for 2 h. The two series of specimens are denoted as [H+ stress (96 h)] and [H + stress (96 h) + 200 °C], respectively. Also, specimens without sustained loading but annealed at 473 K were prepared with the notation of [non-stressed + 200 °C]. Stress–strain curves at tensile tests are shown in Fig. 7.26 [61]. It is to be noticed that a substantial degradation appeared for the [H+ stress (96 h)] series, although hydrogen was absent at the time of tensile testing. The almost complete recovery for the [H+ stress (96 h) + 200 °C] series indicates that vacancy-type defects, created during sustained loading without forming irreversible voids or cracks, cause the degradation. Effects of environmental variations on delayed fracture, described in Sect. 6.4.3b, are similar to stress histories in respect of the damage accumulation. The stress history

202

7 Microscopic Features Characterizing Hydrogen Embrittlement

0.7

Applied Stress Ratio, σ/σB)

0.6 0.5 0.4 0.3 0.2 0.1 0 10-3

10-2

10-1 1 10 Time to Fracture (h)

102

10 3

Fig. 7.25 Delayed fracture diagrams for prefatigued Si–Cr martensitic steel. ⎕: N (without prefatigue), Δ : B (prefatigued close to failure), ◆: B (annealed at 200 °C for 1 h after prefatigue), 〇: A (prefatigued to about one half of fatigue life) (Nagumo et al. [62])

[H+stress (96 h)] [H+stress (96 h)+200ºC] [non-stressed+200ºC]

Fig. 7.26 Tensile curves of high-strength martensitic steel specimens. [H+ stress (96 h)]: Initially sustained-loaded in 20% NH4 SCN aqueous solution for 96 h at 50 °C (323 K), [H+ stress (96 h) + 200 °C]: Annealed at 200 °C (473 K) after sustained loading, [non-stressed + 200 °C]: Annealed at 200 °C (473 K) without sustained loading. All specimens are degassed at room temperature before tensile tests (Doshida et al. [61]. Reprinted with permission from The Iron and Steel Institute, Japan)

References

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effects imply that the function of hydrogen in embrittlement must be examined over the entire fracture process, not merely at the final crack initiation and propagation stages. The cumulative deterioration of material must be a crucial aspect of the function of hydrogen in embrittlement.

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Chapter 8

Microstructural Effects in Hydrogen Embrittlement of Steel

The preceding two chapters describe elementary features characterizing hydrogen embrittlement (HE) of steel. HE of steel is susceptible to microstructures, and understanding of functions of microstructural factors is indispensable to proper designs against environmental degradation. Many studies have been conducted, and early works on material and environmental factors are in a review by Moody et al. for iron-base alloys [1]. Effects of alloying elements focusing on trapping of hydrogen were reviewed by Bernstein and Pressouyre [2]. It should be noted that a procedure to control a specific microstructural factor occasionally affects other factors, and separating each factor’s contributions is not straightforward. For example, the grain refinement conducted by recrystallizing coldworked iron accompanies the recovery of substructures during annealing. Also, the effects of material factors depend on environmental and mechanistic conditions. Comparisons of susceptibilities to HE of different materials must be made under proper conditions. Functions of microstructural factors in HE manifest not only in mechanical properties but also in features such as fracture morphology, strain localization, and damage accumulation. Interactions of hydrogen with lattice defects in processes preceding the final fracture influence the final degradation. Accordingly, functions of microstructural factors must be examined throughout the entire process leading to fracture. However, studies in this context are limited in the literature. Early studies were rather phenomenological, as a matter of course, lacking modern microscopic information. In this section, the stability of substructures against external stress in the presence of hydrogen is paid particular attention to the effects of microstructural factors. It is to be noticed that the mechanism or function of hydrogen presented in each case is a subject revisited with caution.

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 M. Nagumo, Fundamentals of Hydrogen Embrittlement, https://doi.org/10.1007/978-981-99-0992-6_8

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8 Microstructural Effects in Hydrogen Embrittlement of Steel

8.1 Martensitic and Bainitic Steel 8.1.1 Tempering of Martensite and Bainite The microstructure of lath martensitic steel is shown in Fig. 8.1 using an electron back scattering diffraction (EBSD) orientation map and a schematic illustration of structural units [3]. A prior austenite grain consists of several packets, each of which is an assembles of laths of the same habit planes. A packet consists of blocks, each of which is an assembly of laths of the same variants. Tempered martensite is the most common microstructure of high-strength steel. On tempering, internal stress is relieved by rearranging a high density of dislocations to stable structures and by precipitation of supersaturated solute carbon to carbides. Then, two main aspects are on the effects of tempering, one is substructures, and the other is precipitates morphologies. Effects of tempering temperatures on Stage II crack growth rates and fractographic features in fracture mechanics tests are described in Sects. 6.2.2.2 and 7.2.4, respectively, for hydrogen-precharged AISI 4340 steel. An increase in tempering temperatures from 503 to 723 K reduced the yield strength from 1620 to 1340 MPa and Stage II crack growth rates. Fractographic features changed from mixtures of intergranular (IG) and quasi-cleavage (QC) to alternate IG and multiple void coalescence (MVC) regions with 100–200 μm intervals. Gerberich et al. assumed that different brittle fracture initiation sites between the two tempering conditions determine the Stage II crack growth rate [4]. Martensite lath intersections with prior austenite grain boundaries or oxysulfides are the proposed fracture initiation sites for the high- and low-strength steel. Elevated tempering temperatures generally stabilize substructures and reduce the strength of martensite. Effects of tempering temperature are shown in Fig. 8.2 for the threshold stress intensity, K ISCC , at delayed fracture tests of 0.35C–Cr–Mo steel (SCM435 in Japanese Industrial Standard) [5]. The steel was additionally alloyed

(a)

(b) block

Block boundary Packet boundary Prior γ grain boundary

packet γ grain boundary

Fig. 8.1 Structures of acicular martensitic steel. (a) Electron Back Scattering Diffraction orientation map and (b) schematic illustration of structural units (Shibata et al. [3])

8.1 Martensitic and Bainitic Steel

207

Fig. 8.2 Dependence of KISCC on tempering temperatures for medium-carbon Cr–Mo martensitic steels. A 0.04Nb, B 0.04Ti + 0.10 V or C 0.10 V + 0.04Nb (mass%) to the base compositions (Owada et al. [5]. Reprinted with permission from The Iron and Steel Institute, Japan)

with (A) 0.04Nb, (B) 0.04Ti + 0.10 V or (C) 0.10 V + 0.04Nb (mass%) to the base compositions to control the strength level at a given tempering temperature. The delayed fracture test was a cantilever beam bend test in 3% NaCl aqueous solution using fatigue-notched specimens. Figure 8.2 separates the effect of tempering temperature on K ISCC from tensile strength, classifying K ISCC data into three levels in tensile strength. Lower tensile strengths obtained by higher tempering temperatures generally elevate the K ISCC level, i.e., reduce the susceptibility to HE, but higher tempering temperatures increase K ISCC even at a constant strength level. The ratio of K ISCC to the separately measured fracture toughness K I under non-corrosive environment was 0.45 ~ 0.15 at a given tensile strength [5]. A proper alloy design makes it possible to keep a high-strength level while elevating tempering temperature, as shown for Mo-V martensitic steel concerning reduced stress relaxation, Fig. 5.5 in Sect. 5.3.1. Secondary hardening due to the precipitation of VC at tempering of vanadium-bearing martensitic steel enables to raise tempering temperature, keeping the same strength. Improvement in the susceptibility to sustained-loading delayed fracture by the precipitation of VC is shown in Fig. 6.28 [6] for a 0.37C-0.6Si-1.0Mo-0.5Cr-0.54 V (mass%) martensitic steel tempered at 823 and 923 K. The precipitation of VC reduced the stress-relaxation rate and its enhancement by hydrogen, as shown in Fig. 5.5 [6]. Fine VC precipitates are likely to act as barriers to the motion of dislocations and their slip extension, coupled with more stabilized structures of martensite by tempering at a higher temperature. Stabilized substructures by elevating tempering temperature reduce internal strain as observed by a linear decrease in the broadening of X-ray diffraction line width [5]. Figure 8.3 [5] shows good correlations between K ISCC and internal strain estimated from the half-width of the X-ray diffraction line for the steels in Fig. 8.2. The results strongly suggest internal strain or associated dislocation arrangement is a crucial factor controlling the susceptibility to HE of martensitic steels.

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8 Microstructural Effects in Hydrogen Embrittlement of Steel

Fig. 8.3 Relationship between KISCC and internal strain estimated from X-ray diffraction line broadening for the steel in Fig. 8.2. (The unit for strain may not be correct.) (Owada et al. [5]. Reprinted with permission from The Iron and Steel Institute, Japan)

Bainite is a generic term for intermediate microstructures between pearlite and martensite reactions at the austenite decomposition [7]. The apparent structures widely vary according to transformation temperatures. Lower bainite that forms between 323 and 673 K is composed of fine ferrite plates with morphology close to martensite plates. Fe3 C and ε iron-carbide precipitate within the ferrite plates, and the dislocation density is high. The strength of lower bainite is high, but the structures are more stable than as-quenched martensite. Comparisons of the time to fracture at delayed fracture tests for tempered martensitic and lower bainitic steels are shown in Fig. 8.4 [8]. The steels are medium carbon low-alloy steel of various compositions, and some are further micro-alloyed with V, Nb, and Ti. Isothermal transformation at 593 K or oil-quenching from austenitizing at 1273 K was given to produce bainite or martensite structures, respectively. Tempering temperatures were 873 or 773 K for the respective structure. Delayed fracture tests in Fig. 8.4 were by three-point bending at a constant strain under an applied load of 1000 MPa in 0.1 N HCl at 285 K, using circumferentially V-notched round bar specimens of 10 mm in diameter. Superior resistance to delayed fracture of lower bainite compared with martensite is evident. The crack growth in martensitic and bainitic steel was also measured using an electric potential method at a sustained-loading four-point bending test with U-notched rectangular bar shape specimens [8]. Specimens of the two structures were 1500 MPa in tensile strength, and the initially applied stress intensity was 1500 MPa·m1/2 in 0.1 N HCl at 285 K. The incubation time to initiate cracking was 105 and 55 min for bainite and martensite, respectively, and the crack growth rate was about one order of magnitude slower for bainite than martensite. Further, K ISCC , defined as the threshold stress intensity at which a growing crack was arrested, was measured

8.1 Martensitic and Bainitic Steel 1000

Medium C Mn-Ni-Cr-Mo-Cu Steel Tempered Bainite

100

Time to Fracture (h)

Fig. 8.4 Relationship between tensile strength and time to fracture at nominal bending stress of 1000 MPa in three-point bending delayed fracture test in 0.1 N HCl solution (Nakasato et al. [8])

209

Medium C Mn-Ni-Cr-Mo-Cu Steel Tempered Martensite

10

Conventional Steel (SCM3, SNCM8) Tempered Martensite

1 1300

1400 1500 1600 1700 Tensile Strength (MPa)

1800

using a constant-strain wedge opening loading test in 0.1 N HCl at 285 K or in distilled water at 323 K. In that test method, stress intensity decreased with the crack extension, and K ISCC of the two structures were almost the same irrespective of test solutions. A highly supersaturated solute carbon precipitates cementite on tempering, and cementite acts as void nucleation sites on tensile deformation, as observed for spheroidized carbon steel [9], even at low hydrogen fugacity [10]. In the experiment cited above [8], precipitation of cementite along prior austenite grain boundaries was substantial in martensitic structures, and IG fracture was dominant. On the other hand, the cementite precipitation within lath was dominant in bainite structures, and the fracture surface showed QC. The lower crack growth rate in bainitic structures might be ascribed to the cementite morphology. However, some fractions of IG existed for bainite depending on the stress intensity level. The IG fracture mode was dominant for bainitic structures at applied stress levels near K ISCC . Effects of cementite morphology on delayed fracture may depend on stress states and deformation stages. Microstructural alterations caused by tempering martensitic steel are diverse, such as stabilization of dislocation structures, generation of fine precipitates, impurity segregation in grain boundaries, alteration of the strength level, and so on. Which of them is primary in interactions with hydrogen to cause premature fracture must be carefully examined.

8.1.2 Precipitates Most martensitic steel micro-alloyed with Ti, Nb, and V contains uniformly distributed fine carbides and/or nitrides. The precipitates are associated with coherent

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8 Microstructural Effects in Hydrogen Embrittlement of Steel

strain around the particles in the early stage of precipitation and act as obstacles for dislocation motion, retarding the decomposition of martensite and causing secondary hardening. Interactions of hydrogen with the precipitates increase the hydrogen absorption capacity of steel and reduce hydrogen diffusivity. Morphologies of precipitates are strongly dependent on tempering temperatures, and their function in HE is complicated depending on the situation. Effects of V and Ti and additional Mo on sulfide stress cracking (SSC) were examined for 0.4C-1Cr-0.2Mo (mass%) martensitic steel in sustained-loading delayed fracture tests in the NACE solution (5% NaCl+ 0.5% glacial acetic acid saturated with H2 S, pH = 3) [11]. Tempering temperatures of two levels were chosen to give tensile strength in 900/950 and 1000/1050 MPa. Micro-autoradiography revealed fine precipitates, ≤ 20 nm in size. The SSC resistance in terms of the no-failure threshold stress for all the modified steel was higher than the reference steel, which did not contain micro-alloying elements. Tempering temperatures for the two tensile strength levels were between 923 and 983 K, and the best combination of alloying elements for the threshold stress was 0.1 V-0.1Ti-0.8Mo at the tensile strength of 1000 MPa. Concentrations of weakly trapped diffusive hydrogen and diffusivities of hydrogen were also measured, but their differences among various combinations were slight, and no systematic correlations with the threshold stress were found. Charbonnier et al. postulated that the strong hydrogen trapping potentiality of fine carbides was beneficial for the SSC resistance [11]. Their experiments measured hydrogen concentration and diffusivity using permeation and vacuum desorption methods without applying external stress. Accordingly, the trapped states of hydrogen might differ from those in stressed specimens in delayed fracture tests. The tensile strengths of specimens were the same at 1000 MPa, but different tempering temperatures, 973 K for the 0.1 V-0.1Ti-0.8Mo steel and 933 K for another steel, might have stabilized substructures, affecting the SCC susceptibility. The superior resistance to delayed fracture in long-term atmospheric exposure was reported for vanadium-bearing martensitic steels tempered at high temperatures [12]. Steels of various compositions ranging from 1100 to 1630 MPa in tensile strength were exposed at the seaside for up to one year under external stressing. The specimens were circumferentially notched round bars, and the applied external stress was at the yield strengths. The fracture ratio, i.e., the number of failed specimens against the total 60 specimens, was used to measure the susceptibility. The best without failure was a 0.4C-1.2Cr-0.58Mo-0.35 V (mass%) steel tempered at 863 K giving 1450 MPa in tensile strength. However, the effects of vanadium were sensitive to tempering temperatures. For V-bearing steel of 0.3C-1Si-2Cr-0.4Mo-0.35 V (mass%), the fractions of failed specimens were 6.7% and 63% for the tensile strengths of 1537 and 1627 MPa by tempering at 783 and 703 K, respectively. Delayed fracture did not occur for an Altreated 0.2C-0.76Mn-0.64Cr (mass%) martensitic steel tempered at 623 and 713 K to the tensile strength of 1303 MPa and 1078 MPa, respectively. The above results by Yamazaki et al. were a part of studies to assess the susceptibility to delayed fracture, described in Sect. 6.4.4b.

