Engineered Cementitious Composites (ECC): Bendable Concrete for Sustainable and Resilient Infrastructure [1st ed.] 978-3-662-58437-8;978-3-662-58438-5

Table of contents :
Front Matter ....Pages i-xvii
Introduction to Engineered Cementitious Composites (ECC) (Victor C. Li)....Pages 1-10
Micromechanics and Engineered Cementitious Composites (ECC) Design Basis (Victor C. Li)....Pages 11-71
Processing of Engineered Cementitious Composites (ECC) (Victor C. Li)....Pages 73-99
Mechanical Properties of Engineered Cementitious Composites (ECC) (Victor C. Li)....Pages 101-137
Constitutive Modeling of Engineered Cementitious Composites (ECC) (Victor C. Li)....Pages 139-175
Resilience of Engineered Cementitious Composites (ECC) Structural Members (Victor C. Li)....Pages 177-223
Durability of Engineered Cementitious Composites (ECC) and Reinforced ECC (R/ECC) Structural Members (Victor C. Li)....Pages 225-260
Sustainability of Engineered Cementitious Composites (ECC) Infrastructure (Victor C. Li)....Pages 261-312
Applications of Engineered Cementitious Composites (ECC) (Victor C. Li)....Pages 313-369
Multi-functional Engineered Cementitious Composites (ECC) (Victor C. Li)....Pages 371-411
Back Matter ....Pages 413-419

Citation preview

Victor C. Li

Engineered Cementitious Composites (ECC) Bendable Concrete for Sustainable and Resilient Infrastructure

MATERIALS.SPRINGER.COM

Engineered Cementitious Composites (ECC)

Victor C. Li

Engineered Cementitious Composites (ECC) Bendable Concrete for Sustainable and Resilient Infrastructure

With 410 Figures and 37 Tables

Victor C. Li Department of Civil and Environmental Engineering University of Michigan Ann Arbor, MI, USA

ISBN 978-3-662-58437-8 ISBN 978-3-662-58438-5 (eBook) https://doi.org/10.1007/978-3-662-58438-5 Library of Congress Control Number: 2018968114 © Springer-Verlag GmbH Germany, part of Springer Nature 2019 This work is subject to copyright. All rights are reserved 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, express 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-Verlag GmbH, DE, part of Springer Nature. The registered company address is: Heidelberger Platz 3, 14197 Berlin, Germany

Foreword

Those who can, do; those who can’t, teach. Probably no other proverb causes academics and professors to cringe more, but, fortunately, it is wrong. As evidence, I present this wonderful book written by a distinguished professor who did create a new field in civil engineering. Based on the rigorous foundations of micromechanics coupled with an insightful understanding of the microstructure existing in composite cementitious materials, Professor Victor Li developed Engineered Cementitious Composites (ECC), a lasting contribution to the design and construction of the civil infrastructure. One of the major benefits of being invited to write this foreword is that I received an advanced copy of the book. You are in for a treat. Even if you are familiar with ECC and eager to immerse yourself into the rigorous micromechanics foundation (▶ Chap. 2) and its links to mechanical properties (▶ Chap. 4) or to ascertain the ECC constitutive modeling (▶ Chap. 5) or to learn how to design resilient ECC structural members (▶ Chap. 6), I highly recommend that you start with ▶ Chap. 1: it contains a very personal perspective of the early developments and a compelling overview of the unique features of ECC compared to normal concrete and other high-performance concretes. The civil infrastructure in many developed countries is aging fast. For instance, in the United States, out of 614,387 bridges, 56,007 are structurally deficient. Society requires that damaged structures be repaired and that any new construction be lasting and sustainable. Most of the durability problems in reinforced concrete are associated with the penetration of aggressive ions through cracks and connected porosity in concrete. By controlling the crack width in ECC to less than 0.1 mm, the penetration and diffusion of aqueous solutions containing aggressive ions, such as chlorides and sulfates, are significantly reduced, thus increasing the life cycle of the structure even if steel reinforcement is embedded in the matrix. ▶ Chap. 6 presents extensive experimental evidence of the improvement of the ECC transport properties. Considering that the world’s yearly cement production of 4.2 billion tonnes is responsible for nearly 7% of the total global CO2 emissions, concrete manufacturing needs to optimize the cement content, increase the mechanical properties, and extend the life cycle of structures. Although some versions of ECC use more cement than normal-strength concrete, this increased carbon footprint is more than offset by the large increase in the mechanical behavior and durability of v

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the material. Careful life cycle analysis of various scenarios is presented in ▶ Chap. 8, which also discusses the promising sustainable options of using green aggregate and green fiber. Often new construction materials showing exciting laboratory properties do not scale up into engineering practice. In fiber-reinforced cementitious materials, the challenge is to guarantee a uniform dispersion of the fibers and an adequate rheology during the processing of the material. ▶ Chapter 3 presents a detailed presentation of ECC properties in the fresh state and an insightful discussion on the requirements for self-consolidating casting, shotcreting, and extrusion. After presenting the science and technology of ECC, the book discusses various applications of the material in practice (▶ Chap. 10) and introduces today’s cutting-edge research, including selfhealing, self-cleaning, and self-sensing ECC (▶ Chap. 11). In summary, this comprehensive book will be of interest to talented senior students, graduate students, researchers, and professional engineers. My recommendation for those who are searching for a book on engineered fiber-reinforced cementitious materials, including micromechanics, rheology, and structural design, is to search no more. Roy W. Carlson Distinguished Professor Department of Civil and Environmental Engineering, University of California at Berkeley, Berkeley, CA, USA

Paulo J. M. Monteiro

Preface

Although I have been a faculty member since 1981, first at MIT and then at the University of Michigan, this is the first book I have written. Writing this book is a long process, involving multiple false starts. It does have the benefit of training my patience. I feel a certain obligation to write this book on Engineered Cementitious Composites (ECC). As inventor of this material, I have seen the germination of ECC as an idea and theoretical conception, its birth as a material, and its growth into industrial scale structural applications. Since its beginning when the most respectable concrete technologists would only smile at the idea out of politeness (imagine the oxymoron “bendable concrete” in the early 1980s) to today when ECC is deployed in the tallest residential tower in Japan, the body of knowledge on ECC has grown enormously. Today, more than 300 research and development groups worldwide are actively working on ECC and its applications. At national and international conferences, I am often asked where a researcher could best start on the study of ECC. I realized then that the large amount of knowledge on ECC is spread out over many different journals and conference proceedings; a book that provides information on ECC in a coherent organized format is called for. This book is therefore foremost written for graduate students who want to learn the many interesting aspects of ECC and for researchers who want to contribute to expanding the maturation of ECC technologies. Practitioners will also find this book helpful in designing structures beyond the limits of normal concrete or high-strength concrete. But why ECC in the first place? Concrete is arguably one of the most important engineering materials in support of modern civilization as we know it – forming the material basis of most of the transportation, building, water, and energy infrastructure we take for granted every day. While concrete has evolved since its invention about 200 years ago, it has the technical bottleneck of being a brittle material. The brittleness of concrete, I believe, is a fundamental source of disasters during natural hazards, traffic jams associated with repeated road repairs, and global warming caused by pollutant emissions in the making of cement. ECC has been conceived to overcome these challenges in infrastructure resilience, durability, and sustainability. As this book attempts to demonstrate, ECC also forms an excellent platform for multifunctionality that supports the next generation of smart civil infrastructures.

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I am often asked the question how I first conceived of ECC. The truth is the idea came about out of ignorance. As a young assistant professor fresh out of a PhD focused on the study of the mechanics of earthquake rupture, I felt I had to learn something relevant to my students’ interest in a Civil Engineering department. I noticed at that time that a number of prominent professors were directing their efforts in predicting crack paths in concrete structures. I wanted to be part of this community and participated enthusiastically in a number of national and international conferences on this subject, using my background in fracture mechanics that I learned from my eminent mentors, Professor James R. Rice and Professor Benjamin Freund, at Brown University. However, I soon felt disillusioned by the fact that the prediction of crack path would best be satisfying academically but has little impact on the practicing profession of civil engineering. Since I never had the textbook knowledge that concrete cracking is a given, I soon launched a research program on creating ductile concrete, using fracture mechanics on the microstructural scale. Many wellmeaning concrete technologists and senior professors warned me of my foolishness in attempting to defeat a fundamental behavior of concrete that is 200 years old. However, my conviction was strengthened knowing that nature has already made ductile nacre out of brittle aragonite. I am glad that my stubbornness had won out; otherwise this book would not exist. I began working on this book earnestly after my younger son Alex was born. At that time, my focus on using ECC for infrastructure sustainability enhancement has entered into high gear. In retrospect, this is no accident in timing. In many public presentations, I had included my son’s baby picture in my last slide, with the words “creating harmony between the built and natural environment” splashed across the screen. I know that my generation will survive the impacts of climate change. Alex’s generation will literally feel the heat. But I am not so sure how my grandkids will fare – unless we do something now. This recognition has been a big motivator of the continuation of this thrust in ECC research and also serves as a continuous reminder that I need to complete this book. I have the benefit of serving as PhD advisor to about 30 brilliant graduate students who have over the years worked on different aspects of ECC. Their amazing accomplishments are amply incorporated into the different chapters of this book. I have also greatly benefited from many colleagues who have directly or indirectly given me guidance in my career. I want to thank my former advisor, Professor James R. Rice, at Harvard who invested heavily his time and energy to turn me into a person of some usefulness. The late Professor Stanley Backer of MIT introduced me to synthetic fibers and was perhaps the only person in my early career who never doubt my instinct of pursuing ductile concrete. I owe much to Professor Narayan Swamy of Sheffield University, who insisted on “putting me on the map” when I was still a freshly minted PhD, for his confidence in my career path, and to Professor E.B. Wylie who hired me into the faculty at the University of Michigan and was never tired of listening to my global adventures in ECC, even after his retirement. My heartfelt thanks to Professor Herbert Krenchel who saw the promise of ductile ECC even before it became popularly known to the research community, and invited me to collaborate with him at the Technical University of Denmark where I

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eventually received an honorary doctoral degree. I am indebted to Professor Surendra Shah of Northwestern University who was among the first to suggest the value of ECC in enhancing structural durability and encouraged me to pursue research in that direction. My gratitude extends to Prof. Folker Wittmann, former president of RILEM, who promoted ECC through the formation of technical committees in RILEM. I am also grateful to Professor Sun Wei of Southeast University in China. She literally opened the door of China to me and to ECC. A number of chapters were written while I served as a guest professor at Southeast University. More recently, the Institute for Advanced Study at the Hong Kong University of Science and Technology provided me an inspiring environment to complete the book. Beyond academia, I am much indebted to my parents and particularly to my mother, Ms. Yin-Fong Siu, who lived to an old age of 104. While having an education not much more than elementary school, she insisted on her children getting a good education despite limited resources in my family. Without my mom, I would not be writing this book for sure. This book is dedicated to the memory of my mom. I am also deeply grateful to my wife Patricia. She has provided me a warm and loving family environment that anchors my work. My older son Dustin has always been on my side even at the most difficult times. This book has gone through multiple revisions. The various chapters have been reviewed by many colleagues and former and current students/postdocs. I want to particularly mention Gregor Fischer, Peter Kabele, Tetsushi Kanda, Taeho Kim, Christopher Leung, Mo Li, Ravi Ranade, Mustafa Sahmaran, En-Hua Yang, Bao Yi, Gideon van Zijl, Duo Zhang, and Jian Zhou. Their contributions to getting the book to the current form cannot be overstated. I want to particularly credit Tetsushi Kanda who after receiving his PhD at the University of Michigan returned to Kajima Corporation where he succeeded in industrializing ECC in a variety of full scale building, bridge, and other infrastructure. It is not possible to name all who has contributed to my career, ECC development, and this book, but my indebtedness to them is deep in my heart. I hope this book lays a clear path to civil infrastructure that are more resilient to hazards, more durable to everyday use, and more environmentally sustainable. The construction industry evolves slowly. But the need to creating a more harmonious built and natural environment is more urgent than ever. The James R. Rice Distinguished University Professor of Engineering, University of Michigan, Ann Arbor, MI, USA