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211

Thermal desorption profiles of hydrogen introduced to the Mo-V steel tempered at different temperatures are shown in Fig. 3.17, indicating that VC acts as strong trap sites. Hydrogen was the tracer of defects, and Fig. 8.5 [6] shows the amounts of tracerhydrogen recharged to specimens subjected to sustained loading under simultaneous hydrogen charging. Three conditions of specimens, i.e., (a) original without loading, (b) loaded for 8 h at 0.4 of the tensile strength, and (c) subsequently annealed at 473 K, are compared. The open and filled bars in Fig. 8.5 denote measurements after 15 min or 24 h from hydrogen charging, respectively. The difference between the open and filled bars shows the amount of diffusive tracer-hydrogen at room temperature. Figure 8.5 indicates that applying external stress in the presence of VC enhances the creation of not only weak but also strong trap sites that remain at annealing at 473 K. The two tempering temperatures hardly affected the total amounts of diffusive hydrogen, against the presumption that the amount of diffusive hydrogen is decisive to the susceptibility. Comparing loaded and annealed conditions for specimens tempered at 923 K (650 °C) implies that the trap sites of diffusive hydrogen are mostly vacancies because annealing almost annihilated the trap sites. The amounts of diffusive hydrogen are similar between the two annealing temperatures, but the fraction of vacancies is much less in the VC-containing steel. Limitations of using hydrogen concentration are noteworthy in assessing the susceptibility to hydrogen embrittlement. The observed total or the average hydrogen concentration per unit volume is not always a measure of the susceptibility to HE,

Fig. 8.5 The amounts of tracer-hydrogen introduced to three states of martensitic Mo-V steels tempered at 550 (823 K) and 650°C (923 K). (1) Non-loaded, (2) Subjected to delayed fracture tests at 0.4 of the tensile strength, (3) Annealed at 200ºC after delayed fracture tests. ⎕: Measured after 15 min after H-charging, ∎: Measured after keeping at 30°C (303 K) for 24 h. M. Nagumo et al. (2003) [6]

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8 Microstructural Effects in Hydrogen Embrittlement of Steel

since local plastic deformation and, thus, local trapped states of hydrogen are crucial for fracture. As observed, a uniform and dense distribution of VC particles should increase the total hydrogen absorption capacity, but a uniform distribution of VC may reduce strain localization and, thus, the local density of induced lattice defects. Such strain dispersion, rather than hydrogen itself, might be the cause of reducing the susceptibility. Details of structural alterations during straining associated with fine precipitates are not definite. Some stress-induced alterations of dislocation arrangements around the precipitates are possible origins of forming strong trap sites and stabilizing dislocation arrangements, reducing the stress-relaxation rates. Tsuchida et al. conducted transmission electron microscopic observations of martensitic vanadium-bearing steel during tempering, referring to hydrogen absorption behaviors [13]. Effects of precipitates, in many cases, overlap those of stabilized microstructures by tempering that generates precipitates.

8.1.3 Grain-Size Effects The term “grain size” in martensitic steel usually addresses prior austenite grain. The austenitizing temperature is often a controlling variable of grain size, but it accompanies compositional alterations of solute elements, including impurities present in grain boundaries. The apparent effects of grain size on HE in the literature must be carefully examined concerning other contributions like alterations of martensite substructures associated with experimental procedures such as solutionizing or annealing after cold working. (a) Fracture mechanics tests Grain-size effects have been evaluated in fracture mechanics tests about the crack growth rate and the threshold stress intensity K TH at the onset of cracking. Hydrogen effects on crack growth are described in Sect. 6.2.2. An early study by Lessar and Gerbrich for AISI 4340 steel was on grain-size effects on K TH , yield strength, and crack velocity [14]. In the experiments, the prior austenite grain size was controlled from 20 to 140 μm by varying austenitizing temperatures and holding times. Austenitizing at 1173 K for 1 h and 1373 K for 16 h also altered the tensile strength of the steel from 1460 to 1230 MPa. The tempering temperature was 573 K for all specimens. The crack length and the applied stress intensity were calculated from the load versus time record of V-notched double cantilever bend (DCB) specimens under a constant displacement. Hydrogen was precharged by cathodic electrolysis in a poisoned 4 wt.% H2 SO4 solution at a current density of 60A/m2 and was then enclosed by Cd-plating. Figure 8.6 [14] shows Stage I and II crack growth rates of steel of various grain sizes as a function of the applied stress intensity. The test was a K-decreasing type with crack growth, and the results were complicated. Separately conducted plots showed inversely proportional Stage I crack growth rates at 33 MPa·m1/2 to the square of

8.1 Martensitic and Bainitic Steel

213

Fig. 8.6 Stage I crack growth rates at DCB tests for hydrogen-precharged AISI 4340 steels of various grain sizes (Lessar et al. [14])

the grain size. On the other hand, K TH increased with the increasing grain size. The grain-size effects were associated with fracture morphologies. The primary failure mode for all grain sizes was IG, but the smaller grain size, in general, displayed a more significant amount of tear mode failure. Increasing grain size raised K TH , but the net increase in K TH was slight since grain coarsening concomitantly decreased the yield stress. Lessar et al. noticed that the grain size primarily affected the growth rate rather than K TH and suggested that the crack growth kinetics were affected mainly by hydrogen diffusion. When the grain size was significantly large, exceeding the plastic zone size, the increased grain size improved resistance. In the crack growth, the existence of grain boundaries in the crack front plastic zone must be crucial Grain-size effects with constant yield strength were investigated for fcc superalloy IN903 [15]. Varying solution temperatures obtained grain sizes ranging from 23 to 172 μm, and double aging controlled the yield strength, independent of grain size. Slow crack growth was measured using bolt-loaded wedge opening loading (WOL) specimens at 298 K in 207 MPa hydrogen gas. The crack growth threshold K TH increased slightly but proportionately to the square root of the grain size. Comparing data for AISI 4340 and IN 903, Moody et al. concluded that grain-size effects on K TH were the same for the two alloys when IG fracture prevailed [15]. In martensitic steel, impurities substantially affect fracture toughness. Effects of grain size and P-doping on the crack growth rate and the threshold stress intensity K TH for the crack initiation were examined for a 0.3C-3.5Ni-1.7Cr (mass%) martensitic steel of the same yield strength of 1275 MPa, [16]. Austenite grain sizes were varied in the range of 35–450 μm by adjusting austenitizing temperatures. Compact tension

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8 Microstructural Effects in Hydrogen Embrittlement of Steel

(CT) tests were conducted using specimens hydrogen precharged in hydrogen gas at 573 K, giving the hydrogen concentration of 1.2 × 10–4 in atomic ratio. For the undoped steel, the larger grain size brought about a lower growth rate and nearly the same K TH . On the contrary, for the 0.06% P-doped steel, the larger grain size brought the higher stage II crack growth rate and the lower K TH . The grain-size effect on Stage II crack growth rate was opposite in the P-doped and undoped steels of the same yield strength. A high-purity AISI 4340-Type steel (P = 0.003%) exhibited a substantial reduction in K TH with increasing prior austenite grain size when tested in hydrogen gas using bolt-loaded modified wedge opening loading (WOL) specimens at fixed displacement [17]. Hydrogen gas pressure was about 0.1 MPa at room temperature. The magnitudes of K TH in the high-purity steel were five to six times as large as that for commercial steel tested under the same condition, and the fracture mode was mainly transgranular. Banerji et al. considered that high K TH with the transgranular fracture is the intrinsic effect of hydrogen in this steel and that the low K TH with IG fracture was the effect of impurity such as P. Banerji et al. suggested that the austenite grain refinement should be useful as a means to increase the resistance to hydrogen-assisted cracking for high-purity steel. (b) Delayed fracture and tensile tests Refinement of the prior austenite grain size improved the resistance against sulfide stress cracking (SSC) in martensitic steel of 600 to 850 MPa in yield strength [18]. At constant load delayed fracture tests in a 0.5% CH3 COOH+ 5% NaCl solution saturated with H2 S at pH of 3.2, the threshold stress for no failure increased with the yield strength but turned to decrease when the yield strength exceeded a critical value σ c , indicating the involvement of plastic deformation in the effects. Grain refinements shifted σ c to higher values. On the other hand, from microscopic viewpoints focusing on strain-induced lattice defects, grain-size effects on tensile properties were examined for martensitic steel in a fine-grain size range [19]. Plate specimens of 2 mm in thickness and 10 mm in width of 0.36C-0.97Si-0.20Mn-1.0Mo-0.2Cu (mass %) steel were repeatedly inductionheated and water-spray quenched to refine the prior austenite grain size in the range of 24–4.2 μm, followed by tempering at 823 K to the tensile strength of 1350 MPa. Three states of specimens, as-heat treated, plastically deformed to 5%, and subsequently annealed at 523 K for 1 h. Detection of lattice defects in specimens utilized hydrogen as the tracer, evaluating the tracer-hydrogen absorption capacity by TDA. Figure 8.7 [19] shows the amounts of tracer-hydrogen in specimens of various grain sizes at the three states. The amounts in the as-heat-treated specimens substantially increased with the gran refinement below 10 μm. Plastic deformation remarkably increased the hydrogen absorption capacity, in accordance with previous results in Fig. 3.2 for iron, but the total amount of tracer-hydrogen decreased with grain refinement. Subsequent annealing at 523 K after straining eliminated almost the increment due to straining. The results are consistent with Fig. 3.4, implying that vacancytype lattice defects are the trap sites of the incremental amounts of tracer-hydrogen associated with plastic deformation

8.1 Martensitic and Bainitic Steel

215

Fig. 8.7 The amounts of tracer-hydrogen introduced to medium-carbon martensitic steels with various grain sizes. ◯: As-heat treated, ●: Strained to 5%, Δ: Annealed at 250 °C (523 K) for 1 h after straining (Fuchigami et al. [19])

The lower solid line in Fig. 8.7 is the calculated curve of the total hydrogen concentration, C TOT , which is the sum of the hydrogen concentrations in prior austenite grain boundaries C GB and that in the matrix C M , which includes hydrogen trapped in other lattice defects such as dislocations and martensite lath boundaries. The C GB is the product of the total grain-boundary surface area and the hydrogen mass in the unit area of boundaries. C TOT in the mass ratio is CTOT = CGB + CM = 2a/ρ L + CM

(8.1)

where a is the hydrogen mass in unit area, ρ is the density of the steel, and L is the mean lineal intercept of grains obtained experimentally. The numerical values of a and C M were determined from six combinations of observed C TOT for four grain sizes shown in Fig. 8.7. The fit of the calculated curve with experiments implies that the increase in the hydrogen absorption capacity associated with grain refinement is simply due to the increase in grain-boundary surface area when the same hydrogen concentration in the unit area was assumed. The estimated values of a corresponded to the site coverage of 0.14 in grain-boundary areas when the monolayer plane was assumed for boundaries to have the same nearest inter-atomic distance as in bulk. The magnitude of a less than unity is reasonable, but actual values might be less when the thicknesses of boundaries are taken into account. An important result of Fig. 8.7 is that the strain-induced increment of the hydrogen absorption capacity is reduced by grain refinement, i.e., the grain refinement suppresses the strain-induced creation of vacancies. Then, tensile tests were conducted with specimens with and without hydrogen precharging at the strain rate of 2.8 × 10–5 s−1 . Cathodic hydrogen precharging was given under a mild condition in a 3% NaCl aqueous solution containing 3 g/l NH4 SCN at a current density of 10A/m2 for 18 h. Since simultaneous hydrogen charging was absent, the hydrogen

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8 Microstructural Effects in Hydrogen Embrittlement of Steel

Fig. 8.8 Embrittlement index at tensile tests as a function of the increase in the amounts of tracer-hydrogen by straining to 5% (Fuchigami et al. [19])

concentration in the unit area of grain boundaries was constant during the tensile test. Observed degradations of fracture stress and ductility were expressed in terms of the embrittlement indices, EI, defined as the fraction of the decrease in fracture stress σ f or reduction of area RA in the form of EIσf =

σfA − σfH RAA − RAH , EIRA = , σfA RAA

(8.2)

where subscripts H and A denote specimens with and without hydrogen precharging, respectively. Figure 8.8 [19] shows the dependence of EI on the increment of the amount of tracer-hydrogen with straining to 5%. Together with the annealing effect shown in Fig. 8.7, the results of Fig. 8.8 imply that the effects of grain-size refinement on reducing the degradation are due to the decrease in the density of strain-induced vacancy-type defects. The generation of vacancies mostly results from mutual interactions of dislocations. Grain refinement may reduce the slip length and then the densities of dislocations in areas near grain boundaries that impede the slip extension. Correspondingly, the grain-size refinement should reduce hydrogen effects on fracture morphology. The hydrogen effect of changing the fracture mode from dimple to flatter QC was observed for specimens of 24 μm in grain size.

8.1.4 Impurities and Alloying Elements (a) Impurities Intergranular fracture (IG) is typical in HE of severely embrittled high-strength steel, and impurities play a significant role in IG fracture. It has been well established that step cooling at tempering enhances temper embrittlement of martensitic steel, promoting segregation of impurity elements mostly of 14th and 15th groups such as

8.1 Martensitic and Bainitic Steel

217

P, As, Sb, and Sn in the periodic table. Hydrogen accumulates along grain boundaries, as tritium autoradiography shows in Fig. 2.16, but the decrease in the Charpy impact fracture toughness that characterizes temper embrittlement does not appear in the case of hydrogen embrittlement (HE). The origins of IG fracture in temper embrittlement and HE are not certain to be identical. A cooperative relationship between temper embrittlement and HE has been the subject of extensive studies as reviewed by McMahon [20]. The enhanced susceptibility to HE by temper embrittlement was demonstrated in delayed fracture tests of HY 130 steel (0.1C-0.9Mn-0.35Si-5Ni-0.5Cr-0.5Mo0.08 V in mass% and 900 MPa in the yield stress) in 0.1 N H2 SO4 with As2 O5 , using edge-notched cantilever specimens [21] as described about IG fracture in Sect. 7.2.4. Step cooling drastically decreased the lowest applied stress intensity K TH , i.e., the threshold to cause a fracture, from that of unembrittled specimens. K TH normalized by the fracture toughness in the air was much lower for step-cooled specimens than unembrittled ones. Accordingly, a cooperative function of hydrogen and temper embrittlement was concluded. Kameda and McMahon extensively examined the effects of impurities in fracture mechanics tests of 0.3C-3.5Ni-1.7Cr (mass %) steel doped with P, Sn, or Sb [22]. Grain-boundary concentrations C gb of impurity elements were controlled by varying the aging time at 753 K on tempering and were estimated using Auger Electron Spectroscopy (AES). The threshold stress intensity K TH for the first detectable crack extension at compact tension tests using pre-cracked specimens and the threshold stress σ th for the microcrack formation at four-point bend tests using notched specimens were measured. K TH and σ th decreased with increasing C gb of impurity elements in tests in air and 0.17 MPa hydrogen gas. In partially embrittled specimens, significant effects of hydrogen in reducing both K TH and σ th appeared, but hydrogen effects were smaller for lower K TH and σ th levels. The latter results are indicative of the involvement of some plasticity to induce HE. Suppression of IG fracture is a prospective means to reduce the susceptibility to HE for high-strength steel, and reducing impurity segregation in prior austenite grain boundaries must be an effective method. Precipitation of proeutectoid ferrite along austenite grain boundaries was attempted according to this notion [23]. Proeutectoid ferrite of 3.5 ~ 8.4% in the areal fraction on the micrograph was precipitated in medium-carbon martensitic steel by isothermal holding at intermediate temperatures during quenching from the austenitizing temperature. Tensile strengths were fixed at almost the same level of about 1300 MPa by varying tempering temperatures between 623 and 693 K. Sustained-loading delayed fracture tests were conducted by immersing round bar specimens of 5 mm in diameter in 20% NH4 SCN aqueous solution at 323 K. Figure 8.9 [23] shows test results in which open marks denote steels without proeutectoid ferrite. Proeutectoid ferrite markedly improved delayed fracture characteristics. The IG fracture near the crack initiation site for fully martensitic steel was absent by the precipitation of proeutectoid ferrite, and QC replaced IG. Proeutectoid ferrite

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8 Microstructural Effects in Hydrogen Embrittlement of Steel

Fig. 8.9 Delayed fracture diagrams of high-strength martensitic steels. Solid and open marks denote steels with and without intergranular ferrite precipitation (Watanabe et al. [23])

increased the hydrogen absorption capacity, but the amounts of hydrogen at the time of fracture were not systematically correlated with delayed fracture characteristics for different steels, even under the same applied stress. On the other hand, the mean hydrogen occlusion rates, defined as the hydrogen content in a failure specimen divided by the time to fracture, are shown in Fig. 8.10 [23] at the applied stress of 0.8 of the tensile strength. The time to fracture at a given applied stress was substantially scattered, but the no-failure threshold stresses shown in Fig. 8.9 correlated well with the mean hydrogen occlusion rates. The hydrogen content measures lattice defects that operate as hydrogen trap sites. Since most hydrogen in failure specimens is diffusive and vacancies are major trap sites of increased hydrogen contents by straining, the hydrogen occlusion rate likely represents the vacancy creation due to interactions between dislocations near grain boundaries. Proeutectoid ferrite likely reduces the local dislocation density near grain boundaries. 0.05 Hydrogen Occlusion Rate (ppm/h)

Fig. 8.10 Mean hydrogen occlusion rates per hour at sustained-loading delayed fracture tests at the applied stress of 0.8 of the tensile strength. Areal fractions of proeutectoid ferrite are 3.5, 8.4, and 0% for A1, A2, and A3 steels, respectively (Watanabe et al. [23])

0.04 0.03 0.02 0.01 0

A1

A2

A3

8.1 Martensitic and Bainitic Steel

219

(b) Alloying elements Impurity elements play the primary role in temper embrittlement of steel, but common alloying elements Mn and Si in steel also affect the susceptibility to HE [24]. Modified WOL tests for HY 130 steel in hydrogen gas of 0.21 MPa at room temperature exhibited a decrease in the threshold stress intensity K TH , defined as the crack initiation on loading, by step cooling from tempering at 755 K. The degradation was much smaller for steel of very low Mn (0.02%) and Si (0.03%) contents than steel of standard compositions. Four-point bend tests in air and hydrogen gas were also conducted using notched specimens. A steel of standard compositions and stepcooled at 753 K for 1000 h exhibited a prominent decrease in fracture stress when tested in hydrogen gas than in air. Observations of the crack path revealed the crack initiation along plastic hinges or slip lines in the steel with reduced Mn and Si. In the steel of standard compositions, step cooling diminished the extent of the plastic region, and IG fracture mode prevailed. Extensive studies on the effects of Mn and Si, as well as P and S, on the susceptibility to HE, were made by Bandyopadhyay et al., using modified WOL pre-cracked specimens of AISI 4340-type steel of various Mn and Si contents [25]. K th values at the crack arrest in 0.11 MPa hydrogen gas exhibited a linear decrease against a parameter [Mn + 0.5Si + S + P (mass%)] up to 0.2. The decrease in K th was associated with the increase in the area fraction of IG surface. Further, K th values of commercial and high-purity steel in various hydrogen gas pressures were plotted uniquely on a single curve against a parameter [104 C H ] + [Mn + 0.5Si + S + P in mass %]. Estimating the hydrogen concentration C H was from Sieverts’ law, and the accumulation in the stress field ahead of the pre-crack used Eq. (1.11). Bandyopadhyay et al. claimed that hydrogen and metalloid impurities additively operate in intergranular cohesion and that the function of Mn and Si is to control the segregation of P and S in austenite grain boundaries [25]. A cooperative function of P and Mn was observed for the threshold stress for no failure at SSC tests of martensitic steel [18]. The threshold stress decreased with increasing P contents, and the decrease at a constant P content was prominent with increased Mn contents. The yield strength was almost the same, ~745 MPa, but the fracture surface changed from transgranular to partially IG, associated with the decrease in the threshold stress. The enhanced IG fracture by hydrogen at tensile tests of medium-carbon Cr–Mo martensitic steel plates with increasing Mn contents are shown in Figs. 7.6 and 7.7 in Sect. 7.2.4. The fracture mode was mainly IG, and the higher Mn contents caused smoother fracture surfaces and reduced accompanying fine tear patterns. Tensile test results under simultaneous hydrogen charging are shown in Fig. 8.11 [26]. The Mn contents did not affect tensile properties when hydrogen was not present, but the presence of hydrogen decreased the fracture stress and tensile ductility with increasing Mn contents. This result is consistent with other studies on K th for AISI 4340 steel [22]. A crucial finding concerning Mn contents was that higher Mn contents pronounced increased hydrogen absorption capacity after straining, as shown in Fig. 7.20. TDA

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8 Microstructural Effects in Hydrogen Embrittlement of Steel 1300

65

Non-Charged

1150 1100 1050 1000 0 0.5 1.0 1.5 2.0 Mn Content (mass%)

Reduction of Area (%)

4.0 Elongation at Fracture (%)

Tensile Strength (MPa)

1250 1200

75

5.0

3.0 2.0 1.0 0

0

0.5

1.0

1.5 2.0

Mn Content (mass%)

55 45 35 25 15 5

0

0.5

1.0

1.5 2.0

Mn Content (mass%)

Fig. 8.11 Tensile properties of medium-carbon martensitic steels with different Mn contents with/without hydrogen charging (Nagumo et al. [26])

revealed the vacancy-type nature of the trap sites, as shown in Fig. 7.21. The increase in the density of strain-induced trap sites is apparently against the reduction of plasticity on the fracture surface. However, the results are plausible when extremely localized strain in regions close to prior austenite grain boundaries intensifies the accumulation of damage there, leading to premature fracture. A high dislocation density caused by the constraint of the slip extension across grain boundaries must favor the strain-induced creation of vacancies. The microstructural entity of Mn operating for strain localization is not definite quantitatively, but Mn likely affects structural factors such as impurity segregation and precipitation of carbides in grain boundaries, as suggested in preceding studies. Boron is a unique element that intensifies the hardenability of steel with contents as low as ppm by segregating at the austenite grain boundary. Boron combines with nitrogen forming fine BN, and other alloying elements as well as thermal histories affect the states of B in steel. Effects of B on HE were examined at delayed fracture tests for 0.15%C-Si-Mn (mass%) martensitic steel containing different amounts of B and N [27]. A two-step austenitization was occasionally employed to fix B as fine BN precipitates in the matrix. Constant load delayed fracture tests were conducted, using cantilever bend-notched specimens under cathodic electrolysis in a 3% NaCl solution at current densities of 2 ~ 10 A/m2 . The fracture mode was mainly IG, and Auger electron spectroscopy (AES) on the IG fracture surface revealed separate peaks due to B and BN. Figure 8.12 [28] shows the threshold stress for delayed fracture as a function of B concentrations at grain boundaries calculated from AES peak heights. The B concentrations at grain boundaries were substantial, but segregated B was not harmful when its amount was limited. On the other hand, fine precipitates of BN at grain boundaries remarkably decreased the threshold stress. Fixing N as TiN by Ti addition and precipitation of BN in the matrix by two-step austenitization are useful means to suppress detrimental effects associated with B addition.

Fig. 8.12 Threshold stress for no failure at delayed fracture for B-containing martensitic steels as a function of B concentrations at prior austenite grain boundaries. Segregation Boron and BN precipitates are separated by Auger electron spectroscopy (Inoue et al. [28])

221

Threshold Stress for No Failure (GPa)

8.1 Martensitic and Bainitic Steel

1.9

Segregation 17

1.5

BN Precipitates

0.1 0.15 0.0 Boron (mass %) at Grain Boundary

8.1.5 Microscopic Features of Fracture Fractographic features of martensitic and bainitic steel in HE are mainly IG or QC. Kim and Morris noticed {110} or {112} fracture plane after hydrogen embrittlement, while {100} cleavage plane is predominant in low-temperature fracture [29]. The steel was 0.06C-5.86Ni-l.21Mn-0.69Cr-0.2Mo-0.2Si (wt. %) in compositions and 1073 and 873 K of austenitizing and tempering temperatures, respectively. After hydrogen charging by cathodic electrolysis in 1 N H2 504 + small amounts of As2 03 and CS2 at 160A/m2 , which gives a pretty high hydrogen fugacity, a three-point bending test was applied. Hydrogen charging reduced the fracture toughness from 330 MPa·m1/2 to 180 MPa·m1/2 . Scanning electron microscopy (SEM) of the fracture surface exhibited fine, lath-like features comparable in dimension to the martensite laths, as described in Sect. 7.2.3 [29]. Chemical etching of the fracture surface showed etch pits of the elongated-hexagon shape, typical of etch pits on {110} surfaces. Transmission electron microscopy (TEM) of the immediate subsurface region revealed that the fracture surface lies in the lath boundaries over almost its whole length. Further, high-resolution TEM fractography revealed a dense population of fine secondary cracks immediately beneath the fracture surface. The microcracks were found in the first few μm beneath the fracture surface, certainly formed ahead of the propagating crack tip. Shibata et al. precisely observed subsurface microcracks in 0.1%C lathmartensitic steel austenitized at 1323 K and iced-brine quenched [30]. Tensile curves of specimens were similar between specimens with and without hydrogen charging, but fracture of the hydrogen-charged specimen occurred soon after the elastic limit. Almost all areas of the fracture surface consisted of fine and shallow dimple patterns, and microcracks in an area about 200 μm beneath the fracture surface were almost perpendicular to the tensile axis. All observed microcracks were located on or close to the prior austenite grain boundary.

222

8 Microstructural Effects in Hydrogen Embrittlement of Steel

Fig. 8.13 SEM image of the fracture surface of the hydrogen-charged Fe-0.4C steel tempered at 623 K. The white arrows indicate surfaces with striations (Shibata et al. [31])

Shibata et al. compared the fracture surface and the cross-section of as-quenched 0.1% C and tempered 0.4% C martensitic steels [31]. The 0.4% C steel was austenitized at 1123 K and tempered at 573, 623, and 723 K after ice-brine quenching. In the 0.4% C steel, film-like carbides precipitated on martensite lath boundaries, and the dislocation density inside the lath decreased with increasing tempering temperatures. Cathodic hydrogen charging was in 1 N H2 SO4 + 2 mg/l As2 O3 at a current density of 100 A/m2 . On a slow strain-rate tensile test, the hydrogen-charged 0.4% C steel tempered at 573 K and 623 K fractured within the apparently elastic range [31]. As shown in Fig. 8.13 [31], the fracture surface was faceted intergranular (IG)-like, but most of the fracture surfaces exhibited striations, such as tear ledge patterns indicated by arrows. On the cross-section, SEM images revealed several microcracks located along or close to the prior austenite grain boundaries, but they were parallel to {011} planes within the prior austenite grain. Electron backscattering diffraction (EBSD) analysis of the crystallographic orientation demonstrated that the facet components on the fracture surfaces were parallel to {011} planes. The involvement of plasticity in forming fracture surfaces is common for IG, QC, and fine dimples in HE. The preference of each morphology in fracture was investigated by Shibata et al. [32] using fracture surface topography analysis (FRASTA) [33]. The used steel was a 0.1C-8Ni steel sheet of 1.7 mm thickness, austenitized at 1373 K, followed by ice-brine quenching. After hydrogen charging by cathodic electrolysis in 3% NaCl + 3 g/l NH4 SCN at a current density of 5 A/m2 , a slow strain-rate tensile test at 8.3 × 10−6 /s was conducted. FRASTA is a computational reconstruction of the fracture process by comparing topographic features of mating fracture areas [31]. Its application revealed the sequence of fracture morphology change of smooth surface → surface with serrated markings → dimple surface. Figure 8.14 [32] shows the evolution of each fractographic feature on separating the initially matched fracture surfaces. Evidently, the smooth surfaces along prior austenite grain boundaries are the first (weakest) sites to separate. The hydrogen-related fracture of martensitic steel is different from conventional brittle cleavage fracture of iron and steel, and the involvement of local plasticity is

Fig. 8.14 Change in fraction of fracture modes in FRASTA as a function of separation distance between the two topographic maps (Shibata et al. [32])

223

Area fraction (%)

8.2 Multiphase Steel

smooth surfaces with serrated markings with dimples all surfaces

Distance (μm)

definite. The lath structure constrains the operative slip system. Dislocation activities in as-quenched 0.13% C lath-martensitic steel were analyzed by Miyauchi et al. using the EBSD pattern technique [34]. The rotation of each martensite block was investigated and compared with that predicted by the Taylor and Sachs models. Slip systems of slip planes parallel to the lath and block boundaries, i.e., {011} planes, were preferentially activated. From 0 to 8% tensile strain, lath-constrained crystal rotation was confirmed for about three-quarters of all martensite blocks studied. In the early deformation stage, almost only slip systems in the lath-plane operate, and long-distance dislocation slip is not feasible.

8.2 Multiphase Steel Recent industrial developments require materials to fit energy saving, as typical in weight-reducing automobiles. High-strength low-alloy steel has been well developed, but recent advanced high-strength steels (AHSSs) mostly utilize multiphase techniques such as Dual Phase (DP), Transformation Induced Plasticity (TRIP), Twinning-Induced Plasticity (TWIP), Complex Phase (CP), and Ferritic Bainitic (FB) steel. The enhanced susceptibility to environmental degradation is a crucial problem associated with high strengthening. Various factors operate in HE, and comprehensive studies about each type of steel are now in progress [35, 36]. Accordingly, in the present stage, limited descriptions, rather than comprehensive, focus on elementary findings likely common in the fracture process.