Victor C. Li

Contents

1

2

Introduction to Engineered Cementitious Composites (ECC) . . . . 1.1 Concrete Technology Development . . . . . . . . . . . . . . . . . . . . 1.2 What Is ECC? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Integrated Structures and Materials Design (ISMD) for Infrastructure and Environmental Performance . . . . . . . . . . . . 1.4 Organization of This Text . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Micromechanics and Engineered Cementitious Composites (ECC) Design Basis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Introduction: ECC Versus FRC . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Microstructural Features of ECC . . . . . . . . . . . . . . . . . . . . . . 2.3 Micromechanical Model of ECC . . . . . . . . . . . . . . . . . . . . . . 2.3.1 Criteria for Composite Strain-Hardening . . . . . . . . . . 2.3.2 A Theoretical Model of Stress Versus Crack-Opening Relationship σ(δ) . . . . . . . . . . . . . . . . 2.3.3 Experimental Measurement of Stress Versus Crack-Opening Relationship σ(δ) . . . . . . . . . . . . . . . . 2.3.4 Single Fiber Straight Pullout Model P(δ) . . . . . . . . . . 2.3.5 Additional Fiber/Matrix Interaction Mechanisms . . . . 2.3.6 Linking P(δ) to σ(δ) and Micromechanical Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Experimental Determination of Micromechanical Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.1 Determining Fiber/Matrix Interfacial Parameters from Measured P(δ) Relation . . . . . . . . . . . . . . . . . . . 2.4.2 Determination of Matrix Parameters . . . . . . . . . . . . . . 2.5 Material Tailoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.1 Fiber Tailoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5.2 Interface Tailoring by Fiber Surface Coating . . . . . . . 2.5.3 Matrix Tailoring . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 2 4 5 9 9 11 12 14 16 17 24 30 34 37 40 41 42 44 47 48 49 58

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2.6

Fracture Mechanics of Steady State Crack Propagation and Tunnel Crack Propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6.1 Derivation of Eq. (2.3) for Steady State Crack Propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6.2 Derivation of Eqs. (2.12) and (2.120 ) for Single Fiber Debond P(u) Relation . . . . . . . . . . . . . . . . . . . . 2.7 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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63 63 65 68 69

Processing of Engineered Cementitious Composites (ECC) . . . . . . 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Self-Consolidating Casting . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 The Chemical Admixture Approach . . . . . . . . . . . . . . 3.2.2 Liquefaction Approach . . . . . . . . . . . . . . . . . . . . . . . 3.2.3 Full-Scale Field Mixing and Casting . . . . . . . . . . . . . 3.3 Fiber Dispersion Control and Characterization . . . . . . . . . . . . 3.3.1 Fiber Dispersion Uniformity Control by Means of ECC Mortar Viscosity Control . . . . . . . . . . . . . . . . . . 3.3.2 Fiber Dispersion Uniformity Control by Mixing Sequence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Sprayable ECC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Extrusion of ECC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

73 74 74 74 79 81 82

86 89 93 98 99

Mechanical Properties of Engineered Cementitious Composites (ECC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Direct Tension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1 Specimen Geometries . . . . . . . . . . . . . . . . . . . . . . . . 4.2.2 Test Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.3 Stress-Strain Behavior . . . . . . . . . . . . . . . . . . . . . . . . 4.2.4 Measurement of Crack Width . . . . . . . . . . . . . . . . . . 4.2.5 Strain-Rate Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Flexure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.1 Flexural Stress-Deflection Behavior of ECC Beams . . . 4.3.2 Quality Control Based on Beam Test . . . . . . . . . . . . . 4.4 Shear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 Compression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6 Fatigue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.7 Creep . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.8 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

101 102 102 103 105 107 111 114 115 115 119 120 124 127 130 132 135

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Constitutive Modeling of Engineered Cementitious Composites (ECC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Phenomenological Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.1 Modeling ECC Beam Behavior . . . . . . . . . . . . . . . . . 5.2.2 Constitutive Model for 2D Stress State: Monotonic Loading . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.3 Constitutive Model for 2D Stress State: Cyclic Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.4 Constitutive Model for 3D Stress State: Dynamic Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Multiscale Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.1 Scales and Scale-Linking Approach . . . . . . . . . . . . . . 5.3.2 Microscale Models . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.3 Micro-Meso I Linkage . . . . . . . . . . . . . . . . . . . . . . . . 5.3.4 Meso I-Meso II Linkage . . . . . . . . . . . . . . . . . . . . . . 5.3.5 Meso II-Macro Linkage . . . . . . . . . . . . . . . . . . . . . . . 5.3.6 Application of Multiscale Model . . . . . . . . . . . . . . . . 5.4 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Resilience of Engineered Cementitious Composites (ECC) Structural Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Damage Tolerance and Tension Stiffening of Steel Reinforced ECC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 Performance of R/ECC Elements Under Fully Reversed Cyclic Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.1 Performance of R/ECC Beams Under Flexure . . . . . . 6.3.2 Performance of R/ECC Beams Under Shear . . . . . . . . 6.3.3 Performance of R/ECC Columns . . . . . . . . . . . . . . . . 6.3.4 Performance of R/ECC Beam-Column Connections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.5 Performance of R/ECC Frames . . . . . . . . . . . . . . . . . 6.3.6 Performance of R/ECC Enhanced Wall Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4 Resilience of ECC Members Under Impact Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4.1 Rate Sensitivity of ECC . . . . . . . . . . . . . . . . . . . . . . . 6.4.2 Impact Response of ECC Members . . . . . . . . . . . . . . 6.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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139 140 142 142 147 150 157 163 163 167 169 170 171 171 173 174

177 178 179 183 183 190 192 194 199 204 210 211 213 221 222

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Durability of Engineered Cementitious Composites (ECC) and Reinforced ECC (R/ECC) Structural Members . . . . . . . . . . . 7.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1.2 Material Durability Versus Structural Durability . . . . . 7.1.3 ECC Crack Pattern . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 R/ECC Durability: Chloride Diffusivity, Steel Corrosion, and Cover Spalling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.1 Chloride Diffusivity of ECC . . . . . . . . . . . . . . . . . . . 7.2.2 Corrosion Initiation of Steel Reinforcement in ECC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.3 Spall Resistance of ECC Cover . . . . . . . . . . . . . . . . . 7.2.4 Combined Action Against Corrosion Induced Damage to R/ECC . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3 Permeability of ECC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.4 Sorptivity of ECC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.5 Restrained Drying Shrinkage Cracking in ECC . . . . . . . . . . . . 7.6 Long-Term Strain Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.7 Durability of ECC Under Various Exposure Environments . . . 7.7.1 Freeze-Thaw Exposure . . . . . . . . . . . . . . . . . . . . . . . 7.7.2 Freeze-Thaw Exposure in the Presence of De-icing Salt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.7.3 Accelerated Weathering Exposure . . . . . . . . . . . . . . . 7.7.4 Elevated Temperature Exposure . . . . . . . . . . . . . . . . . 7.7.5 High Alkalinity Exposure . . . . . . . . . . . . . . . . . . . . . 7.8 Durability of ECC Under Abrasion and Wear . . . . . . . . . . . . . 7.9 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sustainability of Engineered Cementitious Composites (ECC) Infrastructure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2 The Sustainable Infrastructure Materials, Structures, and Systems (SIMSS) Design Approach . . . . . . . . . . . . . . . . . . . . 8.3 Infrastructure Sustainability Life Cycle Analyses . . . . . . . . . . 8.3.1 Life Cycle Analysis Framework . . . . . . . . . . . . . . . . . 8.3.2 Service Life Estimation of R/ECC Members Exposed to a Corrosive Environment . . . . . . . . . . . . . 8.3.3 LCA for Bridge Deck with ECC Link-Slab . . . . . . . . 8.3.4 LCA for Pavement Overlay . . . . . . . . . . . . . . . . . . . . 8.3.5 Service Life and Life Cycle Cost (LCC) Analysis of R/ECC Bridge Deck . . . . . . . . . . . . . . . . . . . . . . .

225 226 226 227 229 232 232 234 236 237 238 241 242 246 247 247 249 249 251 252 254 256 257

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Greening of ECC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.4.1 Green ECC Development Methodology . . . . . . . . . . . 8.4.2 ECC with Green Binder/Filler . . . . . . . . . . . . . . . . . . 8.4.3 ECC with Green Aggregate . . . . . . . . . . . . . . . . . . . . 8.4.4 ECC with Green Fiber . . . . . . . . . . . . . . . . . . . . . . . . 8.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

286 286 291 301 306 308 310

Applications of Engineered Cementitious Composites (ECC) . . . . 9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2 Building Infrastructure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2.1 Coupling Beams for Tall Buildings . . . . . . . . . . . . . . 9.2.2 External Insulation Wall . . . . . . . . . . . . . . . . . . . . . . 9.2.3 Other Building Application Studies . . . . . . . . . . . . . . 9.3 Transportation Infrastructure . . . . . . . . . . . . . . . . . . . . . . . . . . 9.3.1 Bridge Deck and Pavement Link-Slab . . . . . . . . . . . . 9.3.2 Composite Bridge Deck . . . . . . . . . . . . . . . . . . . . . . . 9.3.3 Tunnel Linings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.3.4 Damper Retrofit of the Seisho By-Pass Viaduct . . . . . 9.3.5 Retrofit of Tokaido Shinkansen High-Speed Rail Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.3.6 Patch Repair of Bridge Decks and Viaduct . . . . . . . . . 9.3.7 Rigid-Frame Railway Bridges . . . . . . . . . . . . . . . . . . 9.3.8 Grouting Materials in Shear Keys Between Voided Slabs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.4 Water Infrastructure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.4.1 Repair and Retrofit of the Mitaka-Dam, Hiroshima Prefecture, Japan . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.4.2 Renovation of Dam at Hydraulic Power Plant Hohenwarte II, Thuringen, Germany . . . . . . . . . . . . . 9.4.3 Repair of Irrigation Channels . . . . . . . . . . . . . . . . . . . 9.4.4 Lining of Water Tunnel for Water Treatment Facility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.5 Other Application Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.5.1 Earth-Retaining Wall Repair . . . . . . . . . . . . . . . . . . . 9.5.2 Steel-Concrete Interaction Zone . . . . . . . . . . . . . . . . . 9.6 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

313 314 315 315 320 321 326 326 331 335 336

351 354 354 358 365 367

Multi-functional Engineered Cementitious Composites (ECC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2 Thermal Adaptive ECC . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

371 372 373

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339 339 344 346 347 348 349 351

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10.3

Self-Healing ECC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3.1 Self-Healing Studies in Cementitious Materials . . . . . 10.3.2 The Nature of Self-Healing in ECC . . . . . . . . . . . . . . 10.3.3 The Robustness of Self-Healing in ECC . . . . . . . . . . 10.4 Photo-Catalytic ECC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.5 Self-Sensing ECC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.5.1 Piezo-Resistivity of ECC . . . . . . . . . . . . . . . . . . . . . . 10.5.2 Meso-macroscale Linkage of Resistivity Change . . . . 10.5.3 Electrical Impedance Tomography of Multiply Cracked ECC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.6 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

378 378 379 384 391 397 398 400

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

413

404 407 409

About the Author

Dr. Victor C. Li is the James R. Rice Distinguished University Professor of Engineering and the E.B. Wylie Collegiate Professor of Civil and Environmental Engineering at the University of Michigan, Ann Arbor. His research interest is in multifunctional materials targeted at enhancing civil infrastructure sustainability and resilience. He led the research team that invented Engineering Cementitious Composites, popularly known as “bendable concrete.” Professor Li was awarded the International Grand Prize for Innovation by the Construction Industry Council and the Lifetime Achievement Award by RILEM in 2016. He received the Distinguished Graduate Mentor Award in 2015 and the Distinguished Faculty Award in 2006 from the University of Michigan. In 2005, he received the Stephen S. Attwood Award, the highest honor bestowed by the College of Engineering at the University of Michigan. In 2004, Professor Li was honored by the Technical University of Denmark with a “Doctor technics honoris causa” in recognition of his “outstanding, innovative contributions to materials research and engineering and providing our society and the construction industry with new, safe and sustainable building materials.” Professor Li is a Fellow of the American Society of Civil Engineers, the American Society of Mechanical Engineers, the World Innovation Forum, and the American Concrete Institute. His research and societal impacts have been featured in the CBS Evening News, CNN, the Discovery Channel, the Architectural Record, the American Ceramic Society, the Portland Cement Association, and the Forbes Magazine, among many other public media. Professor Li is named inventor on ten US patents.