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8 Microstructural Effects in Hydrogen Embrittlement of Steel

8.2.1 Dual Phase Steel The dual phase (DP) steel of microstructures consisting of finely dispersed martensite in ferrite matrix is a prospective type of high-strength steel because of its good combination of strength and workability. In an early work, Davies prepared dual phase structures of ~ 0.1% C steel either by air cooling from the intercritical (α + γ ) region or water quenching from an intercritical temperature and tempering at about 433 K for a few minutes [37]. Hydrogen-charging conditions using cathodic electrolysis in 4% H2 SO4 were determined to produce no permanent damage to the structure. Tensile test results showed a substantial decrease in uniform elongation by hydrogen, but the reduction totally recovered in specimens tempered at 773 K. The fracture surface of the hydrogen-charged specimens showed large dimple-like facets of ~ 5 μm in size but containing river-like striations. Details of microstructures and the crack path were not presented, but Davies showed that the presence of martensite evolved HE of the DP steel. DP steels did not contain boundaries between prior austenite grains but only ferrite-ferrite boundaries and ferrite-martensite interfaces. The no-failure critical stress for delayed fracture decreased by the presence of martensite, but it was above the macroscopic yield stress. It was then concluded that high-carbon martensite is responsible for HE of dual phase steel, but considerable macroscopic deformation is involved in the failure. Davies further prepared DP steel of (0.03–0.12)C-0.2Si-0.5Mn-0.5Mo (mass%) in compositions containing martensite of 5–45% in volume fraction [38]. The tensile strength of the steel increased from about 400–900 MPa with increasing martensite volume fractions, accompanying a decrease in ferrite grain size and an increase in martensite size. The susceptibility to HE was evaluated by tensile tests using specimens hydrogen charged in poisoned 4% H2 SO4 at a current density of 60A/m2 . As a function of martensite volume fraction, the reduction in the uniform elongation of specimens as the ratio between with and without hydrogen charging showed three ranges, as shown in Fig. 8.15: (1) no embrittlement up to 10% martensite, (2) advancing embrittlement from 10 to 30%, and (3) essentially independent of martensite contents above 30%. All regions of martensite were at ferrite grain boundaries. The regions were separated in the steel containing martensite less than 10% but tended to form a network over the range of 10 to about 30%, associated with decreasing ferrite grain size and increasing martensite region size. Martensite likely acts as the easy path for crack propagation. Effects of martensite volume fraction differed by compositions of steel. As included in Fig. 8.15, a commercial DP steel of 0.1C-1.5Mn-0.55Si-0.08 V (mass %) in compositions with fine ferrite grain size of 3–5 μm showed a constant and higher hydrogen degradation than other steels. In the commercial steel, the increase in martensite volume fraction from 20 to 40% raised the tensile strength from 800 to 1100 MPa, but the ferrite grain size was much finer. The estimated carbon content in the martensite for the experiments was more than 0.2%. Koyama et al. prepared a 0.15% C ferrite/martensite DP steel by water quenching from the two-phase region [39]. Tensile test results showed a substantial decrease

Fig. 8.15 Ratios of uniform elongations at tensile tests with/without hydrogen charging for ferrite-martensite dual phase steels. Alloys 1–5 contain about 0.5% Mn and 0.5% Mo, Alloy 6 contains 1.46% Mn and 0.08%V without Mo. Alloy #6 (●) is a commercial dual phase steel (Davies [38])

225

Uniform El(H) / Uniform El(no-H), (%)

8.2 Multiphase Steel

100 80 60 40 20 0

10

20 30 40 50 Percent Martensite

60

in the total elongation by hydrogen charging, and the fracture surface consisted of fine dimples and large brittle feature regions. Hydrogen charging increased the size of the brittle feature region, which contained a considerable number of voids and dimples. In the early stage of failure, in situ SEM observations detected cracking of martensite in both hydrogen-charged and uncharged specimens. Hydrogen effects were apparent in the late stages of deformation. When hydrogen was not present, crack propagation inside the ferrite grains was not observed, consistent with earlier studies [37, 38]. In hydrogen-charged specimens, the crack propagated along the prior austenite grain boundaries through a few neighboring ferrite grains, associated with increased local orientation changes around the crack tip. The findings suggest a cooperative function of martensite and ferrite in hydrogen-related changes of deformation microstructures. Fracture surfaces showed both dimple and brittle features. Hydrogen charging increased the size of brittle feature regions, but sizable brittle feature regions contained many voids and dimples. Koyama et al. also examined microscopic features of fracture in DP steel [39]. Hydrogen promoted the necking onset and the evolution of the damaged area during straining. The term “damage” used by Koyama et al. indicates flaws such as cracks and voids. An image quality (IQ) map in EBSD, that represents the crystallinity of the diffracting area, revealed an incipient crack nucleation in the incubation period, primarily within martensite before a substantial crack growth started, as shown in Fig. 8.16(a), (b) together with the rolling direction inverse pole figure (RD IPF) and Kernel average misorientation (KAM) maps in Fig. 8.16c, d [39]. On the other hand, KAM-distribution measures the orientation difference between neighboring areas. KAM map of undeformed specimens revealed that martensite contains a considerable amount of lattice defects. KAM maps were almost unaffected by the presence of hydrogen on straining up to 7% in both ferrite and martensite phases. The incipient cracks in Fig. 8.16 grew into neighboring ferrite grains in hydrogen-charged specimens. Changes in the local orientation and high KAM values around the crack tip in hydrogen-charged specimens suggested reduced

226

8 Microstructural Effects in Hydrogen Embrittlement of Steel

Fig. 8.16 (a) IQ map at a 1–2% local plastic strain (end of the damage incubation regime). The red arrows indicate cracks. (b) IQ, (c) RD IPF, and (d) KAM maps corresponding to the part surrounded by the square in (a) (Koyama et al. [39])

(a)

10 μm

(b)

(c)

(d)

700 nm

700 nm

700 nm

crack-arresting ability by hydrogen-affected plasticity. Koyama et al. proposed that hydrogen significantly affects the following crack propagation in martensite into the surrounding ferrite grains. Furthermore, when the strain reached 7%, ferrite/martensite interface and martensite interior such as block boundary were also cracked [39]. The hydrogen-assisted cracking at multiple boundaries and crack propagation into ferrite promoted crack coalescence, which resulted in the distinct hydrogen-induced mechanical degradation of DP steel. A comparison of delayed fracture characteristics between tempered-martensite and ferrite/tempered-martensite DP structures of the same tensile strength was conducted by Takahashi et al. for a 0.13C-1.4Si-2.2Mn (mass %) steel [40]. The tempered martensitic steel was prepared by austenitizing at 1153 K, followed by water quenching and tempering at 673 K, while the DP steel was prepared by austenitizing at 1093 K, followed by air cooling to 953 K, water quenching, and tempering at 423 K. The volume fraction of the martensite phase was about 60%. The tensile strength of the single martensitic and DP steel was similar, 1256 and 1217 MPa, respectively, while the yield stress was 1146 and 711 MPa, respectively. The specimens were given pre-loading at 1100 MPa in the air for 1 h just before the sustainedloading test. The applied stress of 1100 MPa at pre-loading was higher than the yield stress of the DP steel, and the pre-loading must have caused work hardening of ferrite, suppressing plasticity that generates damage.

8.2 Multiphase Steel

227

In sustained loading, cathodic hydrogen charging in a 3% NaCl + 0.3% NH4 SCN aqueous solution at a current density of 5 or 50 A/m2 started after applying the sustained loading. Since the specimen size was 6 mm in diameter, the hydrogen distribution in the specimen was not uniform in an early stage of sustained loading, limited by hydrogen diffusion. The time to fracture in the middle range of the applied stress, near the yield stress, was similar between the two structures. However, the critical stress for no failure of the dual phase steel (~400 MPa) was higher than that (~300 MPa) of the single-phase steel. A superior resistance to delayed fracture of 1500 MPa-class bainite/martensite DP high-strength steel, compared to single-phase martensitic steel, was shown by Gu et al. in terms of K ISCC and crack growth rate [41]. The study used modified wedge opening loading (WOL) specimens in a 3.5% NaCl solution at 298 K.

8.2.2 Retained Austenite—TRIP Steel In martensitic or lower bainitic steel, some fractions of retained austenite γ R often exist in the form of thin films along lath boundaries. The hydrogen absorption capacity of the steel increases with the amount of γ R , presumably due to the high solubility of hydrogen in austenite and to hydrogen trapping at the γ R /matrix interface [42]. (a) Basic characteristics Chan et al. prepared martensitic steels of different carbon contents and measured the effects of γ R on the hydrogen content and the effective hydrogen diffusivity [42]. X-ray diffraction analysis detected γ R in steel of carbon contents of more than 0.6%. In high-carbon steel, no appreciable difference in the amount of γ R was detected before and after hydrogen charging. Microstructures of lightly deformed TRIP steel were characterized by Petrov et al. [43]. Electrochemical permeation experiments revealed that increasing carbon content increased γ R and hydrogen contents while hydrogen diffusivity decreased. Table 8.1 [42] summarizes the results. Chan et al. deduced that the retained austenite itself does not trap hydrogen significantly, but the interfaces between γ R and martensitic plates may be the possible trapping sites. Retained austenite partially decomposes when stress is applied. Transformationinduced plasticity is utilized as TRIP steel to have high formability and fracture Table 8.1 Effects of carbon content on the amount of retained austenite, effective hydrogen diffusivity, and hydrogen content in martensitic steel (Chan et al. [42])

Carbon content γ R (Volume %) (wt %)

Deff (cm2 /sec) C H (wt ppm)

0.23

–

4 × 10–7

–

0.44

–

2 × 10–7

–

0.64

3.1

1.4 × 10–7

0.5

0.79

5.9

8 × 10–8

1.1

0.93

9.8

6 × 10–8

1.8

228

8 Microstructural Effects in Hydrogen Embrittlement of Steel

toughness while retaining excellent strength. Kim et al. investigated the γ → martensite phase transformation in the TRIP steel using in situ observation of the change in hydrogen permeation current under loading conditions [44]. A hot-rolled 0.07C5Mn-0.5Si-2Al (mass %) steel sheet was cold-rolled and reheated at 1013 K for 2 min, followed by air cooling at 10 K/sec. The steady-state permeation current (iss ) for the TRIP steel is much lower than that for the ferritic steel. Application of external load exceeding the elastic limit instantly decreased the permeation current due to the trapping of hydrogen atoms by newly generated dislocations. However, the current increased, going up much higher than the iss in the specimen with no additional loading. Kim et al. deduced that the cause is the hydrogen transport by newly generated dislocations and deformation-induced martensitic decomposition [44]. Hydrogen trapping in TRIP steel was investigated by Escobar et al. for 0.17C0.4Si-1.6Mn-0.5 ~ 2Al steel sheets given cold-work of 3%, 10%, and 15% elongation [45]. Thermal desorption analysis (TDA) of hydrogen, introduced as a tracer, exhibited a large peak at about 90 ºC (363 K) and a small peak at about 500 ºC (773 K), as shown in Fig. 8.17 [45]. The main peak was asymmetric and consisted of two peaks. Increasing the degree of cold deformation, i.e., the amount of TRIP, substantially increased the lower-temperature peak and reduced the higher-temperature peak as shown in the inset of Fig. 8.17, consistent with Fig. 3.11 for deformed iron, while the higher-temperature peak at 773 K is from γ R . Indeed, the lower-temperature peak in Fig. 8.17 is the desorption of hydrogen in solid-solution and trapped at dislocations and vacancies. The hydrogen binding energy of γ R obtained by varying the heating rate at TDA was 90 ± 25 kJ/mol. (b) Susceptibility to hydrogen embrittlement TRIP is a useful tool to improve the formability and fracture toughness of highstrength steel, but its susceptibility to environmental degradation is a crucial issue.

H2, (wt ppm/s)

3.0×10-3

2.0×10-3

6×10-6

3×10-6

1.0×10-3 Temperature, (ºC) 0 Temperature, (ºC)

Fig. 8.17 Effects of cold deformation on the TDA spectrum of the TRIP steel. Heating rate 6.66 K min–1 (Escobar et al. [45])

8.2 Multiphase Steel

229

Depover et al. compared hydrogen degradation of low-carbon TRIP, DP, FerriteBainitic (FB), and high-strength low-alloy (HSLA) steel sheets in tensile tests using notched specimens [35]. Details of the sample preparation were not definite, but the tensile strength was 500 ~ 700 MPa levels. The amount of γ R in the TRIP steel was 9.6%. Cathodic hydrogen precharging was in a 0.5 M H2 SO4 + 1 g/l of thiourea solution for 2 h at 26.5 A/m2 . An embrittlement index (EI) was defined as the ratio of the decrement due to hydrogen in elongation or reduction of area to that of in the air. The test results showed that TRIP steel was most prone to hydrogen embrittlement (EI of 66%), followed by DP, FB, and finally the HSLA grade (EI of 32%). On the other hand, the effects of carbon-partitioning in quenched medium-carbon (Q&P) steel [46] on hydrogen embrittlement were compared with a traditional quenching and tempering (Q&T) steel of identical chemical composition by Yang et al. [47]. Diffusion of carbon from martensite to γ R was a means to stabilize γ R against further transformation at lower temperatures. Yang et al. prepared Q&P steel by austenitizing 0.4C-1.5Mn-1.5Si (wt%) steel sheets at 860 °C (1133 K) or 950 °C (1223 K) for 5 min and then immersed some of them in a molten salt bath at a temperature of 513 K (T q ) for 15 s. Immediately transferring into another molten salt bath at 693 K (T p ) for 30 s, final water quenching was given. On the other hand, Q&T specimens were water quenched directly from 1133 K or 1223 K after 5 min holding and then tempered at 693 K for 120 s to prepare nearly the same tensile strength level with Q&P steel. The tensile strengths of the steels were over 1500 MPa. The microstructures of all specimens were lath martensite, but EBSD and TEM observations revealed different amounts and morphologies of γ R . The volume fraction and morphology of γ R in Q&P 950 were about 17% and primarily blocky along martensite boundaries, while negligible volume amount in Q&T 950 specimens. In Q&P 860 specimens, γ R was flake-like and about 18% in the volume fraction, while in Q&T 660 specimens, γ R was film-like and much less volume fraction. The susceptibility to HE was evaluated in slow strain-rate tensile (SSRT) tests using hydrogen-precharged specimens. Hydrogen precharging was by cathodic electrolysis in 0.2 mol/l NaOH with 2 g/l thioureas at a current density of 100 A/m2 . Earlier fractures in tensile tests occurred with longer hydrogen-charging time. The embrittlement index (EI) was defined as the decrement ratio due to hydrogen in elongation or reduction of area to that of in the air. Hydrogen embrittlement was substantial in all steels, but Q&P specimens showed a notably high HE resistance compared to the Q&T. Q&P 860 was the best, although EI was as much as 75% after 60-min hydrogen precharging. On the contrary, a detrimental effect of blocky γ R was reported [48]. Kobayashi et al. prepared bainitic ferrite microstructures of different volume fractions in lowalloyed 0.4% C steel by austempering (isothermal transformation above Ms temperature) at 698 K in a salt bath for various periods up to 104 min after austenitizing at 1223 K [48]. The tensile strength was about 1100 MPa. The amount of γ R was about volume 20%, not systematically dependent on the holding time at austempering, and the carbon concentration in γ R was about 1.2 ~ 1.5 mass %. The morphology of γ R inside the martensite-austenite constituent was blocky and film-like at bainitic ferrite boundaries. Slow strain-rate tensile tests with and without hydrogen charging

230

8 Microstructural Effects in Hydrogen Embrittlement of Steel

exhibited substantial hydrogen degradation in the total elongation, much higher in the presence of blocky γ R . γ R partially decomposed into ferrite and carbides by applying plastic strain, but the effects of hydrogen and morphology on the stability were not so much significant. The effects of γ R on hydrogen embrittlement are complicated, depending on its volume fraction, distribution, morphology, and stability. Fresh martensite, as a product of the decomposition of γ R , is not the definite cause of the degradation.

8.3 Austenitic Stainless Steel Austenitic (γ -) stainless steel is one of the main types of steel with high corrosionand heat-resistances. As described in Sect. 1.1 on solubility and in Sect. 4.1.1 on diffusivity, the basic behaviors of hydrogen in γ -steel are substantially different from those in ferritic steel. Coupled compositional and crystal-structural effects give some specific situations for HE of high alloyed austenitic steel. Attention to be paid is that the hydrogen distribution is often very inhomogeneous in γ -stainless steel due to the very low diffusivity of hydrogen at room temperature. On cathodic hydrogen charging to Type 310 stainless steel (21Ni-23Cr-2Mn-1Si in mass %) in 1 N H2 SO4 with arsenic at a current density of 1000A/m2 , the estimated hydrogen concentration in the near-surface layers amounted to as high as 0.5 ~ 0.8 in H/M atomic ratio [49].