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Contents 1.1 Concrete Technology Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 What Is ECC? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Integrated Structures and Materials Design (ISMD) for Infrastructure and Environmental Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 Organization of This Text . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2 4 5 9 9

Abstract

This chapter provides a broad introduction to Engineered Cementitious Composites (ECC). It describes the historical development of concrete material and the motivation behind the development of ECC. Specifically, the need for further concrete material development for enhancing infrastructure resilience, durability, sustainability, and smartness is discussed. These desirable infrastructure characteristics serve as the backdrop for much of the research and development behind ECC over the last decades. The chapter offers a brief overview of the unique features of ECC in comparison to normal concrete and other high performance concretes. It emphasizes the distinguishing and valued high tensile ductility of ECC, even though ECC with high compressive strength has also been achieved. This introduction chapter also describes the concept of Integrated Structures and Materials Design (ISMD) for infrastructure and environmental performance. The need for such integration and its feasibility offered by ECC is reviewed. ISMD serves as a natural framework for scale linkage from nano-scale to infrastructure and environmental scale.

© Springer-Verlag GmbH Germany, part of Springer Nature 2019 V. C. Li, Engineered Cementitious Composites (ECC), https://doi.org/10.1007/978-3-662-58438-5_1

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1.1

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Introduction to Engineered Cementitious Composites (ECC)

Concrete Technology Development

Since the introduction of concrete [1] as a structural material in the 1800s, it has continuously evolved in response to new requirements in field applications. For example, concrete strength in early 1950s is typically in the 30–40 MPa range and has increased dramatically since then. The compressive strength of concrete used in the Water Tower Plaza in Chicago in 1974 was about 65 MPa, while that of the Two Union Square Building constructed in Seattle in 1989 has a compressive strength exceeding 130 MPa. In general, strength increase of concrete was motivated by the desire to build bigger structures – longer span bridges and taller buildings – and to build faster. This was initially made possible by using cement with increasing fineness. The trend of concrete strength increase was later accelerated by the availability of microsilica and superplastizer, leading to a concrete with higher gel/space ratio while maintaining good workability. By the 1990s, it became clear that high strength alone is inadequate in terms of improving the quality of infrastructure. Instead, a broader concept of high performance was introduced, in recognition of the need to address the premature deterioration of concrete infrastructure in most developed countries around the world. Often, high performance concrete [2] refers to a concrete with enhanced durability, typically attained by the densification of concrete and reflected by a low water permeability as measured in the laboratory (in the uncracked state). In Japan, the concern for the quality of concrete was associated with a lack of skilled workers in the field. The approach to overcoming this challenge was the development of another type of high performance concrete – self-consolidating or self-compacting concrete [3] – in the late 1990s, which eliminated the need for skill-dependent vibration of fresh concrete in the field. The added value of self-consolidating concrete, despite its higher cost, has been substantiated by its increasing usage worldwide. Since around the year 2000, the general desire of sustainable development, associated with the heightened awareness of climate change, began impacting the practice in the construction industry and its materials suppliers. In response, the industry underwent a series of carbon and energy reduction efforts that continue today [4]. These efforts include improving the efficiency in cement production kilns, the blending of portland cement with a variety of pozzolans derived from waste streams of other industries, the development of green or ecological cements, the use of recycled concrete as aggregates, and others. The evolution of concrete to cater to societal needs will likely be even more rapid in the future. While the evolution of concrete strength, durability performance, and material greenness each addresses certain critical needs, the experiences of adopting the new concrete technologies also point to the limitations of the present approaches. For example, the development of high strength concrete does not fully address infrastructure resilience, especially when failure of the structure is not a result of exhausting the compressive strength. Phenomena such as shear induced fracture in short beams or spalling of concrete cover that leads to buckling of the axial steel reinforcement in columns under earthquake loading reflect more of the limitation of the tensile properties of concrete. Further, high strength concrete tends to be even

1.1 Concrete Technology Development

3

more brittle compared to normal strength concrete, leading to a higher tendency to undergo sudden fracture failure. In recent years, the expected infrastructure durability enhancement of densified concrete has been called into question. The discrepancy between laboratory measured low permeability of the densified material and structural degradation in the field arises from the presence of cracks when the concrete is restrained from free deformation and/or is loaded in the field. Thus, water and aggressive agent enter the concrete cover via cracks and attack the reinforcing steel. In other words, the low permeability of the high performance concrete between cracks becomes irrelevant to enhancing the service life of the infrastructure. The inverse relationship between concrete early strength and structural durability has been documented by Mehta and Burrows [5] using concrete strength and bridge deck data in the USA over the period of 1930s to 2000. They emphasized that the increase tendency to crack as concrete strength increase is responsible for the observed unexpected early age deterioration of bridge structures. Most recently, the recognition of the carbon and energy footprints dominated by the use phase of the life-cycle of infrastructures points to the need for concrete to be both green and durable [6]. That is, a green concrete that requires frequent repairs of an infrastructure due to lack of durability will not lower the carbon and energy footprints or other sustainability metrics over the life cycle of the infrastructure. Indeed, Mehta and Burrows were perhaps the first to make a clear linkage between infrastructure durability and sustainability. They raised the alarm of the trend of correlated concrete early strength, cracking tendency, structural deterioration, and repair needs, a trend that presents a big concern to environmental sustainability due to increase of consumption of materials during repair events throughout the long life of infrastructure systems. Hence, infrastructure sustainability demands both concrete material greenness and structural durability during service. The above observations of concrete technology evolutions suggest several lessons that could be important to future concrete developmental needs. In almost all cases of limited resilience, durability, and sustainability of infrastructure, the source may be traced to the tendency of concrete to undergo tensile cracking and fracture. That is, if high strength concrete were not brittle, if high performance concrete retain low permeability in the field in the restrained or loaded state, if green concrete would not require repeated repairs during the infrastructure’s service life, then the desirable objective of resilient, durable, and sustainable infrastructure would be closer at hand. The second lesson that could be learnt is that these desirable objectives should not be orthogonal to each other but should be arrived concurrently in any given infrastructure. Thus, the goal of the next generation concrete development should be a concrete that possesses characteristics that support infrastructure resilience, durability, and sustainability simultaneously. Separate concrete materials that address only one of these three desirable infrastructure needs will not be adequate. In any text discussing advanced materials, it would be a major oversight not to recognize the trend of embedding smart functionalities in an otherwise mundane structural material. Smart functionality is the ability of a material to sense its environment and adapt its own characteristics in response to achieve a certain useful

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purpose, without human intervention. An example of smart concrete is the selfcleaning concrete [7] which takes advantage of the photo-catalytic reactions to achieve the cleaning function. Smart concrete is not an end-goal in itself. Instead, concrete smartness should further enhance infrastructure resilience, durability, and sustainability. In the case of self-cleaning concrete, the photo-catalytic functionality reduces the need for energy/water/labor intensive building cleaning/re-painting during the use-phase and may one day purify the surrounding air in support of air quality enhancement in dense urban cities. This book documents the development of Engineered Cementitious Composites (ECC), a concrete material that attempts to address infrastructure resilience (▶ Chap. 6), durability (▶ Chap. 7), and sustainability (▶ Chap. 8) simultaneously, while possessing smart functionalities (▶ Chap. 10) that further support the attainment of these desirable features. ECC has been under research and development since around 1990. While it has been applied to full-scale infrastructure, the material continues to undergo advances that add value and further improvements. Many researchers and practitioners have contributed to the development of the design theory, material processing, material mechanical and durability characteristics, structural design basis, structural element performance, and full scale infrastructure design and construction. This book represents a first attempt to organize this increasing body of knowledge into a form that is useful for advanced students, researchers, and practioners alike.

1.2

What Is ECC?

ECC belongs to the broad class of fiber reinforced concrete (FRC) [8], as it contains fiber in a cementitious matrix. However, under tensile loading, FRCs exhibit a tension-softening behavior after the appearance of a crack that continues to widen as the load bearing capacity decreases. The elastic limit for both normal concrete and FRC is reached at about 0.01%. A relatively newer class of Ultra-High Performance Concrete (UHPC), with optimized gradation of granular constituents, emphasizes high compressive strength (over 150 MPa) and can sustain post-cracking tensile strength of 5 MPa [9–12]. In general, UHPC has tensile strain capacity of 0.2% or less (Fig. 1.1). ECC represents a family of materials with the common feature of being ductile, with tensile strain capacity typically beyond 2% (Fig. 1.1) [13–15]. The design basis of ECC is also significantly different from those of high strength concrete (HSC) or UHPC. HSC and UHPC are designed based on dense particle packing. Instead, the material microstructure of ECC is systematically tuned for synergistic interactions between the microstructural components, based on a body of knowledge known as ECC micromechanics. In other words, the fiber, matrix, and fiber/matrix interface features are deliberately engineered to interact with one another in a certain prescribed manner, when the composite is loaded. Emphasis of this design basis is the reason behind its name Engineered Cementitious Composites. Details of the design basis of ECC can be found in ▶ Chap. 2.

1.3 Integrated Structures and Materials Design (ISMD) for Infrastructure and . . . 16

Tensile Stress (MPa)

Fig. 1.1 The performance of ECC emphasizes tensile ductility, with a wide range of compressive strength feasible. The strain capacity of ECC is typically over 2% or 200 times that of normal concrete or FRC. The compressive strength of ECC ranges from a few MPa to over 200 MPa, designed to meet different demands of different applications

5

Ultra-high strength ECC (fc' = 205 MPa)

UHPC (fc' = 200 MPa)

12

8 ECC (fc' = 40 MPa) 4

0

0

1

2

3

4

5

% Tensile Strain

The design basis of ECC aims at overcoming the essential shortcoming of conventional concrete, that is, the lack of tensile deformation capacity. As a result, ECC has a stress-strain curve that is more akin to that of a metallic material, having a distinctive “yield” strength followed by tensile strain-hardening behavior. During strainhardening, the stress-strain relationship can be approximated by a linear line with a lower slope than the elastic modulus, the linear relationship punctuated by multiple load-drops with magnitude dependent on the particular ECC. For this reason, ECC is also known as Strain-Hardening Cementitious Composites (SHCC), a name that emphasizes the shape of its almost bi-linear tensile stress-strain response and its usefulness in structural design. The tensile ductility, the strain capacity at peak strength, of ECC is typically two orders of magnitude higher than that of normal concrete, while its compressive strength ranges from a low of a few MPa (e.g., a fire-resistive highly insulative ECC for steel protection [16] to over 200 MPa (ultra-high strength ECC designed for impact and blast resistance [17]). Figure 1.1 shows the tensile stress-strain curves of these two types of ECCs. The deformability and multiple cracking characteristic of ECC is illustrated in Fig. 1.2. The emphasis of ECC on tensile ductility is evident and aims at supporting infrastructure resilience, durability, and sustainability by suppressing fracture failure.

1.3

Integrated Structures and Materials Design (ISMD) for Infrastructure and Environmental Performance

At present most concrete materials design and concrete structural design are carried out independent of each other and typically by different parties. The structural designer is concerned with the safety and serviceability of the structure, with structural geometry, member dimensioning, steel reinforcement ratio, and concrete compressive strength as design variables. Once the concrete design strength is specified, the concrete engineer ensures a required strength that reflects the specified design strength, the material

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Fig. 1.2 ECC has high deformability while suppressing brittle fracture. Under (a) bending load and (b) direct tension. Multiple cracking provides the tensile ductility, or “give” to the material when overloaded beyond the elastic state

variability (standard deviation), and meeting of the code requirements in terms of reliability. In addition, the durability of the structural member is taken into consideration in terms of the choice of cement type, air entrainment, and chloride content for a given service environment of the structure. The main connection point between structural design and material design is the concrete compressive strength. There are at least three concerns with the scenario of the limited connected-ness between material design and structural design as described above. First and foremost, collapse of reinforced concrete (R/C) structures under extreme loading such as earthquakes is often accompanied by brittle fracture failure of concrete. It is not uncommon to see buckling of or local plastic yielding of steel reinforcement following the loss of concrete cover of an R/C structure. This suggests that the bottleneck in concrete property is not necessarily the compressive strength but is often in the low tensile resistance. In other words, the current concrete emphasis on compressive strength as the “quality” indicator may be overly simplistic. The second concern with the separation between structural design and concrete design is one reflected by a current dilemma. As alluded to earlier, high performance concrete designed by concrete engineers and proven to have low permeability in the laboratory does not often lead to durable infrastructure, due to cracking of concrete in the field even when code provisions on steel reinforcements are followed by the structural engineer. This apparent discrepancy of performance expectation arises due to the fact that the concrete material is designed and tested in the laboratory without consideration of the restrained and loaded conditions of the material in the field structure where concrete cracking is not uncommon.

1.3 Integrated Structures and Materials Design (ISMD) for Infrastructure and . . .

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Fig. 1.3 Currently, materials, structure, and infrastructure system designs are loosely connected, with (usually initial) economic cost as the sole optimization indicator

The third concern is that most infrastructure systems have been designed for safety and economics, with little attention paid to the impact on the natural environment. Although this is gradually changing, there remains little collaboration between the structural designer and the concrete material designer to achieve the common goal of infrastructure sustainability. The current situation is best illustrated in Fig. 1.3. To address the three concerns described above, there needs to be an integration platform between concrete material design, structural design, and infrastructure maintenance, as illustrated in Fig. 1.4. This integrated platform [18] utilizes material properties and structural properties as natural linkages between the three design scales which also represent three important phases of a life-cycle of an infrastructure system, i.e., the material production phase, the structure construction phase, and the system maintenance and end-of-life phase. Life cycle analysis tools can be developed and utilized for evaluation of economic, social, and environmental indicators, the result of which can be fed back to material-structure-system design for optimization purpose. Infrastructure sustainability indicators may be utilized as objective functions, while infrastructure resilience may serve as constraints in the design of the material/structure system. The success of this integrated platform relies on the assumption that the material microstructure can be tailored to achieve material properties desired for a given structure, whose properties lend themselves to achieving optimal infrastructure performance. Further, from a performance based design point of view, the specification of desirable infrastructure performance should lead to the selection of structural and material properties and eventually tailoring of the material microstructure. A critical element to making the integrated platform effective is therefore a

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Fig. 1.4 An integrated platform for materials, structure and infrastructure system design (ISMD) that utilizes economic, social, and environmental indicators for evaluation and optimization. The linkage between ECC microstructure and properties is provided by micromechanical models (▶ Chap. 2). The linkage between ECC material properties and structural behavior can be captured using Finite Element Analysis incorporating ECC constitutive models (▶ Chap. 5). Life-cycle assessment models support the link between infrastructure system performance and sustainability metrics (▶ Chap. 8). Infrastructure sustainability evaluation can be used to inform material ingredient selection, processing routes, structural design, and maintenance scheduling

quantitative linkage between material microstructure (▶ Chap. 2) and material properties (▶ Chap. 4), accompanied by a viable processing route (▶ Chap. 3). This is represented by the lower trapezoid in Fig. 1.4. The integrated design platform depicted in Fig. 1.4 makes feasible the systematic development of ECC. ECC is therefore not just a concrete with high ductility. It is also a cement-based composite with a theoretical design basis and serves as an enabler for sustainable infrastructure design. ECC is emerging from the laboratory and moving into field applications (▶ Chap. 9). ECC has been applied in repair, retrofit, and new constructions. Repair applications include external walls of concrete buildings [19], highway patch repair [20], railway infrastructure repair [21], irrigation canal repair [22], and dam repairs [22]. Retrofit applications include bridge deck link-slabs [23], tunnel lining strengthening [22], and viaduct deck-pier dampers for seismic retrofit. New constructions include exterior building insulation wall [24], coupling beams in the core of tall buildings [25], and composite bridge decks [22]. These applications cover the building and transportation, and water and energy domains. Application methods include cast-in-place, precast, and spray (shotcrete). The Japan Society of Civil Engineers has published a recommendation document [26] for the design and application of this special class of ductile concrete materials.

References

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9

Organization of This Text

This book is organized into ten chapters. The present chapter is an introduction to ECC, and paints in broad strokes the motivation behind the design and the distinctive behavior of this material. It is also meant to provide the appropriate mind-frame for understanding the following chapters. ▶ Chapter 2 lays down the microstructure and design basis of ECC, which are very different from other concrete material. The micromechanics theoretical basis is then discussed in the context of material tailoring. Processing of ECC is necessary to transform the material ingredients into a composite material and structural element. This is presented in ▶ Chap. 3, which also discusses fresh rheology control for uniform fiber dispersion purpose. ▶ Chapter 4 focuses on the mechanical properties of ECC important for structural design. Constitutive modeling of ECC and FEM analyses of structural elements are necessary to understand and predict the performance of ECC structural members subjected to various types of loading. ▶ Chapter 5 brings together the current stateof-the-art on this subject, critical in paving the linkage between the unique properties of ECC materials and ECC structural members. ▶ Chapters 6 and ▶ 7 document experimental knowledge on the resilience and durability of ECC materials and structural members. A detailed discussion on the sustainability of ECC infrastructure is given in ▶ Chap. 8. ▶ Chapter 9 presents case studies of demonstration projects as well as full scale commercial projects. In the final ▶ Chap. 10, ECC with specialized attributes, and ECCs endowed with smart functionalities are presented. This chapter points to the continuing development of ECC, serving as a smart concrete that drives civil infrastructure resilience, durability, and sustainability.

References 1. Mehta, P.K., Monteiro, P.J.M.: Concrete: Microstructure, Properties, and Materials, 4th edn. McGraw Hill, New York (2014) 2. Aïtcin, P.-C.: High Performance Concrete. E & FN Spon, New York (1998) 3. Okamura, H., Ouchi, M.: Self-compacting concrete. J. Adv. Concr. Technol. 1(1), 5–15 (2003) 4. Meyer, C.: The greening of the concrete industry. Cem. Concr. Compos. 31(8), 601–605 (2009) 5. Kumar Mehta, P., Burrows, R.W.: Building durable structures in the 21st century. Concr. Int. 7, 57–63 (2001) 6. Keoleian, G.A., Kendall, A., Dettling, J.E., Smith, V.M., Chandler, R.F., Lepech, M.D., Li, V.C.: Life cycle modeling of concrete bridge design: comparison of engineered cementitious composite link slabs and conventional steel expansion joints. J. Infrastruct. Syst. 11(1), 51–60 (2005) 7. Cassar, L.: Photocatalysis of materials: clean buildings and clean air. MRS Bull. 29, 328–331 (2004) 8. Bentur, A., Mindess, S.: Fibre Reinforced Cementitious Composites, 2nd edn. E & FN Spon, London (2007) 9. O’Neil, E.F., Neeley, B.D., Cargile, J.D.: Tensile properties of very-high-strength concrete for penetration-resistant structures. Shock. Vib. 6(5), 237–245 (1999) 10. O’Neil, E.F.: On Engineering the Microstructure of High-Performance Concretes to Improve Strength, Rheology, Toughness, and Frangibility, PhD Thesis, Northwestern University, Evanston, Chicago, IL (2008)

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Introduction to Engineered Cementitious Composites (ECC)

11. Chanvillard, G., Rigaud, S.: Complete characterization of tensile properties of Ductal ® UHPFRC according to the French recommendations. In: 4th International Workshop High Performance Fiber Reinforced Cement Composites (HPFRCC4), Ann Arbor, MI, no. 33, pp. 21–34 (2003) 12. Benjamin A.G.: Material Property Characterization of Ultra-High Performance Concrete, no. FHWA-HRT-06-103, p. 186 (2006) 13. Li, V.C.: From micromechanics to structural engineering – the design of cementitious composites for civil engineering applications. JSCE J. Struct. Mech. Earthq. Eng. 10(I-24), 37s–48s (1993) 14. Li, V.C., Wang, S., Wu, C.: Tensile strain-hardening behavior or polyvinyl alcohol engineered cementitious composite (PVA-ECC). ACI Mater. J. 98(6), 483–492 (2001) 15. Li, V.C.: On engineered cementitious composites (ECC). A review of the material and its applications. J. Adv. Concr. Technol. 1(3), 215–230 (2003) 16. Zhang, Q., Ranade, R., Li, V.C.: Feasibility study on fire-resistive engineered cementitious composites. ACI Mater. J. 111(1–6), 1–10 (2014) 17. Ranade, R., Li, V.C., Stults, M.D., Heard, W.F., Rushing, T.S.: Composite properties of highstrength, high-ductility concrete. ACI Mater. J. 110(4), 413–422 (2013) 18. Li, V.C.: Integrated structures and materials design. Mater. Struct. 40(4), 387–396 (2007) 19. Cheung, A.K.F., Cheung, C.Y.N., Leung, C.K.Y.: A protective pseudo-ductile cementitious layer for external walls of concrete buildings. In: Fourth International Conference on Concrete Under Severe Conditions, Published by Seoul National University, Korean Concrete Institute, Seoul, Korea, pp. 1192–1199 (2004) 20. Lepech, M.D., Li, V.C.: Long term durability performance of engineered cementitious composites. Restor. Build. Monum. 2(2), 119–132 (2006) 21. Kunieda, M., Rokugo, K.: Recent progress on HPFRCC in Japan required performance and applications. J. Adv. Concr. Technol. 4(1), 19–33 (2006) 22. Uchida, Y., Fischer, G., Hishiki, Y., Niwa, J., Rokugo, K.: Review of recommendations on design and construction of different classes of fiber reinforced concrete and application examples. In: 8th International Symposium on Utilization of High Strength and High-Performance Concrete, Tokyo, Japan, pp. 92–110 (2008) 23. Lepech, M.D.M.D., Li, V.C.: Application of ECC for bridge deck link slabs. Mater. Struct. 42(9), 1185–1195 (2009) 24. Zhang, J.: Report on “External building wall with thermal insulation and pre-cast fiber reinforced ECC panels,” Tsinghua University, pp. 113 (2014) 25. Kanda, T., Nagai, S., Maruta, M., Yamamoto, Y.: New high-rise R/C structure using ECC coupling beams. In: 2nd International RILEM Conference on Strain Hardening Cementitious Composites, Rio de Janeiro, Brazil, no. December, pp. 289–296 (2011) 26. Japan Society of Civil Engineers: Recommendations for design and construction of high performance Fiber reinforced cement composites with multiple fine cracks (HPFRCC). Concrete Engineering Series, vol. Concrete L. (2008)

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Micromechanics and Engineered Cementitious Composites (ECC) Design Basis

Contents 2.1 2.2 2.3 2.4 2.5 2.6

Introduction: ECC Versus FRC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Microstructural Features of ECC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Micromechanical Model of ECC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Experimental Determination of Micromechanical Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . Material Tailoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fracture Mechanics of Steady State Crack Propagation and Tunnel Crack Propagation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.7 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

12 14 16 41 47 63 68 69

Abstract

One of the unique features behind the high ductility of Engineered Cementitious Composites (ECC) is a design basis that is distinctly different from that of high strength concrete. For high strength concrete or members of this family of concrete materials, high compressive strength is reached by particle tight packing. The design basis of ECC, however, is based on synergizing the mechanical interactions between fiber, matrix, and interfaces of the composite so that multiple cracking in tension is attained. This design basis is embodied in a body of knowledge known as the micromechanics of ECC. Micromechanics of ECC serves as a powerful foundation for design of ECC for various performance needs for different target applications. In this sense, micromechanics is an effective tool for efficient design of ECC with optimized mechanical, physical, and functional properties, avoiding costly trial and error approach that seems to pervade the study of fiber reinforced concrete. This chapter describes the details of micromechanics of ECC, relating properties from the macro- to meso- to microscales. In so doing, the relevant phenomena, material features, and mechanisms at specific length scales are incorporated into the micromechanical model. Most of the parameters in the

© Springer-Verlag GmbH Germany, part of Springer Nature 2019 V. C. Li, Engineered Cementitious Composites (ECC), https://doi.org/10.1007/978-3-662-58438-5_2

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resulting micromechanical model can be physically measured and therefore support the selection and if needed the tailoring of the ingredients that make up the ECC. As a physics-based rational model of material behavior, micromechanics often suggests insights into material design that may appear contradictory to conventional wisdoms. These include, for example, the deliberate weakening of fiber/matrix bond and the introduction of artificial flaws into the matrix. Extensive amount of experiments at different length scales have verified the appropriateness of these concepts. Such knowledge is included in this book chapter.