8.3.1 Hydrides and Phase Changes Three types of hydrides have been reported on hydrogen charging to Ni-containing γ -stainless steel; β- and β ' -phases of face-centered cubic (fcc) structures and the ηphase of a hexagonal close-packed (hcp) structure [50]. The η-phase is also denoted as ε' since η has a lattice constant some percent larger than that of ε-martensite. Hydrides form when hydrogen concentration is high enough. Figure 8.18 [51] shows X-ray diffraction patterns of Type 304 steel specimens of 0.8 mm in thickness and strongly cathodic hydrogen charged in poisoned 1 N H2 SO4 at current densities of 100 ~ 1000A/m2 at 293 K. At an early charging stage, ε' and an fcc Y-phase appeared. With increasing the charging time, Y-phase disappeared and ε' decomposed into body-centered tetragonal α ' -martensite and ε phases. The lattice constant of ε' is almost constant, implying that ε' is a hydride, whereas that of ε was larger than that of ε formed on cooling or straining. Hydrogen charging at 333 K (60 °C) induced two fcc phases instead of Y, likely corresponding to β and β ' . The phase separation into ε' and fcc γ ' -phase from γ was also reported for Type 310S steel when hydrogen concentration was 18 and 25 at.% at 308 K (35 °C) and 348 K (75 °C), respectively [51]. The Y-phase reported by Kamachi [51] may correspond to the γ ' -phase reported by Ulmer and Altstetter [52].

8.3 Austenitic Stainless Steel

γ(111)

231

γ(200)

α’(110) ε(10.1)

22 h

190 min 175 min 160 min 115 min 65 min 45 min

Y(200) ε’(10.1)

30 min 15 min virgin

Fig. 8.18 Change in X-Ray diffraction patterns with the progress of hydrogen charging at 20 °C into Type 304 γ-stainless steel sheet (Kamachi [51])

The presence of α ' , susceptible to HE, is an issue as the origin of HE of unstable γ -stainless steels as described in the following Sect. 8.3.2. Crack path associated with α ' is often observed in failure specimens. In this respect, an important finding is the reversible phase change of ε' to α ' and ε during aging at room temperature, as shown in Fig. 8.19 [51]. Simultaneously conducted transmission electron microscopy observations revealed the formation of band-like α ' within ε [51]. A similar formation of α ' together with γ ' and ε' was reported by Narita et al. during aging hydrogen-charged Type 304 [53]. The formed α ' disappeared when hydrogen was recharged, indicating that α ' and ε are reversible. An observed crack path after the crack extension was through or along α ' , but the actual crack extension might be

232

8 Microstructural Effects in Hydrogen Embrittlement of Steel

γ(111) α’(110) ε(10.1) 257 min 98 min 71 min 57 min 45 min 34 min

ε’(10.1)

23 min Aging 11 min As H-Charged virgin

Fig. 8.19 Change in X-ray diffraction patterns from hydrogen-charged Type 304 γ -stainless steel during aging at room temperature (Kamachi [51])

through or along ε. For Type 310S, the formation of α ' was not observed at hydrogen charging and outgassing. Two different hydrogen functions have been proposed as the driving force of hydrogen-induced phase changes. The one is the stress-induced effect due to a significant lattice expansion that interstitial hydrogen causes. As a support, stress-induced cracking associated with hydrogen degassing appeared as fine surface cracks by shrinkage in hydrogen-charged Types 304 and 310S steels [53]. Very high concentrations of hydrogen favor to occur such situations. In this case, the stress-induced phase change is not likely in Type 310S because the deformation-induced martensite start temperature, M d , is well below room temperature. Alternatively, Iyer discussed some intrinsic effects of hydrogen on the thermodynamic stability of γ -phase [54]. In analogy to other interstitial solute atoms such as carbon and nitrogen, hydrogen was assumed to stabilize the γ -phase, retarding the transformation to martensite. Some observations, such as a more considerable

8.3 Austenitic Stainless Steel

233

amount of retained austenite associated with higher hydrogen content, support the notion. However, no effects of hydrogen were observed for the martensite start temperature, M s , of Fe-30Ni alloy for hydrogen up to 400 at. ppm, i.e., no effect in stabilizing austenite [55]. Also, hydrogen did not affect volume fractions of deformation-induced α ' and ε in Type 304L and α ' in Types 301 and 310S [55]. Narita et al. postulated that hydrogen stabilizes ε [53]. Since hcp ε-phase may form as the result of the motion of partial dislocations leaving arrays of stacking faults, increases in M S and M d are feasible if hydrogen lowers the stacking fault energy. However, reported hydrogen effects are not always consistent. Hydrogen effects on γ -steel depend on experimental conditions such as hydrogen concentration, temperature, and specimen thickness. Careful examinations are necessary for employed experimental procedures.

8.3.2 Compositional Effects on Hydrogen Embrittlement The susceptibilities to HE of γ -stainless steel vary by the type of steel. Figure 8.20 shows tensile test results of Types 304 and 310 steel sheets, hydrogen precharged to about 12 mass ppm and continuing charging during tensile tests [56]. Unnotched smooth specimens of 0.1 mm in thickness were cathodic hydrogen charged in poisoned 0.5 N H2 SO4 at current densities ranging from 0 to 300A/m2 . The yield stress was not affected by hydrogen, whereas the elongation to fracture and the area under the tensile stress–strain curve decreased with increasing current densities. The degradation appeared in each steel but more pronouncedly for Type 304 steel. (a) Stability of austenite The stability of γ -stainless steel against martensite transformation is crucial for HE. Effects of test temperatures and nickel contents on hydrogen degradation are shown in Fig. 8.21 [57] for three types of steel containing 18% Cr and different nickel contents. The contours in Fig. 8.20 show equal fracture strain in percent, and the filled marks and the region under the dotted line indicate the presence of α ' martensite after the test. The region of significant degradation overlaps, though not exactly, that of α ' formation. The specification of a steel type admits certain compositional ranges. Table 8.2 shows the chemical compositions of two Type 304 steel. Steel B is slightly more stable than Steel A against the deformation-induced α ' -transformation according to magnetic measurements [58]. Susceptibilities to HE differed between the two steels of the same type. Hydrogen effects on the threshold stress intensity K TH for the crack initiation and the crack growth rate were measured using single-edge-notched specimens under constant load at room temperature. Hydrogen up to 50 mass ppm was uniformly precharged by cathodic electrolysis in a molten salt bath at 553 K. The K TH decreased with increasing hydrogen contents, but K TH was higher, and the Stage II crack growth rate was lower for Steel B than Steel A at the same hydrogen

60

300

(a) TYPE 304

Elongation (%)

50 40

200

30 Elongation

20

200

10

0 250 2% Flow Stress 100 Yield Stress

150 100 0

0

(b) TYPE 310

Elongation (%)

50 40

300

Elongation

30 200

20 10

0 250

Stress (MPa)

0

2% Flow Stress

200

100 Yield Stress

150

100 0

0

30 300 Charging Current Density (A/m2)

0

Area Under Stress-Strain Curve (kg·min)

60

30 3 300 Charging Current Density (A/m2)

Area Under Stress-Strain Curve (kg·min)

Fig. 8.20 Tensile properties of Type 304 and Type 310 steels under hydrogen charging at various current densities (Inoue et al. [56])

8 Microstructural Effects in Hydrogen Embrittlement of Steel

Stress (MPa)

234

contents. However, the amounts of deformation-induced α ' were not affected by hydrogen for these steels. It may suggest that the stability of the γ -phase is crucial to HE, but the effect not necessarily results from the formed α ' -martensite. (b) Sensitization Sensitization, i.e., isothermal heat treatments in the temperature range between 773 and 1123 K, enhances intergranular corrosion and stress corrosion cracking of γ stainless steel. The reason is the precipitation of chromium carbides at grain boundaries, resulting in the depletion of Cr and C around the precipitates. Enhanced susceptibilities to HE by sensitization were reported for Type 304 steel [58]. On delayed fracture tests using smooth bar specimens under cathodic hydrogen charging, the lowest applied stress to cause delayed fracture decreased by the sensitization associated with IG fracture morphology.

8.3 Austenitic Stainless Steel

235

Fig. 8.21 Isoductility diagram for hydrogen-charged Fe–Cr-Ni alloys. Contours show equal values of plastic strain (Caskey [57])

Table 8.2 Chemical compositions of two Type 304 stainless steel (in mass %) (Singh et al. [58]) Alloy

C

N

Cr

Ni

Mn

Si

Mo

Cu

A

0.061

0.041

18.0

8.54

1.72

0.58

0.18

0.28

B

0.061

0.027

18.2

9.42

1.33

0.59

0.14

0.26

Susceptibilities to HE on tensile tests of various γ -stainless steel at low temperatures in 1 MPa hydrogen and He gases are shown in Fig. 8.22 [59] in terms of the ratio of the reduction of area in the two environments. Notations (S) and (SD) in Fig. 8.22, respectively, indicate “sensitized” and “desensitized” by annealing at 1193 K for 8 h. The maximum degradation by hydrogen occurred at the test temperature of around 220 K, and the degradation in Type 304 was more prominent than Type 316. However, the effects of sensitization on further degradations and its recovery by desensitization were significant in Type 316, while almost immune in Type 304. Fracture morphologies IG in sensitized and QC in desensitized specimens were common in the two steel types. Transmission electron microscopy revealed Cr23 C6 and α ' along grain boundaries in sensitized Type 304. In desensitized specimens, discontinuous carbides along grain boundaries still existed, but no α ' was identified. The case of Type 304 implies that α ' itself is not the cause of degradation, and the low stability of γ in Type 304 might be influential in degradation. Fractographic features of sensitized and desensitized specimens are described in the following Sect. 8.3.3. In Fig. 8.22, stable Type 310S did not exhibit HE. Type 309S (0.06C-14Ni-23Cr in mass %) was also stable without degrading at tensile tests in 69 MPa hydrogen gas at room temperature [60]. However, increasing the hydrogen concentration by

Fig. 8.22 Temperature dependencies of the susceptibility to hydrogen embrittlement of sensitized (S) and desensitized (SD) γ -stainless steels. The susceptibility to hydrogen embrittlement is expressed in terms of the ratio of reduction of areas in H2 and He gas environments (Han et al. [59])

8 Microstructural Effects in Hydrogen Embrittlement of Steel

310S 310S(S) 316 316(SD)

1.0

Relative Reduction of Area (iH2/He)

236

0.8

316(S)

0.6 304

0.4

304(SD) 304(S)

0.2 0 100

200 300 Temperature (K)

400

thermal hydrogen precharging to 425 at. ppm, about six times as large as the solid solubility, lowered the reduction of area from 45 to 27% and from 43 to 30% at notched-tensile tests for normal and sensitized specimens, respectively [60]. By the sensitizing heat treatment at 975 K for 15 or 300 min, the relative reductions by hydrogen were almost the same in the original and sensitized specimens. It implies no cooperative effects between hydrogen and sensitization in Type 309S. (c) Prestrain Strain-induced α ' , highly susceptible to HE, has often been postulated to play the primary role in HE of unstable γ -stainless steel. A unique correlation between the susceptibilities to HE and the amounts of deformation-induced α ' on tensile-fracture surfaces was shown for Types 304, 316, and 316L steel tested in high-pressure 90 MPa hydrogen gas at 228 ~ 358 K [61]. However, contrary findings were that the more significant amounts of α ' introduced by prestraining reduced more pronouncedly slow crack growth rates for Type 301 (6 ~ 8Ni-16 ~ 18Cr) steel [62]. In the experiments, prestraining was given by rolling to a 30% reduction in thickness either at room temperature or 383 K. The amounts of α ' were 57 and 0.5%, respectively, at the two temperatures. The increased amount of α ' elevated the threshold stress intensity K TH for the crack initiation and reduced the Stage II crack growth rate at sustained-loading tests in 108 kPa hydrogen. The results are against a common notion that α ' provides a favorable crack path. On the other hand, the suppression of martensite transformation by prestrain is well known. If the function of prestrain was to suppress microstructural alterations in the γ -phase preceding the martensite transformation, or if dislocation dynamics associated with martensite transformation, rather than martensite itself, were crucial for causing embrittlement, the reduced susceptibility by prestraining would be feasible.

8.3 Austenitic Stainless Steel

237

Compositional effects appear in deformation microstructures and are described in Sect. 8.3.4.

8.3.3 Fractographic Features Fractographic features of hydrogen-degraded γ -stainless steel are quite similar to those of ferritic steel stated in Sect. 7.2, such as fine dimple size on hydrogencharged and tensile-fractured Type 309S [61] and striations on facets in transgranular fracture surfaces of severely hydrogen-charged and tensile-fractured Type 316 steel [63]. Facets containing slip lines corresponding to {111} planes were observed for hydrogen-charged and tensile-fractured Type 310S steel specimens [50]. Facets are likely due to cracking along the grain or twin boundaries. Cracks at intersections of slip bands were observed on the side surface of tensile-fractured Type 304 steel specimens containing about 10 at. ppm hydrogen [51]. Quasi-cleavage (QC) appeared at slow-elongation rate tests of Type 301 steel in 108 kPa hydrogen gas at room temperature, and the fraction of QC decreased, and fine dimples increased as the test temperature was raised [62]. Transgranular QC surfaces associated with secondary cracks were also reported on slow crack growth regions of hydrogen-charged Type 304 steel [64]. Figure 8.23 shows tensile-fracture surfaces of Type 304 steel specimens [65]. The distribution of the charged hydrogen of 30 ~ 35 mass ppm was uniform. Coarse dimples in the hydrogen-free specimen changed to a mixture of fine dimples, QC, and facets in the hydrogen-charged specimen. Hydrogen degradation evolves even in stable Type 310 steel, as shown in Fig. 8.20, without forming α ' . However, the instability of γ -stainless steel inducing the α ' formation has been considered the primary cause of enhanced embrittlement.

(a)

(b) (d)

Fig. 8.23 Tensile-fracture surfaces of Type 304 stainless steel (a) with and (b) without hydrogen charging (Hatano et al. [65])

238

8 Microstructural Effects in Hydrogen Embrittlement of Steel

Enhanced degradation by sensitization is an example of claiming the role of α ' . In fact, strain-induced α ' was present along grain boundaries for sensitized Type 304. However, a substantial degradation by hydrogen still occurred in desensitized specimens, while no α ' was observed at grain boundaries. It indicates that α ' is not essential for the large hydrogen degradation of Type 304 at 220 K. The fracture morphology of sensitized specimens was macroscopically IG accompanying secondary cracks vertical to the fracture surface along grain boundaries for both Types 316 and Type 304 and in both helium and hydrogen gases [59]. Close examinations of IG fracture surfaces revealed that macroscopically IG surfaces were not entirely smooth, with different morphologies depending on steel and environments. Microvoid coalescence (MVC) covered IG-like surfaces of both Type 304 and 316 when tested in helium. In hydrogen gas, dimples on IG-like surfaces of sensitized Type 304 were extremely fine, and the apparent surfaces were brittle-like. Very fine dimples on IG surfaces are due to increased nucleation sites of fine voids. Desensitization of sensitized steels hardly changed MVC fracture morphology in helium, but it changed IG to QC in hydrogen for both Types 316 and 304. The change from MVC in helium to QC in hydrogen also appeared on transgranular fracture surfaces of solution-treated specimens. Promoting voids nucleation and their premature coalescence associated with plastic deformation is possibly the essential function of hydrogen common to both sensitized and desensitized specimens. The compositional effect is likely a matter to be examined regarding deformation microstructures in the γ-phase.