2.1

Introduction: ECC Versus FRC

For ordinary fiber reinforced concrete (FRC) loaded under uniaxial tension, deformation localization occurs at the first (and only) crack site, with fibers pulling out or breaking as the crack opens, while overall load carrying capacity drops. This tension-softening behavior commonly observed in FRC is considered advantageous when compared with normal concrete which fails in a brittle fracture mode. Tensionsoftening in FRC is valued for its more gradual loss of strength and its ability to limit the width of cracks by the bridging fibers, resulting in a quasi-brittle material response. An example of tension-softening behavior is illustrated in Fig. 2.1 which shows the uniaxial tensile stress versus crack opening relationship [1] of an FRC reinforced with 2% polypropylene (pp) fiber. The insert photo shows the pp-fiber bridging across the opening crack of approximately 0.8 mm in width. In a structure, fiber bridging behind the crack tip can slow its propagation, effectively toughening the concrete in fracture mechanics terms. A major difference between ECC and FRC is their behavior after first cracking. Instead of tension-softening, ECC undergoes strain-hardening as shown in Fig. 2.2. This means that the material continues to bear higher loads at increasing imposed strain on the uniaxially tensioned specimen. Unlike FRC, the growing tensile deformation in ECC is nonlocalized but spreads from the first crack to multiple cracks covering an enlarging specimen volume. Indeed, it is the increasing number of microcracks, with crack widths controlled to typically less than 100 μm, that gives rise to the tensile ductility of ECC. In contrast to FRC, the multiple microcracks in ECC during composite strain-hardening exist as material damage; the microcracking process represents a volumetric inelastic strain deformation analogous to plastic yielding of a ductile metal. In a large structure, the inelastic deformation of ECC is reflected as ductile response of the structure (▶ Chap. 6), suppressing the common notion of brittle fracture failure, thus rendering fracture mechanics, even nonlinear fracture mechanics, inapplicable. It is often thought that the transition of FRC tension-softening response to ECC strain-hardening response takes place as the fiber volume content increases. While

2.1 Introduction: ECC Versus FRC

13

5.00

σ (MPA)

4.00

3.00

2.00

1.00 FRC 0.00

0

50

100

150 w (μm)

200

250

300

Fig. 2.1 Tension-softening in FRC is accompanied by continuous crack opening and generally decreasing load bearing capacity. The data shown are for crack width up to 0.3 mm. The tensile load continuously drops to zero as the crack width reaches about half the fiber length of 12 mm. The solid line shows the σ-w curve predicted by a micromechanics model of FRC tension-softening which accounts for aggregate (maximum size of 8 mm) bridging and fiber bridging. (Adapted from [1])

this is a generally correct observation, it may take a large volume, say 5% or 10% of fibers to reach this transition for an arbitrary set of ingredients. In some situations, no amount of fiber can turn the quasi-brittle composite into a ductile composite. Further, a high fiber content, even if it does result in a strain-hardening composite, leads to poor workability and difficulty in material processing, in addition to impractically high cost. ECC design basis is born out of this recognition; fiber content is not the only controlling parameter. Instead, fiber properties (aspect ratio, mechanical properties), matrix properties (mechanical, initial flaw size distributions), and fiber/ matrix interfacial properties (chemical bond, frictional bond, and other fiber/matrix interaction properties) must all play a role in governing the transition from tensionsoftening to strain-hardening. With this recognition, two observations can be made: (1) an optimal fiber content high enough to achieve composite strain-hardening while still meeting workability and cost constraints may be determined, and (2) a theoretical model is needed to conduct composite optimization; empirical experimentation would be too inefficient given the large set of fiber, matrix, and interface property parameters and their range of plausible values resulting in effectively infinite number of combinations. The theoretical model that arises from the above consideration for tensile strainhardening with the minimum fiber content is now known as the micromechanical model of ECC and forms its design basis [2–4]. In the following sections, the microstructural features of ECC will be described first (Sect. 2.2). Section 2.3 presents the micromechanical model, model parameter measurement methodology, and experimental verification of the effectiveness of the micromechanical model. Section 2.4 applies the model to material ingredient tailoring. In ▶ Chap. 10,

2 Micromechanics and Engineered Cementitious Composites (ECC) Design Basis 5

60

Stress

50

Stress (MPa)

4 Crack width

3

40 30

2 20 1

Crack width (μm)

14

10 ECC

0

0 0

1

0

3

4

5

Strain (%)

Fig. 2.2 Tensile strain-hardening of a ECC (containing 2% volume fraction of PVA fibers) maintains load-bearing capacity even under high strain of several percent, with width of multiplecracks limited to below 60 μm

ECCs deliberately designed for various useful attributes and special functionalities, based on the micromechanical model, will be described. Micromechanical models are also useful as a means to scale-linking between material microstructure and composite properties, thus providing a basis for developing physics based constitutive models useful for structural modeling. The subject of constitutive modeling of ECC is taken up in ▶ Chap. 5.

2.2

Microstructural Features of ECC

As its name suggests, the micromechanical model of ECC focuses on microstructures and phenomena occurring at the micron-scale, including fiber diameter (typically less than 50 μ), interfacial slippage associated with chemical or adhesive debonding (typically on the order of 10 μ or less), and microcrack opening (typically less than 100 μ). However, relevant features at higher length scales, such as flaws (typically several mm) and fiber lengths (on the order of 10 mm), are also captured in the model. Nano-scale material structure such as fiber surface coating (on the order of 10–100 nm) or nano-particles (on the order of 10–100’s nm, if included) are not explicitly accounted for in the model but subsumed in the properties of the fiber/ matrix interface properties and the matrix properties. Figure 2.3 shows the microstructure of an ECC at two different scales. The ECC micromechanical model is a three-phase composite model that distinguishes between the mechanical (and geometric where relevant) features of the matrix, the fibers, and the fiber/matrix interface. Figure 2.4 shows a cross-section

2.2 Microstructural Features of ECC

15

Fig. 2.3 (a) Back Scatter Electron image showing fibers (black elliptical shape), air pores (larger black circular shapes), sand particles (dark grey), hydrated products (grey), unhydrated cement grains (white spots) (Adeoye, private communication, 2017), (b) SEM image of ECC microstructure showing fiber, matrix, and interface. (After [5])

Fig. 2.4 SEM photo of an ECC. PVA fibers (black dots) and sand (irregular gray phase) are surrounded by cementitious binder. Due to random fiber orientation, the fiber intersecting the image plane may appear to have an elliptical shape and not perfectly rounded [6]

of ECC with more fibers oriented perpendicular to the image plane than that for Fig. 2.3a. For simplicity, the quartz sand, air pores, hydrated Portland cement binder, reacted fly ash, and unhydrated cement particles and unreacted fly ash particles are all lumped together and treated as a “homogeneous” matrix with uniform properties. Because of the fineness of sand particles relative to fiber length, the matrix is assumed to undergo rapid tension-softening behavior and is treated as an ideally brittle material. The presence of the quartz sand, with an average and maximum size of 110 and 200 μm, does influence the matrix fracture toughness. Larger river sand with size up to 2.4 mm has been successfully used in ECC. Because of the tendency of matrix toughness to increase with sand particle size, the presence of larger particles requires appropriate adjustments of the binder [7].

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Fig. 2.5 Air voids from ECC sections sampled from a coupon specimen [6]

As will be discussed later, excessive increase of matrix toughness is not conducive to tensile strain-hardening. In the model, the short (discontinuous) fibers are assumed to be uniformly dispersed in the matrix. Figure 2.4 shows that this assumption is at best a crude approximation. (In ▶ Chap. 3, it is shown that special processing methodologies could be effective in enhancing the fiber dispersion uniformity.) In any given crackedsection of ECC, the load capacity is strongly influenced by the amount and orientation of bridging fibers. In practice, in a multiple cracking scenario, the crack plane with the lowest load capacity (due to the least amount of fiber in that specimen section) will dictate the final failure in the form of a localized fracture of the specimen. Prematurely reaching this failure state limits the composite tensile strain capacity. Material flaws play an important role in ECC’s mechanical behavior. Figure 2.5 shows naturally existing air voids in four sections from a coupon specimen. The larger flaws on the order of 1 mm dictate the crack initiation stresses during tensile loading, and small flaws may never be activated prior to specimen failure. The density of multiple cracks is dictated by the distribution of flaw sizes in an ECC matrix.

2.3

Micromechanical Model of ECC

In this section, we start with the big picture and progressively move to physical phenomena at smaller length scales. By considering the conditions under which tensile strain-hardening occurs, we set up criteria for multiple cracking (centimeter scale) in terms of a composite fiber bridging traction-crack opening (σ–δ) relationship. We then describe how such a composite relationship σ–δ relationship on each of the multiple cracks (opening at 0–100 μm scale) could be modeled in terms of bridging forces carried by fibers oriented at different angles and with different embedment lengths. This in turn requires a model description of a single fiber undergoing interfacial debonding and sliding out of the matrix (at the submicron to micron scale), i.e., a P(δ) relationship in terms of interfacial properties. This scale-linking approach provides both a systematic means to understanding ECC and its tensile behavior and a

2.3 Micromechanical Model of ECC

17

modular model with flexibility in adapting to new phenomena when new ingredients, microstructure, and micromechanisms are introduced or uncovered in ECC.

2.3.1

Criteria for Composite Strain-Hardening

Figure 2.6 shows the general framework of the micromechanics model for ECC. The goal of this model is to set up criteria for the composite to achieve strainhardening, determining the combinations of fiber/matrix/interface micromechanical parameters that would allow composite strain hardening to prevail over tension-softening. The strength criterion puts a limit on the tensile stress when crack initiation from a preexisting flaw (upper left panel) occurs. The energy criterion pertains to the mode of flat crack propagation (upper right panel) to

Fig. 2.6 The micromechanics modeling framework: Initiation of microcracks from flaws occurs at σ c and steady-state flat crack propagation occurs at σ ss. When both strength (upper left panel) and energy (upper right panel) criteria are met, multiple cracking prevails, reflected by tensile strainhardening response of ECC. The matrix cracking strength is a function of matrix toughness Km and flaw size c and may also depend on fiber bridging properties in the case of bridged flaws. The fiber bridging capacity σ o must exceed the cracking strength σ c for any crack to successfully initiate without failing the specimen. The complementary energy Jb0 (Fig. 2.7) is a function of the fiber content and properties, fiber/matrix interface, and snubbing effects; the fiber orientation may be influenced by processing details

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preserve the integrity of the bridging fibers during crack extension and opening. If either of these criteria is not met, the composite defaults to the tension-softening response of ordinary FRC. As a model that is based on micromechanics, it should incorporate essential microstructural details and micromechanisms of deformation. All micromechanical parameters in the model should be physically measurable. These characteristics distinguish micromechanical models from phenomenological damage models. A micromechanical model with measurable parameters would lend itself to design, tailoring, and optimization of the composite. That is, a successful micromechanical model serves both as a forward composite property predictive tool (once micromechanical parametric values are known) and a tool for back-calculation of micromechanical parameters that guide selection and/or tailoring of material ingredients for desirable composite properties. In both strength criterion and energy criterion, fiber bridging plays an important role. The multiple cracks in ECC are bridged by fibers that take over the load shed by the matrix. Because of the small diameter fibers (less than 100 μ and often below 50 μ) typically used in ECC, each square centimeter of crack surface will be bridged by over a thousand fibers (Fig. 2.7a). The bridging fibers partially debond and stretch across the opening crack, carrying an increasing amount of load, until more and more fibers complete debonding and pull out or break. This process defines a fiber bridging stress versus crack opening relationship, σ(δ), schematically shown in Fig. 2.7b. The peak load carried by the bridging fibers defines a fiber bridging capacity σ o. The complete derivation of the σ(δ) relationship is given in Sect. 2.3.2.

2.3.1.1 Strength Criterion for Crack Initiation As suggested by Figs. 2.6 and 2.7, the tensile stress to initiate a crack from a preexisting flaw will depend on the flaw size, c, and the matrix fracture toughness, Km. (If flaws are bridged by fibers, then the cracking strength will also depend on a

b

Fig. 2.7 Stress carried by (a) fibers across an opening crack is quantified by (b) the σ(δ) curve. The image in (a) is deliberately chosen from a specimen reinforced with low modulus fiber to clearly show the bridging fibers of an opening crack. The crack width of actual ECCs is typically much tighter. Even with random orientation, bridging fibers tend to realign to the tensile stress direction, necessitating their bending and snubbing against the matrix

2.3 Micromechanical Model of ECC

19

fiber bridging properties.) Larger size flaws will be the sites of cracks initiated at lower loads. As the tensile load increases, additional cracks will be initiated from the smaller size flaws. If the tensile load σ c necessary to initiate a new crack from a flaw of size c exceeds the capacity σo of bridging fibers at any of the already formed multiple cracks, localization of fracture will occur at that tensile load and at the site where the fiber bridging capacity has been exhausted. This means that for the multiple cracking process to continue, it is necessary that: σ c ðcÞ < Min fσ o ðalready formed multiple cracksÞg

(2:1)

In other words, initiation of a new multiple crack from a preexisting flaw size of c must occur at a tensile stress level that does not exceed the fiber bridging capacity σ o of the already formed multiple-cracks. As for all materials, ECC possesses microstructure variability. Eq. (2.1) assumes two types of variability in ECC. The first variability originates from the random flaw size c resulting from air voids associated with composite processing. The second variability comes from that of the crack bridging fibers; crack planes with lower fiber content will have a lower value of σ o that may terminate the multiple cracking process. If Eq. (2.1) is violated by the very first crack, i.e., if the first crack initiation stress exceeds the fiber bridging capacity of that same crack, then only a single crack can form, with no composite ductility. To avoid a single crack fracture failure and to achieve multiple cracking, it is necessary to assure σ fc ðcfc Þ < σ o fc

(2:2)

This crack initiation criterion provides design guidance for fiber bridging capacity (right hand side of (2.2)) as well as control of matrix fracture toughness (Km) and flaw size distribution (left hand side of (2.2)).

2.3.1.2 Energy Criterion for Flat Crack Propagation In general, cracks propagate in a manner such that the maximum crack opening scales linearly with the square root of the crack length (Fig. 2.8a). This is the case for normal concrete and essentially remains the case for FRC with the exception that the opening of the crack flanks close to the crack tip may be modified by bridging fibers. For this crack propagation mode, fibers away from the crack tip will either be pulled out or break as the mid-crack opening δm enlarges indefinitely with crack length. A direct consequence of this phenomenon is that the ambient load σ1 must decrease to maintain equilibrium as the crack extends, leading to a tension-softening response of the material. The complete passage of the propagating crack will result in the loss of load carrying capacity of the composite given the loss of bridging fibers. This crack propagation mode, also called Griffith type crack propagation, is not desirable for multiple cracking since continuous unloading (softening) of the specimen follows the appearance of a matrix crack. The Griffith crack propagation mode eliminates any possibility of initiating another crack from a site of a smaller flaw at a higher load.

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a

b

Fig. 2.8 (a) Griffith crack propagation leads to indefinite increase in crack width δm, while (b) steady-state flat crack propagation limits the crack width to δss [8]. Flat crack propagation allows formation of multiple cracks that lead to tensile ductility

An alternative flat crack propagation mode (Fig. 2.8b) was suggested by Marshall and Cox [9] for ceramic composites reinforced with continuous fibers. In this mode, apart from a small region near the crack tip, the crack is essentially flat with a constant crack opening δss under a constant ambient load σ ss. This flat crack propagation mode prevails over the Griffith crack propagation mode provided the following criterion is met: δðss

σ ss δss 

σ ðδÞ dδ ¼ J tip

(2:3)

0

where Jtip represents the toughness of the matrix material at the crack tip and approaches Km2/Em for small fiber content (where Km and Em are the fracture toughness and Young’s modulus of the matrix, respectively), σ(δ) represents the complete stress vs. crack-opening relationship of the bridging fibers (Fig. 2.7b), and δss is the steady state crack opening corresponding to the steady state bridging stress σ ss. During steady state flat crack propagation, the ambient load and the crack opening remain constant, while the crack length extends indefinitely. A complete derivation of (2.3) can be found in Sect. 2.6.1. Although Eq. (2.3) was originally derived for a ceramic composite reinforced with continuous fibers, it is equally applicable to any brittle matrix composite with fiber bridging, including randomly oriented discontinuous fibers as in ECC. Equation (2.3) captures the energy balance concept during flat crack propagation. The term σ ssδss represents the work done (by the applied load) on the cracked body during the steady state cracking process. Part of this energy is consumed by the bridging fibers behind the crack tip as the crack opens from zero opening (at the

2.3 Micromechanical Model of ECC

21

crack tip) to the steady state opening δss, corresponding to the integral term in (2.3). The remaining available energy is consumed by matrix material breakdown processes that dissipate energy at the crack tip, i.e., the Jtip term. The left-hand side of Eq. (2.3) can be defined as the complementary energy Jcomp, the shaded area to the left of the σ(δ) curve bounded by the y-axis in Fig. 2.7b. Since the σ(δ) curve has a peak value, Jcomp will also have a maximum value Jb0 (hatched area in Fig. 2.7b). In other words, to guarantee the satisfaction of the energy criterion, it is necessary to meet the following inequality: δð0

σ 0 δ0 

σ ðδÞ dδ  J b 0  J tip

(2:4)

0

Equation (2.4) suggests that the maximum complimentary energy Jb0 must exceed the matrix toughness Jtip for flat crack propagation to prevail over that of the Griffith crack propagation mode, after a crack initiates from a flaw site. This can be achieved by limiting the matrix toughness Jtip which is governed by the material ingredient make-up of the matrix. This consideration provides design guidelines for the matrix of ECC. Alternatively, increasing Jb0 will also promote flat crack propagation and therefore multiple cracking. This consideration provides design guidelines for the fiber and interface of ECC. For this purpose, it is necessary to understand in greater detail the origin of the σ(δ) relationship. A detail exposé of the σ(δ) relationship is given in Sect. 2.3.2. Based on the above discussion, a theoretical ratio of σ o/σ fc  1 and Jb0 /Jtip  1 is necessary for ensuring multiple cracking. In practice, however, the theoretical ratios exceeding unity is found to be insufficient due to material variability as explained in the following sections. It has been determined from experimental data that σ o/σ fc  1.3 and Jb0 /Jtip  2.7 are needed to attain robust tensile strain-hardening [10].

2.3.1.3 Numerical Verification of Energy Criteria for Flat Crack Propagation So far, there has been no direct experimental observation of the two modes of crack propagation: flat crack propagation versus Griffith crack propagation. However, Yang and Li [8] employed numerical techniques to simulate these two crack propagation modes. The commercial finite element software DIANA was coupled with a cohesive model for simulation of crack propagation of a 2-D center crack on a plate structure remotely loaded in tension by σ1. Figure 2.9 shows a quarter of the plate (taking advantage of the symmetry about the x- and y-axis of the plate). A cohesive model was employed for the interface elements (on the line y = 0 where the initial cracklike flaw lies) to capture the σ(δ) relationship of the bridging fibers and the toughness Jm of the matrix. To emulate the brittleness of the mortar, the matrix retention force was deliberately reduced to zero rapidly at small crack opening. Figure 2.10a shows the cohesive laws used for the case when Eq. 2.4 is violated, by deliberately choosing a fiber bridging σ(δ) relationship with a relatively small

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Fig. 2.9 An FEM model to simulate flat crack versus Griffith crack growth [8]. Interface 1 elements have fiber bridging but no matrix retention, to represent a matrix flaw. Thus, this model assumes a bridged flaw. Interface 2 elements combine both matrix retention and fiber bridging

a

b

Fig. 2.10 The cohesive models used to simulate (a) the case of Jtip > Jb0 , and (b) the case of Jb0 > Jtip [8]. The latter is a necessary condition for tensile strain-hardening in ECC

complementary energy Jb0 in comparison to Jtip. (Jtip = area under the matrix tension-softening curve.) The resulting crack propagation mode is clearly that of the Griffith type. Figure 2.11 indicates that crack propagation initiates shortly before the peak load is reached, after which the standard expanding elliptical crack profile is observed, with continuously increasing mid-crack opening δm as the crack extends. Figure 2.10b shows the case where the fiber bridging σ(δ) relationship has a substantially larger complimentary energy Jb0 in comparison to Jtip, so that (2.4) is satisfied. For this case, the resulting crack propagation mode is decidedly different, as shown in Fig. 2.12. After the crack initiates and after a short propagation distance,

2.3 Micromechanical Model of ECC

a

b

23

c

Fig. 2.11 Model results for the case of Jtip > Jb0 , resulting in the Griffith crack propagation mode. (a) Ambient load drops soon after crack extension, resulting in (b) the common Griffith crack opening profile (only a quarter shown due to symmetry) with (c) increasing mid-crack opening with crack length [8]. The circle in (b) highlights the influence of fiber bridging on the cusp-shaped crack profile near the tip region

a

b

c

Fig. 2.12 Model results for the case of Jb0 > Jtip, resulting in the flat crack propagation mode. (a) Ambient load reaches a steady-state after some amount of crack extension, resulting in (b) the signature flat-crack opening profile with (c) steady state mid-crack opening that eventually becomes independent of crack length [8]

the flat crack mode is achieved, with the ambient load and the mid-crack opening maintained at constant values. That is, the flat crack propagates at steady state, with ambient stress σ 1 = σ ss. These modeling results confirm the importance of meeting the criteria (2.4) for multiple cracking to be possible. In the Griffith crack propagation mode, the ambient load drop associated with the crack propagation implies that no further defects can be activated. In contrast, the steady state flat crack propagation mode implies that the bridging fibers carry the load shed by the matrix and further increase of ambient load above σss will then activate another defect of a smaller size than those already activated, thus continuing the multiple cracking process, as long as σ ss for the newly formed cracks remains below σ o. In this simulation, the cracking stress σ c at about 4.2 MPa is below the fiber bridging capacity σ o of 6 MPa, thus satisfying the strength criteria (Eq. 2.3) as well. The above numerical simulations of Griffith type crack extension and flat-crack extension illustrate the important role that fiber bridging plays on the mode of crack

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2 Micromechanics and Engineered Cementitious Composites (ECC) Design Basis

propagation. Specifically, the flat-crack propagation mode necessary for composite ductility takes place only when the strength criterion (Eq. 2.2) and energy criterion (Eq. 2.4) are satisfied.