8.3.4 Deformation Microstructures (a) Phase changes Besides the high susceptibility to HE of strain-induced α ' , deformation microstructures in the γ -phase are essential aspects for degradation. Transmission electron microscopy (TEM) is a powerful tool to reveal deformation microstructures associated with the crack propagation that constructs fracture surfaces. A high density of dislocations and the formation of ε and α ' martensite were observed near the crack tip in Type 304 and Type 310 steel specimens tensile strained under cathodic hydrogen charging [56]. Increasing current densities enhanced the formation of stacking fault and ε-martensite, and the crack path was mainly along the interface between γ and ε phases. The crack propagation along the interface between γ and ε phases was also reported using high voltage TEM in Type 304 steel specimens tensile strained after cathodic hydrogen precharging [66]. As for α ' produced at the transformation, a completely α-phase was shown in front of the crack tip and along the crack by Debye rings of selected area diffraction (SAD) in Type 304 steel foils tensile-fractured in an environmental cell of 108 kPa hydrogen gas [67]. The finding suggested that the α-phase was the precursor of crack extension. The difference in the SAD patterns of α’ and α was not discernible, and Narita

8.3 Austenitic Stainless Steel

239

and Birnbaum pointed out two possible hydrogen effects, increased M d temperature favoring transformation to α ' and enhanced plasticity at the crack tip. However, SAD patterns from more stable Type 310 also showed Debye rings characteristic of a very fine-grain γ -phase at the crack tip and along the crack. (b) Strain localization On the other hand, stacking fault and ε-martensite are sites along which strain localization and associated damage accumulation preferentially take place. Accumulation of damage is the precursor of the crack nucleation and growth as described in Sect. 7.3. Figure 8.24 [65] shows kernel average misorientation (KAM) maps obtained from electron backscatter diffraction (EBSD) for Type 304 austenitic stainless steel tensile strained to 24% at room temperature with and without gaseous hydrogen precharging under high pressure at elevated temperature. The KAM map represents orientation differences between neighboring pixels and measures the amount of strain. Blue to red colors in the KAM maps denotes five levels from 0 to 5°. The strain distribution is not uniform, and the increased areal fractions of bright (orange and red) regions imply enhanced strain localization. The decrease in tensile ductility by hydrogen was substantial in Type 304, while Type 316L was immune to hydrogen. However, enhanced strain localization by hydrogen is present in Type 316L, though to a less extent compared to Type 304. Figure 8.25 [65] shows a quantitative comparison of strain localization in terms of area fractions of orange and red color regions for Types 304 and 316L steels strained to 24% with and without hydrogen charging. The hydrogen effect enhancing strain localization is much more distinct in Type 304 than in Type 316L. The preferential strain localization in Type 304 is due to the stacking fault energy. Fig. 8.24 Kernel average misorientation (KAM) maps of EBSD for Type 304 austenitic stainless steels tensile strained to 24% (a) without and (b) with hydrogen precharging. Blue to red denotes higher misorientations between neighboring pixels. The arrow in (b) indicates annealing twin boundary (Hatano et al. [65])

(a)

(b)

30µm

Fig. 8.25 Areal fractions of highly strained regions of orange and red colors in Fig. 7.13. Data for Type 316L are also added. Suffixes “V” and “H” denote without and with hydrogen charging, respectively (Hatano et al. [65])

8 Microstructural Effects in Hydrogen Embrittlement of Steel

Areal fraction of regions above orange color

240

0.25

0.2

0.15

0.1

0.05

0

304-V

304-H

316L-V

316L-H

The decrease in the stacking fault energy enhances strain-hardening and fractions of resultant phases, such as stacking fault and ε-martensite, act as barriers for the slip extension. High densities of fine stacking faults and streaks of ε-martensite characterize microstructures of hydrogen-charged and deformed Type 304 austenitic steel [65]. The deterioration of crystallinity associated with strain localization is described in Sect. 7.3.2. Concurrently conducted positron annihilation spectroscopy (PAS) exhibited a more noticeable increase for Type 304 than for Type 316L in the mean positron lifetime associated with straining [65]. PAS to identify the type of hydrogen-enhanced strain-induced lattice defects is described in Sects. 3.2.2 and 7.4.1.2. Isochronal annealing of strained iron showed that the hydrogen effect on increasing positron lifetime is due to the enhanced creation of vacancies. For austenitic stainless steels, vacancy clustering proceeded more prominently in Type 304 than in Type 316L. Effects of enhanced strain localization on hydrogen embrittlement are relevant to the enhanced creation of vacancies and their clusters. Other possibilities, such as the buildup of high local hydrogen concentration, are not feasible because of the very low diffusivity of hydrogen in austenitic stainless steel. Strain-induced transformation to martensite was not detected even in a region about 0.5 mm from the fracture surface of Type 304 [65]. The strain localization was associated with the planarity of the dislocation slip and with barriers for the slip extension. TEM micrograph Fig. 8.26 [65] for hydrogencharged Type 304 strained to 5% shows high densities of stacking faults and fine streaks of ε-martensite, as confirmed with electron microdiffraction from the red dot in Fig. 8.26(b). High dislocation densities along grain boundaries and annealing twin boundaries were also revealed. Inhomogeneous microstructures made quantitative comparisons difficult, but stacking faults, twins, and ε-martensite were observed

8.3 Austenitic Stainless Steel

241

much more frequently in hydrogen-charged Type 304 than in Type 316L. Further, dislocation structures in Type 316L were tangled with a few stacking faults [65]. The stacking fault energy (SFE) dominates the formation of stacking fault and ε-martensite in γ -steel. The SFE of Type 304 and Type 316L estimated by a firstprinciples calculation [68] was about 2 and 30 mJ·m−2 , respectively [65]. Experimentally, the sensitization of Type 309S steel reduced SFE in the area near grain boundaries from 35 to 22 mJ·m-2 due to Cr depletion [63]. Reductions in SFE of γ -stainless steels by hydrogen are in Sect. 7.3.1. Reductions of SFE of about 20–30% by hydrogen were reported for Type 304 [56] and Type 310 [69]. The stability of γ -phase indeed originates in SFE, dominating deformation microstructures. Plausible functions of hydrogen on the susceptibility to HE of γ -stainless steels are two-fold; one is the enhancement of strain localization through the decrease of SFE, and the other is that of the strain-induced creation of vacancies. Effects of hydrogen in various γ -stainless steel possibly originate in deformation microstructures in the γ -phase.

Fig. 8.26 TEM micrograph of hydrogen-charged Type 304 steel strained to 5%, showing (a) annealing twin band and high dislocation densities along twin and grain boundaries. Magnified view (b) shows high densities of stacking fault and ε-martensite (Hatano et al. [65])

242

8 Microstructural Effects in Hydrogen Embrittlement of Steel

References 1. N.R. Moody, S.L. Robinson, W.M. Garrison Jr., Res Mechanica 30, 143–206 (1990) 2. I.M. Bernstein, G.M. Pressouyre, in Hydrogen Degradation of Ferrous Alloys, ed. by R.A. Oriani, J.P. Hirth, M. Smialowski (Noyes Pub., Park Ridge NJ, 1985), pp. 641–685 3. A. Shibata, Y. Momotani, T. Murata, T. Matsuoka, M. Tsuboi, N. Tsuji, Mater. Sci. Tech. 33, 1524–1532 (2017) 4. W.W. Gerberich, T. Livne, X.-F. Chen, M. Kaczorowski, Metall. Trans. A 19A, 1319–1334 (1988) 5. N. Owada, H. Majima, T. Eguchi, in Advances in Delayed Fracture Solution—Report of Research Group (Iron Steel Institute, Japan, 1997), pp. 111–114 6. M. Nagumo, T. Tamaoki, T. Sugawara, in Hydrogen Effects on Materials Behavior and Corrosion Deformation Interactions, ed. by N.R. Moody, A.W. Thompson, R.E. Ricker, C.W. Was, K.H. Jones (TMS, Warrendale PA, 2003), pp. 999–1008 7. H.K.D.H. Bhadesia, in Bainite in Steels, 2nd edn (The Institute of Materials, London, 2001) 8. F. Nakasato, F. Terasaki, Tetsu-to-Hagané 61, 856–868 (1975) 9. I.-G. Park, A.W. Thompson, Metall. Trans. A, 21A, 465–477 (1990) 10. R.A. Oriani, P.H. Josephic, Scr. Metall. 13, 469–471 (1979) 11. J.C. Charbonnier, H. Margot-Marette, A.M. Brass, M. Aucouturier, Metall. Trans. A 16A, 935–944 (1985) 12. S. Yamazaki, T. Takahashi, Tetsu-to-Hagané 83, 454–459 (1997) 13. T. Tsuchida, T. Hara, K. Tsuzaki, Tetsu-to-Hagané 88, 771–778 (2002) 14. J.F. Lessar, W.W. Gerberich, Metall. Trans. A 7A, 953–960 (1976) 15. N.R. Moody, R.E. Stoltz, M.W. Perra, Scr. Metall. 20, 119–122 (1985) 16. J. Kameda, Acta Metall. 34, 1721–1735 (1986) 17. S.K. Banerji, C.J. McMahon Jr., H.C. Feng, Metall. Trans. A 9A, 237–247 (1978) 18. H. Asahi, Y. Sogo, M. Ueno, H. Higashiyama, Corrosion 45, 519–527 (1989) 19. H. Fuchigami, H. Minami, M. Nagumo, Phil. Mag. Lett. 86, 21–29 (2006) 20. C.J. McMahon Jr., Eng. Fract. Mech. 68, 773–788 (2001) 21. K. Yoshino, C.J. McMahon, Metall. Trans. 5, 363–370 (1974) 22. J. Kameda, C.J. McMahon Jr., Metall. Trans. A 14A, 903–911 (1983) 23. J. Watanabe, K. Takai, M. Nagumo, Tetsu-to-Hagané 82, 947–952 (1996) 24. Y. Takeda, C.J. McMahon Jr., Metall. Trans. A 12A, 1255–1266 (1981) 25. N. Bandyopadhyay, J. Kameda, C.J. McMahon Jr., Metall. Trans. A 14A, 881–888 (1983) 26. M. Nagumo, H. Matsuda, Phil. Mag. A 82, 3415–3425 (2002) 27. T. Inoue, K. Yamamoto, M. Nagumo, in Hydrogen Effects in Metals, ed. by I.M. Bernstein, A.W. Thompson (Metallurgical Society of AIME, Warrendale PA, 1981), pp. 777–784 28. T. Inoue, K. Yamamoto, M. Nagumo, K. Miyamoto, in Hydrogen in Metals, Proceedings of 2nd International Symposium, Supplement of Transactions of Japan Institute of Metals, vol 21 (1980), pp. 433–436 29. Y.H. Kim, J.W. Morris Jr., Metall. Trans. A 14A, 1883–1888 (1983) 30. A. Shibata, H. Takahashi, N. Tsuji, ISIJ Int 52, 208–212 (2012) 31. A. Shibata, T. Murata, H. Takahashi, T. Matsuoka, N. Tsuji, Metall. Mater. Trans. A 46A, 5685–5696 (2015) 32. A. Shibata, T. Matsuoka, A. Ueno, N. Tsuj, Int J Fract 205, 73–82 (2017) 33. T. Kobayashi, D.A. Shockey, Eng. Fract. Mech. 77, 2370–2384 (2010) 34. M. Michiuchi, S. Nambu, Y. Ishimoto, J. Inoue, T. Koseki, Acta Mater. 57, 5283–5291 (2009) 35. T. Depover, D. Pérez Escobar, E. Wallaert, Z. Zermout, K. Verbeken, Int. J. Hydrogen Energy 39, 4647–4656 (2014) 36. Q. Liu, Q. Zhou, J. Venezuela, M. Zhang, A. Atrens, Corros. Sci. 125, 114–138 (2017) 37. R.G. Davies, Metall. Trans. A 12A, 1667–1672 (1981) 38. R.G. Davies, Scr. Metall. 17, 889–892 (1983) 39. M. Koyama, C.C. Tasan, E. Akiyama. K. Tsuzaki, D. Raabe, Acta Mater. 70, 174–187 (2014)

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Chapter 9

Mechanistic Aspects of Fracture I—Brittle Fracture Models

The fracture of materials is a mechanistic event, and the mechanistic scheme and describing the function of hydrogen in the fracture process are required. In the latter half of the twentieth century, recognition of the involvement of hydrogen in the failure of structural steel components, like delayed cracking and degradation in mechanical testing, overlapped with developing fracture mechanics that addressed brittle fracture. Hydrogen-related fracture of high-strength steel is mostly brittle-like without substantial apparent plasticity. It was then a natural consequence to consider hydrogen-related fracture as a type of brittle fracture and to include the function of hydrogen in the controlling process of the fracture, i.e., the thermodynamic instability of a crack as the critical stage. In the following, major brittle fracture models so far proposed are reviewed from mechanistic viewpoints. However, experimental difficulties, particularly in detecting hydrogen behaviors and revealing fine microstructural details, made early works on the function of hydrogen rather conceptual.

9.1 Internal Pressure Theory Historically, internal cracks named “snowflakes”, “fisheyes” or “white spots” are the earliest known hydrogen-induced defects in steel. Bright and shiny facets suggested high-pressure molecular hydrogen precipitation, and the precipitation sites were assumed to be “inter-block disjunctions” in crystals causing local cleavage and rupture [1]. The hydrogen source is mostly moisture in the atmosphere during the fabrication process of steel. The hydrogen solubility in bcc iron in thermal equilibrium with hydrogen gas of pressure P follows Sieverts’ law in Eq. (1.1). For iron, when hydrogen introduced under a hydrogen atmosphere of 0.1 MPa at 1273 K (1000 °C) is quenched to room temperature, the expected pressure of internally precipitated hydrogen gas is 4 × 106 MPa in equilibrium with the supersaturated lattice hydrogen concentration, enough to © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2023 M. Nagumo, Fundamentals of Hydrogen Embrittlement, https://doi.org/10.1007/978-981-99-0992-6_9

245

246

9 Mechanistic Aspects of Fracture I—Brittle Fracture Models

Fig. 9.1 Geometry of an elliptical hole in homogeneous linear elastic solid under applied tensile stress σ

σ

b

a

σ

cause cracking. Estimated hydrogen fugacity at various cathodic electrolysis methods is shown in Table 2.1. (a) Griffith Condition The internally pressurized crack can act as an incipient crack for brittle fracture. The basic notion of brittle fracture is the classical Griffith condition proposed for the fracture of glass. A model describes the thermodynamic instability of an elliptical hole in a homogeneous linear elastic solid under tensile stress, as illustrated in Fig. 9.1. The critical condition for unstable crack growth is that the release of the potential energy supplied by the internal strain and external force exceeds the increase in the surface energy. The expression for a crack of half-length a in a solid of surface energy γ and Young’s modulus E in plane-strain condition is, σf =

√

2Eγ /π(1 − v 2 )a,

(9.1)

where σ f is the fracture stress and ν is Poisson’s ratio. The surface energy is defined as the energy to create a unit area of the new surface. The lower γ and the longer a decreases σ f . Tetelman and Robertson detected microcracks of 10–4 m in length on {100} planes of 3%Si-iron single crystals by hydrogen introduced under strong cathodic charging in 4% H2 SO4 added with CS2 and As2 O3 at a current density of 160A/m2 at room temperature [2]. Arrays of decorated dislocations were revealed, indicating intermittent growths of cracks associated with plastic deformation. The reasonable origin is a buildup of internal pressure by hydrogen and its decrease associated with the crack growth. Tetelman et al. replaced σ f in Eq. (9.1) with the internal pressure P for a penny-shaped crack and calculated stress fields around the crack tip. The calculated results matched well the observed growth of the crack and slip traces. The deduced ratio of the energy expended in restarting the crack to the energy expended in moving it was of the order of unity for cracks 10–4 m long, implying a small contribution of plasticity that blunted the crack in this case. The internal pressure estimated from Eq. (9.1), neglecting the contribution of plasticity, was about 100 MPa.