2.3.2

A Theoretical Model of Stress Versus Crack-Opening Relationship s(d)

2.3.2.1 Problem Formulation: Summing Forces Carried by Bridging Fibers The σ(δ) relationship represents the uniaxial tensile stress σ carried by a matrix crack of uniform opening δ, as illustrated in Fig. 2.7. In general, crack-bridging fibers contributing to the composite σ(δ) relationship may have (a) random embedment length varying from zero to half the fiber length Lf/2 and (b) random inclination angles between the fiber axis to the (normal of the) crack plane as shown in Fig. 2.13. The σ(δ) relation can be obtained by averaging the load carried by individual bridging fibers P(δ) [12]: Vf σ ðδ Þ ¼ Af

ϕ ð1

ðLf =2ðÞ cos ϕ Pðδ, Le ÞgðϕÞpðϕÞpðzÞdzdϕ

ϕ0

(2:5)

z¼0

The P(δ, Le) relationship for a single fiber aligned normal to the crack plane and with embedment length Le (Fig. 2.14) emphasizes the dependence of the bridging force of the fiber as a function of the relative displacement of the fiber front end exiting the matrix relative to the matrix crack surface. This displacement will in turn depend on the stretching of the debonded segment and sliding of the fully debonded fiber. The sum of such displacements from both crack surfaces must be equal to the

a

b

Bridging stress (σ)

Fibers Crack opening (δ)

Fig. 2.13 Illustration of randomly oriented fibers relative to a crack plane (a) x-ray image of 2D random (steel) fibers (adapted from [11]) in a cracked matrix, and (b) schematics showing fibers with different embedment length and inclination angles. Some fibers may be undergoing debonding, while others are sliding out, completely pulled out or fractured at a given crack opening

2.3 Micromechanical Model of ECC

25

P

Fig. 2.15 Inclined fibers, showing centroidal distance z and inclination angle ϕ. The upper fiber bridges the crack with the embedment length of Le. The lower fiber barely touching the crack plane has a centroidal distance (Lf/2)cosϕ. Fibers with z  (Lf/2)cosϕ will not be counted as bridging fibers

Le

Lf - L e

Fig. 2.14 The crack opening δ is made up of stretching and/or sliding of the fiber segments on either side of the crack and is a unique function of P, for a single fiber aligned normal to the crack plane with embedment length Le and total fiber length Lf

Fiber δ Matrix

Le

z Lf /2

z

Crack Plane

f

Fiber centroid

crack opening δ. In Eq. 2.5, for a given crack opening δ, fibers with different embedment lengths Le are expected to have different values of P. The randomness in fiber inclination angle is captured by the probability density function p(ϕ), where ϕ is measured as the angle between the fiber axis and the normal of the crack plane. The randomness in the fiber centroidal location (z = (Lf/2 – Le) cosϕ) is captured by the probability density function p(z), where z is the distance between the fiber centroid and the crack plane (Fig. 2.15). The double integral in Eq. (2.5) can be interpreted as the summation of forces carried by groups of bridging fibers within the incremental angles of ϕ to ϕ + δϕ, and of centroidal distance of z to z + δz. The ϕ integration limits between ϕ0 and ϕ1 reflect the fiber inclination angle range that may be governed by composite processing (casting, spraying, etc.), mold/ specimen dimensions, and fiber length. The z integration limits between 0 and (Lf/2) cosϕ ensure counting only fibers that are actually bridging the crack. Specifically, for fibers with a centroidal distance z larger than (Lf/2)cosϕ, the fiber tip will not reach the crack plane and hence there is no bridging effect (Fig. 2.15). Vf and Af in Eq. 2.5 are the fiber volume fraction and cross-sectional area, respectively. Vf/Af defines the number of fibers per unit crack plane area when fibers are aligned normal to the crack plane.

26

2 Micromechanics and Engineered Cementitious Composites (ECC) Design Basis

Equation 2.5 can then be understood as the crack traction or stress averaging the forces carried by all bridging fibers over a unit crack area.

2.3.2.2 The Probability Density Functions p(f) and p(z), and Fiber Count The fibers inclined to the matrix crack plane embody both geometric and mechanical effects on the σ(δ) relation (Eq. 2.5). The geometric effect is described by the probability density functions p(ϕ) and p(z) introduced above and will be detailed in this section. The mechanical effect of inclined fiber interacting with the matrix is described by the g(ϕ) function in Eq. 2.5 and will be discussed in Sect. 2.3.2.3. For the 2D uniform random fiber distribution case, ϕ varies from 0 to π/2 and p(ϕ) = 2/π reflecting the same probability of finding fibers oriented within the expected range of inclination angles and recognizing the symmetry of fiber orientation around ϕ = 0. For the 3D uniform random fiber distribution case, it is helpful to visualize the spatial orientation of fibers by considering the case of a fiber with a fixed arbitrary embedment length Le and with one end fixed in space. By varying the orientation of the other fiber end in 3D space, it can be visualized that this fiber end will sweep out a hemispherical surface of radius Le, as illustrated in Fig. 2.16a. For the group of fibers within the small solid inclination angle ϕ and ϕ + dϕ, their fiber ends will be lying on the strip on the hemispherical surface with differential area dA = 2πLe2 sin ϕdϕ. Since the total area of the hemisphere is A = 2πLe2, it can be deduced that the probability density function p(ϕ) is given by Eq. 2.6 and illustrated in Fig. 2.16b. pð ϕÞ ¼

a

1 dA ¼ sin ϕ A dϕ

(2:6)

b

Fig. 2.16 (a) Visualization of fiber orientation in 3D space for computing the probability density function p(ϕ) plotted in (b). The crack plane is lying horizontally. With one end of the fiber (with embedment length Le) fixed at the origin, the other end sweeps out a hemispherical surface when the solid inclination angle ϕ varies from 0 to π/2

2.3 Micromechanical Model of ECC

27

Table 2.1 Probability density functions p(ϕ) and bridging efficiency factor ηB for 1D, 2D, and 3D uniform random fiber distribution p(ϕ) ηB p'(ϕ) ηB 0

1D δDirac(ϕ) 1 – –

2D 2/π 2/π 1/(2ϕ*) sin(ϕ*)/ϕ*

3D sin(ϕ) 1/2 sin(ϕ)/{1 – cos(ϕ*)} sin2(ϕ)/[2{1 – cos(ϕ*)}]

The probability density function p(ϕ) for 2D and 3D cases are summarized in Table 2.1. It should be emphasized that the probability density function p(ϕ) assumes uniformly random fiber orientation. In reality, this may only be a crude approximation. There is experimental evidence [13] that actual fiber orientation may deviate from this assumption substantially. Theoretically, specimens with thickness less than fiber length will also limit the range of orientation angles of fibers [14]. As expected, the actual fiber orientation plays a strong role in governing the composite σ(δ) relation. If the inclination angle is limited to within the range of ϕ0 = 0 to ϕ1 = ϕ* < π/2, possibly due to processing or mold size, then the probability density function and the bridging efficiency factor are shown in Table 2.1 as p0 (ϕ) and ηB0 . For describing the variation of the centroidal location z, the probability density function p(z) takes on a simple single value of 2/Lf, since only fibers with centroids between the values of zero and Lf/2 can bridge the crack. This is illustrated in Fig. 2.17. (By limiting z to equal to or less than Lf/2, we prevent double counting the bridging force P from the same fiber.) Thus, pðzÞ ¼ 2=Lf

(2:7)

Using the same concept for “counting” fibers, Eq. (2.5) in a modified form may also be used to describe the total number of bridging fibers across unit area of the matrix crack NB:

Fig. 2.17 Probability density function of p(z) for 2D or 3D is a constant equal to 2/Lf

p(z) = 2/Lf

28

2 Micromechanics and Engineered Cementitious Composites (ECC) Design Basis

NB ¼

Vf η Af B ϕ ð1 ðLf =2ðÞ cos ϕ

ηB ¼

(2:8) pðϕÞpðzÞdzdϕ

ϕ0

z¼0

where ηB can be treated as an efficiency factor less than unity when fibers are not aligned normal to the matrix crack. The values of ηB are given in Table 2.1 as well. It can be seen that when fibers are uniformly random in 2D, the number of fibers is reduced by a factor of 2/π compared to that of the aligned fiber case. When fibers are uniformly random in 3D, the reduction factor becomes 1/2, i.e., only half as many fibers are bridging a crack as for the aligned fiber case. As an additional insight, Eq. (2.8) implies a large number of fibers when fiber diameter is small, for a given volume fraction Vf. For example, for the aligned fiber case and for a fiber with a diameter of 40 μm, a composite with 2% by volume of fiber will have about NB = 1600 fibers crossing each square centimeter of crack surface! For fibers with a 400 μm diameter (e.g., typical of steel fibers), this number reduces drastically to only 16 fibers! For fibers with a 1 mm diameter, this number further reduces to less than 3! For randomly oriented fibers, these numbers will have another reduction factor of ηB as discussed above. The number of bridging fibers is important since it directly contributes to the σ(δ) relation in Eq. 2.5. High fiber number, however, also creates difficulty in their uniform dispersion in the fresh mix. This implies an optimal fiber diameter that is small enough to generate a composite with a large fiber/matrix interfacial area, but not too small to prevent balling of fibers and disruption of fiber bridging efficiency. Fundamentally, the ductility or “give” of ECC under tensile load is derived from controlled slippage of the interfaces between fiber and matrix. Thus, a large surface area for such slippage is desirable. The fiber/matrix surface area S in a volume of 1 cm3 can be computed as S ¼ number of fibers in 1cm3  surface area of each fiber in this volume      df Lf 1 cm ¼ 2N B 2π Lf 2 2 by considering the number of fibers crossing the top and bottom faces of a box of 1  1  1 cm and recognizing that the fiber length in this volume will vary between 0 and Lf. For PVA fibers of diameter of 40 μm, NB = 1600 and S = 20.1 cm2.

2.3.2.3 Mechanistic Effect of Inclined Fibers When the fiber is inclined, like that shown in Fig. 2.18, it is possible that the bridging force could be mechanically modified from that given by P(δ, Le) for the case of a fiber aligned normal to the crack plane. For steel fiber, the bending of the fiber as it exits the matrix may lead to local plastic yielding. In polymer fibers that are flexible to bend, the enlarged bearing force of the fiber on the matrix wedge may

2.3 Micromechanical Model of ECC

29

Fig. 2.18 Inclined fiber needs to bend to cross the crack plane, inducing additional fiber/matrix interaction effect

P(f) Fiber Matrix

f

a

b

Fig. 2.19 (a) Maximum pullout force Pϕ can be several times higher than that of straight pullout P (ϕ = 0), (b) best fit to data suggest an Euler pulley type relationship for two synthetic fibers [15]

lead to additional frictional resistance against the fiber slipping out of the matrix. In either case, the inclined fiber bridging force Pϕ is higher than the straight pullout fiber bridging force P(δ, Le) and can be related to each other via the term g(ϕ) in Eq. (2.5), i.e., Pϕ ¼ Pðδ, Le ÞgðϕÞ

(2:9)

Equation (2.9) assumes that the inclination effect is independent from any other factors that influence the straight pullout case. This assumption seems to be supported by experimental data of inclined fiber pullout. Figure 2.19 shows inclined fiber pullout data of Nylon and Polypropylene [15]. In both cases, an exponential relationship between the normalized maximum pullout force P to the inclination angle ϕ was found. That is, the “snubbing” effect can be captured by Pϕ ¼ Pðϕ ¼ 0Þef ϕ

(2:10)

30

2 Micromechanics and Engineered Cementitious Composites (ECC) Design Basis

Fig. 2.20 SEM image showing microspall induced by compressive forces of an inclined bridging fiber bearing on the matrix wedges. (J. Zhou, Personal communication, 2017)

100 μm Mic

roc

Fiber

rac

k

Matrix

Microspall

For polymer fibers that are flexible, the inclination angle amplifies the pullout resistance analogous to the Euler friction pulley. Thus, the g(ϕ) function in (2.5) for polymeric fibers may be generally written in the form g ð ϕÞ ¼ ef ϕ

(2:11)

with the value of snubbing coefficient f dependent on the particular fiber/matrix combination. For the Nylon and polypropylene fibers and the matrix used in Li et al. [15], f = 0.99 and 0.7 give the best fits to the experimental data. It should be noted that the experimental pullout data shows increasing scatter at high inclination angles. This is likely a result of the spalling of the wedge under the exiting fiber caused by the increasing bearing force on the brittle matrix, leading to a sudden release of the fiber. Figure 2.20 shows a SEM image of the spalling phenomenon. The mechanics of microspalling is discussed in Sect. 2.3.5.1. With the exception of the single fiber straight pullout function P(δ, Le) which will be detailed in Sect. 2.3.4, we now have all the terms inside the double integral in Eq. (2.5) to evaluate the σ(δ) relation.

2.3.3

Experimental Measurement of Stress Versus Crack-Opening Relationship s(d)

The σ(δ) relationship can be measured directly in ECC by tracking the opening across a crack as tensile load is increased, using a notched specimen [16]. For ECC that has the natural tendency to undergo multiple cracking, a viable approach to artificially suppress this tendency is to introduce a deep and thin notch so that the opening of a single crack is developed during the test. Figure 2.21 shows such a specimen with a 0.5 mm thick notch cut using a small diamond cutting disc. The 0.5 mm notch thickness is chosen to be less than the expected multiple crack spacing in ECC when full multiple cracking in an unnotched coupon specimen is achieved. Care is needed to avoid causing damage in the specimen during notch preparation.