9.1 Internal Pressure Theory

247

(b) Incipient crack The existence of an incipient crack is a crucial premise for brittle fracture. The void formation at non-metallic inclusions, like elongated MnS in particular, has been wellknown concerning hydrogen-induced cracking (HIC) for line-pipe steel exposed to humid environments containing H2 S [3]. The molecular precipitation of hydrogen entering from environments forms voids. On the other hand, some models for the plasticity-induced nanocrack formation for brittle fracture have been proposed as schematically shown in Fig. 9.2: (a) Stroh’s model for the pileup of dislocation groups at the interface such as grain boundaries [4] and (b) Cottrell’s model for coalescence of dislocations moving on intersecting slip planes [5]. In the former, the critical shear stress τ c acting on pileup of n dislocations to coalesce into a crack is. ( ) 12γ τc = τi + , (9.2) nb where τ i is the friction stress in the slip plane, γ is the surface energy, and b is the Burgers vector. The smaller n needs the larger τ c to coalesce piled-up dislocations. Cottrell pointed out the vital role of hydrostatic tension in the growth of a crack nucleus [5]. The instability of a microcrack under external stress, in addition to internal pressure, was given by Garofalo et al. [6] and Bilby et al. [7]. The basic idea is the same as the Griffith model, i.e., a crack’s catastrophic growth occurs when the Gibbs free energy change is negative. For a wedge-shape crack produced by n dislocations running into the crack on a slip plane, the instability condition under an internal pressure p and applied external stresses, which produce a normal stress σ 1 and a shear stress σ 2 , was given in the form, [ ]1/2 4γ , + [(σ1 + p)sinθ − σ2 cosθ ] ≥ (σ1 + p)2 + σ22 nb

(9.3)

where θ is the angle between the crack and the slip plane, γ is the surface energy, and b is the Burgers vector of the dislocations [7]. The critical length 2c* of the crack σ

τ Grain Boundary

τ

Crack

(a)

(b)

σ

Fig. 9.2 Dislocation models for nanocrack formation. (a) Stroh’s model for pileup of dislocations at interface such as grain boundaries. (b) Cottrell’s model for coalescence of dislocations moving on intersecting slip planes

248

9 Mechanistic Aspects of Fracture I—Brittle Fracture Models

was 2c∗ = 4μγ {π (1 − ν)ϕ[ϕ + (σ1 + p)sinθ − σ2 cosθ ]}−1 ,

(9.4)

where μ and ν are the shear modulus and Poisson’s ratio, respectively, and ϕ is defined as ϕ 2 = (σ1 + p)2 + σ22 .

(9.5)

Another expression of 2c* in terms of n is 2c∗ = nbμ[π (1 − ν)ϕ]−1 .

(9.6)

The magnitude of 2c* in Eq. (9.4) was computed assuming hydrogen pressure corresponding to the lattice hydrogen concentration of 8 mass ppm and γ values that include an expected decrease due to hydrogen adsorption on the crack surface (described in Sect. 9.2). The calculated 2c* for the observed fracture stress of mild steel at 158 K was about 6 or 4 nm, assuming γ of 0.83 or 0.52 J/m2 . The values are much shorter than observed 1 ~ 4 μm for hydrogen-free cases [6]. The assumed hydrogen concentration was under an unrealistically high p-value of 3100 MPa. Also, the assumed γ was much less than γ considering plastic deformation around the crack. Usually, observed hydrogen is mainly trapped hydrogen rather than in solid solution, and nanoscale cracks predicted by the models in Fig. 9.2 have not been observed experimentally. Application of Stroh’s model to actual brittle fracture has some other difficulties, such as the sharpness of the crack tip, the relaxation of high stresses on piled-up dislocations due to the activation of secondary slip systems, and complex microstructures particularly near grain boundaries in high-strength steel.

9.2 Surface Adsorption Theory A decrease in the surface energy γ in the Griffith condition Eq. (9.1) promotes the instability of a crack. Lowering of γ of metals by hydrogen adsorption on the surface is given as Eq. (5.10) in Sect. 5.3.3 according to the Gibbs adsorption isotherm and the Langmuir adsorption. Petch assumed a crack ahead of arrays of n edge dislocations held up at some obstacle under a shear stress τ [8]. The Stroh model for the microcrack formation gives a relationship among τ, n, and γ in the form τ = 12γ /nb.

(9.7)

The dislocation arrays produce normal stress as a part of the fracture stress superposing the external stress. Also, assuming that the array length is one-half the grain diameter, Petch calculated γ as a function of the hydrogen concentration using

9.3 Lattice Decohesion Theory

249

Eq. (5.10) and Sieverts’ law that related the internal pressure to the hydrogen concentration. The results for α-iron at room temperature are shown in Fig. 5.8. The initial decrease in γ amounts to almost 90% by hydrogen concentrations less than 1 mass ppm. The calculated decrease in γ at very low hydrogen concentrations amounts to ~ 2 J/m2 , about 40% of the true surface energy γ 0 of metals, but it is still a very small fraction of the effective surface energies for fracture of the order of kJ/m2 , estimated from fracture toughness data of steel. A decrease in γ due to the surface adsorption of hydrogen is viable, but its quantitative contribution to observed degradation is an issue, as described in Sect. 5.3.3. According to his surface energy theory, Petch explained the observed fracture stress of mild steel with different grain sizes [8]. However, the amount of hydrogen used for his estimation was as much as 10 mass ppm. The used cathodic electrolysis in 4% H2 SO4 containing poison at a current density of 3200A/m2 was very strong, surely producing extraneous defects by electrolysis. Tromans calculated more precisely changes in γ of α-iron due to hydrogen adsorption using a suitable adsorption isotherm [9]. The calculated decrease in γ from the value in vacuum was 0.5 J/m2 at 100 MPa hydrogen gas at 298 K. Tromans also showed effects of local stress on γ instead of internal pressure. Hydrostatic stress increased the activity of hydrogen, and the calculated decrease in γ by local hydrostatic stress of 1 GPa was 0.2 J/m2 . The fracture surface in hydrogen embrittlement (HE) often exhibits a fine mixture of plastic shearing-off and cleavage-like fracture. As described in Sect. 6.2.2.1 on the crack growth rate in gaseous hydrogen environments, the model by Vehoff and Roth on the crack-tip opening assumed that the fractional hydrogen coverage of particular sites right at the tip of a stressed crack controls the crack propagation in HE [10].

9.3 Lattice Decohesion Theory 9.3.1 Stress-Controlled Criterion The Griffith condition, Eq. (9.1), is a thermodynamic criterion for the onset of instability of a crack without referring to the microscopic processes of crack extension. In the mechanistic aspect, the break of atomic bonds is to occur for the crack extension, and the stress concentration at the crack tip must exceed the cohesive strength. This is the stress-controlled criterion of brittle fracture. The Griffith model assumed an elliptical hole of 2a in length and the radius of curvature of ρ. The mechanistic condition of the bond separation by the stress concentration at the hole edge is σmax

( √ ) √ a a E ≈ 2σa = σa 1 + 2 > σth ≈ , ρ ρ 6

(9.8)

250

9 Mechanistic Aspects of Fracture I—Brittle Fracture Models

where σa is the applied stress and σth is the ideal strength of metal with Young’s modulus E. The magnitude of σ max is very high. A numerical estimation for σa = 100 MPa, 2a = 10 μm, and E = 300 GPa requires a very sharp ρ of atomistic scale as small as 1.6 × 10–10 m, unfeasible in practical steel. Oriani and Josephic formulated a stress-controlled unstable crack advance criterion for HE [11]. The work to cut n atomic bonds per unit area is twice the true surface energy γ , ∞ 2γ = n

F(z)dz,

(9.9)

z0

where F(z) is the cohesive force, z is the interatomic distance, and z0 is the stress-free equilibrium value of z. A further difficulty in the criterion is that the bond separation is not a sufficient condition in unstable crack extension. In the above numerical assumptions, γ must be low enough, close to the true surface energy of metals ~ 2 J/m2 , to satisfy the thermodynamic Griffith condition. When plasticity is involved in the crack extension, the magnitude of γ substantially increases, and a larger γ requires a higher σ f in Eq. (9.1). Troiano assumed the hydrogen-decreased cohesive strength for the delayed fracture of high-strength steel but thought the formation of fracture embryo due to activated dislocation arrays [12]. An involvement of plasticity in the creation of new surfaces remarkably increases the effective surface energy. A critical condition for the start of a crack is that the concentrated stress at the crack tip exceeds the maximum cohesive force as expressed k ' σ (L/ρ)1/2 = n Fm (c' ),

(9.10)

where σ is the applied tensile stress, L is the crack length, ρ is the crack-tip radius, n is the number of atoms per unit area of the crystallographic plane, F m (c' ) is the maximum cohesive force at a local hydrogen concentration c' , and k ' is a numerical parameter. The assumption that Oriani and Josephic made [11] was that F m decreases in proportion to hydrogen concentration c, Fm (c) = Fm0 − αc,

(9.11)

where F m 0 is F m of the hydrogen-free lattice and α is an unknown parameter. The model was thus designated as the hydrogen-enhanced decohesion (HEDE) theory. Estimating F m (c) is difficult, but it is included in the stress intensity factor K, a parameter to express stress fields near the crack tip, described in the following Sect. 9.3.2. Using Eq. (9.10) for the stress-controlled brittle fracture, K is ( ) K = k '' ρ 1/2 n Fm c' ,

(9.12)

where k '' is a numerical parameter. A buildup of c' by hydrostatic stress at the crack tip was considered in the calculation. Oriani et al. embedded F m (c' ) in the critical stress

9.3 Lattice Decohesion Theory

251

intensity K cr for the onset of unstable fracture, using numerical F m (c' ) determined with experimental parameters. The local hydrogen concentration c is a function of the hydrostatic stress. Oriani et al. derived a relation between the environmental hydrogen gas pressure and K, using F m (c) and crack-tip radius as parameters. The ad hoc parameters were determined to fit the calculation using the formula with the experimental dependence of the critical hydrogen pressure on K. The model was examined by experiments using WOL specimens of AISI 4340 steel in hydrogen and deuterium gases of pressures lower than 0.1 MPa at room temperature. Examples of thus determined parameters for K cr of 20 ksi·in1/2 (= 22 MPa·m1/2 ) were the hydrostatic pressure of 2.49 × 103 ksi (= 17.4 GPa), the local hydrogen concentration of 6.75 × 10−6 β (H/M), and F m (c)/F m 0 of 0.34. Experimental data Oriani et al. referred to were of intergranular (IG) fracture, and the unknown parameter β for the local hydrogen concentration was estimated to exceed 103 at grain boundaries. The fit between experimental and theoretical dependencies of p on K was good, but the estimated values of the hydrostatic stress and the local hydrogen concentration are not likely realistic. Hydrogen effects on the crack-tip sharpness is a vital issue in HE of steel. A molecular dynamics (MD) simulation demonstrated a suppressed dislocation emission from the crack tip in iron by hydrogen, preventing blunting of the crack tip [13]. Two crack-tip geometries and orientations were considered, the crack plane normal of (111) [112] and (111)[110] both orientations having a dislocation slip system available for easy dislocation emission. The system was initially deformed to a load K I = 0.8 MPa m1/2 that provided a driving force for hydrogen segregation toward the crack tip. Hydrogen atoms were then randomly inserted into interstitial sites within a cylindrical region of radius 10 nm around the crack tip. The fracture events at the crack tip were then investigated as a function of the applied load and the extent of hydrogen aggregation around the crack tip. Hydrogen atoms segregated to the crack surfaces started to aggregate in the vicinity of the loaded crack tip and formed a hydrogen-rich region. A local phase transformation from bcc to fcc structures occurred in the hydrogen-rich region. When the hydrogen concentration increased to 35 ~ 122/nm, the hydrogen-rich region blocked dislocation emission, and instead, with increasing applied load, brittle cleavage occurred. A crack-tip ductile-to-brittle transition induced by hydrogen aggregation was the main result of the study, but the hydrogen-rich zone was like a hydride.

9.3.2 Local Stress Intensity Approach An alternative and general expression of the brittle fracture model is to use the stress intensity factor K. K expresses stress fields near the crack tip in the regime of linear elasticity as, σi j = √

K 2πr

f (θ )

(9.13)

252

9 Mechanistic Aspects of Fracture I—Brittle Fracture Models

in polar coordinates. Events that happen near the crack tip are controlled by K. For a through-crack of length 2a in an infinite plane at right angles to a uniform stress field σ, K is expressed as √ K = σ πa.

(9.14)

The critical value of K gives a failure criterion in a zone of a certain extent, but it per se does not specify the microscopic fracture process. K cr is useful as a parameter to express the fracture toughness of materials for engineering purposes, but the viability of expressing stress fields in terms of K breaks down in regions very close to the crack tip and in the presence of local plasticity. As described in Sect. 9.4.2(a), the immediate vicinity of the crack tip is crucial for the crack extension. Some modifications have been proposed for such local situations. The fracture criterion Eq. (9.12) that uses the maximum cohesive force, Eq. (9.10), is for the case of the stress-controlled fracture. However, it is to be noticed that observed critical values of K for fracture do not specify microscopic processes that cause the fracture event. Dislocations near the crack tip affect the crack-tip stress fields. When a crack is figured to occupy the negative real axis in the complex plane and dislocations are situated at points ζ j , the stress at a point z is the superposition of the stresses exerted by the crack and the dislocations as expressed in the form, σ =√

K 2π z

+

∑ μ bj j

√

2π

ξj 1 , z z − ςj

(9.15)

if, for simplicity, the distribution is symmetric about the x-axis [14]. The second term on the right-hand side is due to dislocations. By defining k D and the local stress intensity factor k as. μb , kD = √ 2π ς ∑ k=K− k D ( j ),

(9.16) (9.17)

j

σ (z) near the crack tip is expressed as [15] σ (z) ≈ √

k 2π z

.

(9.18)

Then, k is the effective stress intensity factor that determines the local stress fields in the presence of a dislocation group. Marsh and Gerberich derived a relation between the plane-strain fracture toughness K IC and the plane-strain Griffith local stress intensity for fracture k G [16]. A simplified approximation was developed from computer simulations for the closest

9.4 Theories of Intergranular Fracture

253

approach of the nearest dislocation to the crack tip. The obtained relation is KIC

( 2 ) k 1 ≈ ' exp 'I G , β α σy

(9.19)

where α ' and β ' are parameters, and σ y is the yield stress. Marsh and Gerberich assumed that the local hydrogen concentration C H could proportionately lower k IG to k IH in the form k I H = k I G − αC H .

(9.20)

hydrogen gas environments was to equate k IH with √ An estimation of k IH under Eγ , using about 1.5 ~ 1 J/m2 for γ calculated according to Tromans’ first-principles method [9]. The estimated k IH replaced k IG , and K IC in the presence of hydrogen was calculated from Eq. (9.19). Using also separately determined parameters α ' and β ' in Eq. (9.19) to fit fracture toughness data of steel, the calculated threshold K decreased with increasing hydrogen gas pressures along a curve nearly coincident with observed data for AISI 4340 steel in hydrogen gas [11]. The fracture mode for the observed data was IG described in Sect. 7.2.4. The local stress intensity factor does not explicitly incorporate F m , but Gerberich et al. ascribed the fit to the hydrogen-enhanced decohesion mechanism expressed by Eq. (9.12) [17].

9.4 Theories of Intergranular Fracture 9.4.1 Interface Decohesion Enhanced embrittlement associated with the segregation of impurities in prior austenite grain boundaries is well-known concerning temper embrittlement of steel [18]. Enrichment of hydrogen along grain boundaries of steel has been revealed using tritium autoradiography [19, 20] and discussed concerning IG fracture [21]. Thermodynamics of the impurity adsorption at the interface affecting interfacial embrittlement has been presented in the literature [22–24]. The transition of a system from non-equilibrium to equilibrium states is associated with a net decrease in energy, as the Griffith condition expresses. Crack extension under an external force releases the internal strain energy U while the external force does work F. The driving force of the crack extension is the net change of the energy. The energy release rate or the crack driving force or the crack extension force, G, is defined as G=−

d (U − F), dA

(9.21)

254

9 Mechanistic Aspects of Fracture I—Brittle Fracture Models

where A is the crack area. The net change of the energy is transferred to the work to create new surfaces, W s , and the equilibrium condition for the crack is −

d dWs . (U − F) = dA dA

(9.22)

In the Griffith condition, the right-hand side of Eq. (9.22) is 2γ , and the surface energy term in the Griffith condition expresses the crack extension force. A general and extensive energy balance criterion for the crack extension was in a pioneering work by Rice [25]. When the separation of material surfaces incorporates microstructural processes associated with plasticity, the meaning of the right-hand side of Eq. (9.22) is not identical to the surface energy. Descriptions of Rice’s model are at the end of Sect. 9.4.2(a). Rice and Wang presented a fundamental idea for the crack advance accompanying gradual interface decohesion, schematically shown in Fig. 9.3 [23]. The crack extension force G along the transition zone of length ω between two elastic solids is defined as.  ∞ G= σ (δ)dδ ≡ 2γint , (9.23) δ0

where δ is the local interfacial opening. In this model, the separation is reversible on stressing, i.e., the separated faces rejoin when removed the applied stress. 2γ int in Eq. (9.23) is the thermodynamic threshold for growth without including plastic work. Fig. 9.3 Model of interface decohesion. (a) Interfacial brittle crack between phases A and B. (b) Region of gradual decohesion neat tip over a size scale ω. (c) Tensile stress σ versus separation distance δ normal to the interface (Rice et al. [23])

σ σmax

(c) 2γint

δ A

ω S

A b δ B

a

(a)

B

(b)

9.4 Theories of Intergranular Fracture

255

The impurity segregation at the interface increases the energy of the interface by the potential energies of segregants. The energy change du associated with the reversible change of a state is du = T ds + σ dδ +

∑

μi d⎡i ,

(9.24)

i

where T is temperature, s is entropy, and μi and Gi are, respectively, the equilibrium chemical potential and concentration of the i-segregant. Using Eqs. (9.23) and (9.24), Rice and Wang formulated the change in 2γ int for the interface separation under a constant concentration or chemical potential of a segregant. The segregation of impurities was assumed to follow the Langmuir-McLean theory that derived the fractional monolayer segregation to minimize the energy of the system, ) ( ⎡ Δg , = x exp − ⎡ max − ⎡ RT

(9.25)

where x is the fraction of available sites in the bulk to be occupied by the segregant and Δg is the Gibbs free energy of segregation per mole of segregant. Rice and Wang derived an approximate form of 2γ int for the case of fixed and low G in the form, ) ( 2γint = (2γint )0 − Δgb0 − Δgs0 ⎡,

(9.26)

where suffixes 0, b, and s abbreviate, respectively, segregant-free, boundary, and surface. Reported values of (Δgb 0 − Δgs o ) for P, Sn, and Sb are in the range 50 ~ 100 kJ/mol. When one assumes that segregants occupy of one-quarter of possible adsorption sites, the second term of the right-hand side of Eq. (9.23) is 0.35 ~ 0.70 J/m2 , a substantial fraction of the true surface energy of metals. Following Rice-Wang’s theory, Novak et al. proposed a model that a dislocation pileup against a grain-boundary carbide which leads to interface decohesion and IG fracture, as an explanation of the role of hydrogen-enhanced plasticity in IG fracture [26]. Assumed hydrogen functions were in two ways: one was to reduce the reversible work for the decohesion along the carbide/matrix interface and the other was to enhance dislocation motion increasing the number of piled-up dislocations. Novak et al. applied the model to four-point bending tests of thermally hydrogencharged AISI 4340 steel. Many assumptions and numerical estimations were made as listed below for quantitative analyses: (1) In the second term on the right-hand side of Eq. (9.26), (Δgb 0 − Δgs o ) of hydrogen was set to 74.5 kJ/mol, within the same range as that for P, Sn, and Sb. (2) Trapped hydrogen in dislocations affects decohesion, rather than hydrogen strongly trapped in other sites such as grain or interface boundaries. The hydrogen occupancy for dislocations, θT(d) , was used in the interfacial coverage G,

256

9 Mechanistic Aspects of Fracture I—Brittle Fracture Models

⎡ = η θT(d) ⎡max ,

(9.27)

with a fitting parameter η. The number of trap sites per unit area of the interface, Gmax , was determined from observed carbide size and frequency. (3) The hydrogen concentration at the interface was estimated assuming transport by dislocations. The density of dislocations near the notch root was calculated using a finite element method. (4) The weakest-link model was applied to estimate the fracture stress caused by the carbide/matrix interface decohesion. (5) The effective surface energy, γ eff, in the Griffith condition for the instability of the interface-crack, included plastic work γ p accompanying the decohesion initiation event, in the form γeff = 2γint + γp ,

(9.28)

γp = A(2γint )q ,

(9.29)

with parameters A and q. The parameters were determined to fit calculated fracture stress with observed ones for various hydrogen concentrations. The second term on the right-hand side of Eq. (9.26) expresses the reduction in 2γ int by hydrogen segregation. The expression of Γ is in Eq. (9.27), and the estimated value of ⎡ was 5 × 10–5 mol/m2 (= 3 × 10–19 /m2 ) for the average hydrogen concentration of 1 at ppm. The calculation used assumed or calculated values [26], i.e., Δgb = −25.5 kJ/mol, Δgs = −100 kJ/mol, θT(d) = 5 × 10–4 , η = 0.01, and ⎡ max = 6.17 × 1024 /m2 . The estimated reduction in 2γ int by hydrogen was 3.8 J/m2 , which is about one order of magnitude larger than the values by the segregation of P and Sn, and almost completely cancels out the true surface energy of metals. The effective surface energy, considering the energy dissipation due to plasticity, was obtained from Eqs. (9.28) and (9.29). Taking A = 0.02 and q = 6, the estimated magnitude of γ p was 82 J/m2 for 2γ int of 4 J/m2 . The crack extension force in Eq. (9.23) or 2γ int in Fig. 9.3 is the essential quantity in the interface separation. Hydrogen effects on 2γ int are included in the Gibbs free energy changes in Eq. (9.26), and the involvement of plasticity makes an estimation of 2γ int complicated. Instead, Yamaguchi et al. conducted first-principles calculations on grainboundary embrittlement in metal-hydrogen systems [27], calculating the total segregation energy changes, ΔE gb seg and ΔE s seg , when hydrogen atoms move from the bulk to grain boundary or free surface. Yamaguchi et al. defined 2γ int as the difference between 2γ S and γ GB , as schematically shown in Fig. 9.4. The first-principles calculations by Yamaguchi et al. used the unit cell consisting of 76 Fe atoms and ∑ 3(111) symmetrical tilt grain boundaries in a bcc lattice. One hydrogen atom was

9.4 Theories of Intergranular Fracture Fig. 9.4 Work for grain-boundary separation 2γ int with and without hydrogen segregation (Yamaguchi et al. [27])

257

2γs Δ

2 γgb

2γint

Δ E H-Segregation

successively inserted at each interstitial site in the unit cell until the segregation energy reached a constant value. Calculated values of ΔE gb seg on Fe∑3(111) grain boundary and ΔE s seg on Fe(111) are − 45 and − 79 kJ/mol, respectively. The total segregation energy decreased with the hydrogen concentration, and the resultant decrease in 2γ int was as much as 40% when six immobile hydrogen atoms were present in a unit cell area of 0.278 nm2 on a Fe∑3(111) boundary. Yamaguchi et al. also showed a more pronounced decrease in 2γ int when hydrogen atoms were mobile, while the concentrations in the boundary and free surface in thermal equilibrium were the same as in bulk [28]. However, 2γ int shown in Fig. 9.4 was the difference of the total energies before and after the interface separation. Their definition is not the crack extension force in Fig. 9.3(c). 2γ int in Fig. 9.4 is the driving force for the interface separation, but the separation does not proceed spontaneously. Overcoming the energy barrier is also a necessary condition for fracture. Kirchheim et al. applied the DEFACTANT mechanism described in Sect. 3.1.2 to the grain boundary or interface decohesion [29]. The reduction of the interfacial energy by impurity segregation is expressed by Eq. (9.3.11) in Sect. 3.1.2 in terms of the excess chemical potential of impurities. dγ = −⎡ A dμ A .

(9.3.11)

However, a significant chemical potential or hydrogen pressure is requisite to cause a remarkable reduction of the work to fracture, defined as the difference between the newly created surface energy and the interface energy before separation. Quantitative estimations for an iron–hydrogen system predicted hydrogen pressure above 1GPa or hydrogen fugacity 108 bar to decrease the work to fracture. The vapor pressure of liquid water of about 20 mbar at room temperature gives about 20 MPa or 200 bar hydrogen fugacity in iron [29]. When dislocations or vacancies are present, enhancements of both the generation and movement rates by hydrogen are feasible.

258

9 Mechanistic Aspects of Fracture I—Brittle Fracture Models

9.4.2 Meaning of Surface Energy in Fracture Criteria (a) Effective surface energy A critical problem in applying the Griffith condition to IG fracture is the physical meaning of the surface energy γ . The effective surface energy “γ ” derived from the observed fracture strength or K cr using Eqs. (9.1) and (9.14) is of the order of 1 kJ/m2 , about three orders of magnitude higher than the true surface energy γ of metals. A common understanding of the difference is the involvement of plastic work γ p in γ , as conventionally written as Eq. (9.28). However, the plastic processes that compose γ p are difficult to figure for estimating γ p . McMahon and Vitek considered the work done by plastic deformation around the crack tip [30]. A model that McMahon and Vitek proposed was that the plastic region associated with the crack growth was a strip laid down along either side of the crack path. The plastic work W p is proportional to the effective applied tensile stress σ eff and plastic strain εp , Wp ∝ σeff εp Vp ,

(9.30)

where V p is the volume of the plastic region. McMahon and Vitek considered γ p as the change of W p at the crack extension, i.e., γp =

dWp . da

(9.31)

The plastic strain rate ε˙ p associated with the crack extension is proportional to ∂εp /∂a, and ε˙ p is empirically related to stress σ as, m ε˙ p ∝ σeff ,

(9.32)

Since γ p relates to ε˙ p according to Eqs. (9.30) and (9.31), γ p also relates to σ eff . Utilizing differentiation of logarithmic functions, the relation of γ p with σ eff is dγp dσeff ≈ (m + 1) . γp σeff

(9.33)

McMahon and Vitek assumed two processes at the crack tip, one is bond stretching and rupture, and the other is dislocation emission and motion. A further assumption was that the two processes were independent and the crack extension was very fast, the bond stretching occurring only at the crack tip [30]. The purpose of the assumption was to separate the true surface energy γ from γ p. The local stress at the crack tip dominates the bond breaking and is proportional to σ eff . Since the true surface energy γ is the work done by the local stress, γ is proportional to σ eff . Then, from Eq. (9.33), a relation between γ and γ p was obtained in the form

9.4 Theories of Intergranular Fracture

dγp dγ ≈ (m + 1) . γp γ

259

(9.34)

The impurity segregation reduces the ideal surface energy γ , and the problem is whether the reduction in γ affects γ p . That hydrogen reduces not only the reversible work but also the attendant plastic work was the implicit assumption of Eq. (9.29) that Novak et al. applied to decohesion of the carbide/matrix interface. Alternatively, Jokl et al. considered a moving microcrack under stress and assumed concomitant bond breaking and dislocation emission from the crack tip [31]. In their model, the stress ahead of the crack and the microcrack opening displacement varied with time, and the plastic work γ p was ascribed to the energy consumed by dislocation emission. Jokl et al. derived a thermodynamic criterion for the unstable microcrack extension taking into account the movement of newly created dislocations. Using the relationship between stress and dislocation velocity of the form of Eq. (9.32), γ p was numerically computed as a function of the ideal work for fracture γ with several adjustable parameters. The calculated γ p values were about 2 ~ 5 times as large as γ. McMahon and Vitek’s model could correlate a significant change in γ p with a small change in γ . The crack-tip condition determines the instability of a crack, and Rice formulated under a thermodynamical scheme a general crack instability criterion incorporating plastic work [25]. Figure 9.5 shows his model [25]. In contrast with the Griffith model in Fig. 9.1, a cracked continuum is loaded by forces per unit area T on the portion of bounding surface At and per unit volume F throughout the region V occupied by the body. Displacements U are imposed on the portion of bounding surface AU . No particular assumptions are made in the constitutive equations that relate stresses and strains. The crack extension increases the tractionfree crack surface by an amount A' . The energy balance criterion is that the work of applied forces during crack extension equals the change in stored elastic energy, dissipated energy, kinetic energy, and Fig. 9.5 Model of cracked continuum loaded by surface and body forces, imposed displacement on the portion of bounding surface. The crack extension increases the traction-free crack surface (Rice [25])

260

9 Mechanistic Aspects of Fracture I—Brittle Fracture Models

energy of the newly created surface. The last term is γ A' . The fracture criterion is then, ⎫ ⎧ ⎪  ⎪ (b) ⎨ [( b ) ) ]]⎬ [( b 1 dV = γ, (9.35) σi j − σi j dεi j + ρ u¨ i − u¨ i du i lim ' ⎪ ⎪ A ⎭ ⎩ V0

(a)

where V 0 denotes any arbitrary small region surrounding the crack tip and ρ is the mass density. Superscript a or b in Eq. (9.35) on any mechanical quantity denotes its value in the initial or extended states, respectively, in Fig. 9.5. Rice calculated each term of the energy change with the configurations depicted in Fig. 9.5 for an infinitesimal crack extension. The derived fracture criterion states that the crack instability is determined solely by singularities in the stress and deformation fields at the crack tip, i.e., by the local stresses and deformations in the immediate vicinity of the crack tip. The immediate vicinity means an arbitrarily small portion that surrounds the crack tip and contains A' . The physical meaning of γ A' is the work done by the new crack surfaces against forces tending to hold them together. The value of γ A' is determined independently of the changes of elastic and dissipated energies, and its estimation needs microstructural considerations on processes separating material surfaces. (b) Griffith condition for plasticity-induced crack at carbide The presence of an incipient crack is a premise of energy balance criteria. Observed fracture toughness values include energies dissipated in forming the incipient crack, adding to energies needed for the crack instability. McMahon and Vitek considered the brittle crack nucleation at carbides in grain boundaries located a distance x from the precrack tip [30]. The crack was assumed to be formed by the pileup of dislocations at the carbide/boundary interface. Formerly, Smith formulated the Griffith condition for a crack produced by dislocation pileup at a carbide of 2c in length [32]. When the crack length along the interface between the carbide is c, and the dislocation pileup length is L, the Griffith condition for the crack, using Eq. (9.28) for γ eff , was, σ L2

+

2 τeff

[( ) ]2 ) ( 4E 2γ + γp L 1/2 4 τf ) , + ≥ ( c π τeff π 1 − ν2 c

(9.36)

where σ L is the local stress ahead of the precrack, τ eff is the effective shear stress on the dislocation pileup, E is Young’s modulus, and ν is Poisson’s ratio. In this case, the local stress σ L at the carbide in terms of the critical stress intensity K C is KC , σL = √ 2π x0

(9.37)

9.5 Summary of Brittle Fracture Models

261

where x 0 is the distance from the pre-crack tip to the point of microcrack nucleation. Equation (9.36) is the instability criterion for the newly created microcrack, but the magnitude of γ p can be expressed in terms of the macroscopic fracture toughness K IC or crack extension force GIC that characterizes stress fields around the pre-crack under plane-strain condition. Using Eq. (9.36) and assuming τ f