2.3 Micromechanical Model of ECC

a

31

b 50 mm

12 mm 25 mm 0.5 mm 70 mm

25 mm 2 mm

8 mm 10 mm

10 mm

Fig. 2.21 (a) Specimen configuration for a single crack σ(δ) experiment and (b) test setup. (After [16])

Figure 2.22 shows experimental data of σ(δ) relationship for composites reinforced with PVA, PP, and four types of PAN fibers with different strength and diameters. All composites contain the same fiber dosage Vf = 2% except for that containing PVA fibers which also includes data for 1%. It is clear that the measured σ(δ) behaviors are very different for different fiber composites. In particular, composites with PVA fibers at both 1% and 2% show high complementary energy Jb0 , whereas all the composites containing PAN fiber types show very low Jb0 . The PP fiber composite shows an intermediate value for Jb0 , although the bridging capacity σ o is substantially smaller compared to that of the PVA fiber composite at the same 2% fiber content. Tensile strain-hardening with saturated multiple cracking in unnotched coupon specimens was confirmed for the 2% PVA fiber ECC [16]. The stiffness of the (slope of rising branch of) σ(δ) relationship is controlled by the volume fraction, stiffness, and diameter of the fiber as well as the fiber/matrix interfacial properties. The maximum bridging stress σ o is controlled by fiber volume content, fiber length and strength, and interface properties. The low Jb0 for the PAN 1.5 and PAN 3.0 are likely associated with high interfacial bond characteristics, despite their relatively high σ o. It should be pointed out that while the stiffness of the fiber bridge is influenced by the fiber elastic modulus as intuitively expected, it is even more strongly influenced by the interface bond properties. High chemical and/or frictional bond diminishes the amount of fiber slippage and therefore the opening magnitude of the crack that critically governs the magnitude of Jb0 . Note that the initial data points in the plots in Fig. 2.22 at CMOD (δ) = 0 are not part of the σ–δ relationship. The initial data points in these test curves are the tensile stresses necessary to break the matrix material (so that a through crack bridged by fibers is formed) thus initiating the σ(δ) curves.

2 Micromechanics and Engineered Cementitious Composites (ECC) Design Basis

7

7

6

6

Tensile Stress (MPa)

Tensile Stress (MPa)

32

5

2% PVA

4 3

1% PVA

2 1 0 0.0

0.5

1.0

1.5

5

3 2 1

7

7

6

6

2% PAN 6.7

4

2% PAN 30

3 2 1 0 0.0

0.5

1.0

1.5

CMOD (mm)

0.5

1.0

1.5

2.0

CMOD (mm)

Tensile Stress (MPa)

Tensile Stress (MPa)

CMOD (mm)

5

2% PAN 1.5

4

0 0.0

2.0

2% PAN 3.0

2.0

5

2% PP

4 3 2 1 0 0.0

0.5

1.0

1.5

2.0

CMOD (mm)

Fig. 2.22 Measured σ(δ) relationships for various fiber types and dosages [16]. The initial load drop is not part of the σ(δ) curve, but is associated with the breaking of the matrix ligament before engagement of fibers that bridge the crack. Composites reinforced with PVA and PP fibers tend to have higher complementary energy than those reinforced with PAN fibers, making them more favorable for multiple cracking and tensile ductility

Yang et al. [17] conducted a similar single crack coupon test for the same PVA fiber but at lower dosages of 0.1% and 0.5% (Fig. 2.23). (At lower fiber content, the multiple cracking tendency is easier to suppress, and the σ(δ) curve can in principle be linearly scaled to a higher fiber content, assuming no fiber-fiber interaction.) Comparisons were made between the σ(δ) relationships measured and computed using Eq. (2.5) and assuming a 2D fiber distribution. For the computation, parametric values of the micromechanical properties embedded in the P(δ) relations are needed. The P(δ) model and associated parametric values employed are discussed in Sects. 2.3.4, 2.3.5, and 2.3.6. The predicted σ(δ) are in reasonable agreement with experimental data, particularly for the case of Vf = 0.5. Although the general shape of the curve is well

2.3 Micromechanical Model of ECC

33

a

b

Fig. 2.23 The computed σ(δ) curves (using Eq. 2.5) for composites containing PVA fibers capture the general trend of experimental data obtained from notched tensile specimens for (a) Vf = 0.1% and (b) Vf = 0.5%. (After [17])

a

b

50 mm

15 mm 25 mm 0.5 mm 70 mm

LVDT 25 mm 3 mm

9 mm 10 mm

10 mm

Fig. 2.24 Multiple cracking within the gage length of the LVDT was found in the interior of (a) single notched ECC specimen. (b) Such multiple cracking may lead to an apparent δ-value measured by the LVDT larger than the actual crack opening [18]

captured, the model has a tendency to predict a stiffer rising branch than that revealed by data. Apart from simplified assumptions (such as perfectly uniform 2D fiber distribution) in the theoretical model, it is plausible that the data at small δ is contaminated by tension-softening of the matrix material. Further, what appears to be a single crack on the specimen surface may in fact be multiple cracks in the interior (Fig. 2.24), due to the intrinsic strain-hardening property of ECC [18]. As a result, the measured crack opening may include inelastic deformation from the interior multiple microcracks, thus shifting the measure σ–δ curve to the right. Nevertheless, for determination of whether or not the strain-hardening criteria

34

2 Micromechanics and Engineered Cementitious Composites (ECC) Design Basis

Eqs. (2.2) and (2.4) are satisfied, the accuracy of the predicted Jb0 based on Eq. 2.5 is expected to be adequate. Otherwise, direct measurement of σ(δ) as described can also be used to distinguish fibers and composites that could be good candidates for strain-hardening.

Single Fiber Straight Pullout Model P(d)

2.3.4

Figure 2.25 shows the results of a single fiber pullout test using PVA fibers with two different lengths. In this experiment, the fiber was aligned with the loading direction resulting in a straight pullout with no inclination angle effect (Sect. 2.3.2.3). The pullout load P versus pullout displacement u curves show distinct regions (A-F) reflecting different mechanisms of fiber/matrix interfacial interactions at different stages of loading. The displacement u denotes the relative movement of the fiber exit point to the matrix free surface. While u contributes to crack opening δ, they are not the same quantity as will become clear later in this section. In region OAB which shows a nonlinear P-u relationship, the fiber/matrix interface undergoes debonding, i.e., the chemical bond is progressively broken starting from near the fiber exit point and extending towards the embedded fiber end. At point B, the first peak in the P-u curve, complete debonding is achieved resulting in a sudden load-drop C. The load-drop is arrested by interfacial friction after which sliding of the whole fiber out of the matrix tunnel assumes. For PVA fiber, a slip-hardening phenomenon CDE is observed whereby increasing load is required to pull the fiber out. This phenomenon has been associated with the abrasion of the surface of the synthetic fiber (Fig. 2.25b) by the rough matrix tunnel [19]. The surface damage results in peeling off of the fiber surface that bulks against the matrix tunnel and increasingly jams the fiber from further slippage.

Pullout load, P(N)

1.0

a

E

0.8

D

0.4 0.2 0.0 0.0

Le = 1.18 mm

B

0.6 A

b

ruptured

Pulled out

C

Le = 0.597 mm F

0.4 0.2 Pullout distance, u (mm)

200 μm 0.6

Fig. 2.25 Single fiber pullout experiment of a PVA fiber shows (a) distinct regions of the P-u curve associated with interface debonding (OAB), debonding completed (B), slippage initiation (C), sliphardening (CDE), fiber rupture (E), or pulled out (F). Slip hardening is apparently caused by fiber surface abrasion (b) and jamming by the bulking of fiber peel inside the matrix tunnel [19]

2.3 Micromechanical Model of ECC

35

The slip-hardening mechanism can lead to a tensile load that eventually exceeds the strength of the fiber, resulting in fiber rupture at point E. For the fiber with a shorter embedment length shown in Fig. 2.25a, complete pullout of the fiber is achieved before the tensile stress reaches the fiber strength. In principle, the load should drop to zero at a pullout distance equal to the embedment length (Le = 0.597 mm in this experiment). The fact that the experimental curve shows a termination point at less than 0.4 mm indicates that the abrasion effect may have resulted in shearing off a portion of the fiber [19]. In ECC, the embedment length is expected to range between zero and Lf/2, where Lf is typically between 8 mm and 12 mm. Thus, both scenarios, complete pullout and fiber rupture as depicted in Fig. 2.25, may occur in the ECC composite. To capture the essence of the single fiber straight pullout behavior, and to generalize it to beyond PVA fiber type, Fig. 2.26 shows schematically the three cases with slip-softening (β < 0), slip-hardening (β > 0), and constant frictional sliding (β = 0). The debonding process can be modeled [4, 20] as a tunnel crack whose propagation is resisted by the debonding fracture energy Gd (often referred to as the chemical bond). The debonded surface in contact with the matrix experiences frictional resistance to sliding. For the relatively small (on the order of microns to tens of microns) amount of sliding during the debonding stage, this friction τo can be assumed constant. Thus, the tensile load P carried by the fiber during the debonding stage can be expressed as a function of the fiber exit point displacement u (see inset of Fig. 2.26): sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Ef d 3f ð1 þ ηÞ PðuÞ ¼ π ðτ0 u þ Gd Þ 2

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 8Gd E f ð1 þ ηÞ df

(2:13)

P

u

b>0

Le

Fig. 2.26 Schematic of single fiber pullout behaviors [17]

(2:12)

P

where

2τ0 L2e ð1 þ ηÞ Le u0 ¼ þ Ef df Ef

for u  u0

b=0 b u0 df during which the displacement of the fiber is dominated by the amount of sliding (u  u0). Elastic deformation of the fiber and matrix is negligible during this sliding stage. Thus, the (Le  (u  u0)) term in Eq. 2.14 is the remaining embedment length inside the matrix. In general, this leads to a reducing load-bearing capacity as the fiber slides out. However, slip-hardening may counteract this effect, represented by a positive value of β as is the case for PVA fibers, and effectively amplifying the value of τo. A full derivation of Eqs. 2.12 and 2.120 for single fiber straight pullout can be found in Sect. 2.6.2. Equations 2.12 and 2.14 completely describe the P-u relationship illustrated schematically in Fig. 2.26, when pullout occurs from one side of the crack. For crack opening, δ, less than 2u0 (u0 defined by shorter embedded side of the fiber Ls), the pullout load, P, is given by Eq. 2.12 with u = δ/2. For crack opening larger than 2u0, the pullout load is given by Eq. 2.14 with u  δ, neglecting the contribution to the crack opening from the minor debonding stage displacement on the long embedded side relative to the pullout stage displacement on the short embedded side of the fiber. This is the case for interfaces with β equal to or less than zero. When slip-hardening occurs (for β > 0), however, the rising load after the shorter embedded end of the fiber begins sliding may lead to increasing debonding and eventual sliding of the longer embedded end of the fiber on the other (long embedded) side of the crack, as the pullout load on the short embedded side exceeds the load required to completely debond the long embedded side. In other words, for a given load carried by the bridging fiber, the crack opening has contributions from debonding and sliding on both sides – known as the two-sided fiber pullout phenomenon [17, 22, 23]. This case is illustrated in Fig. 2.27, where δL and δs denote the crack opening contribution from the longer and shorter embedded fiber segments, and Pd and Pp denote the fiber loads during fiber debonding (Eq. 2.12) and pullout

2.3 Micromechanical Model of ECC

37

Fig. 2.27 Two-sided fiber pullout case induced by slip-hardening interface. The crack opening δ is made up of fiber end displacements from both short and long embedded segments of the fiber. The load carried on either segments must always be equal as required by equilibrium

(Eq. 2.14). In this case (when β > 0), the pullout displacement on the long embedded side of the fiber is no longer negligible (as assumed for β  0) and must be determined using compatibility and equilibrium equations as follows: δ ¼ uL þ uS uL ¼ uS ; PðδÞ ¼ Pd ðuS Þ ¼ Pd ðuL Þ for δ  2u0S PðδÞ ¼ Pd ðuL Þ ¼ Pp ðuS , LS Þ for 2u0S < δ  u0S þ u0L PðδÞ ¼ Pp ðuL , LL Þ ¼ Pp ðuS , LS Þ for δ > u0S þ u0L

(2:15)

The debonding load Pd and pullout load Pp are determined from Eqs. 2.12 and 2.14 by substituting uS and uL for u, and LL and LS for Le. The critical relative displacement u0 for short (u0S) and long (u0L) embedded sides of the fiber are determined from Eq. 2.13 by substituting LS and LL for Le, respectively. The P(δ) relations expressed in Eq. 2.15 capture the essence of the debond and pullout behavior of a fiber aligned normal to a matrix crack and can be integrated into the σ(δ) relation expressed in Eq. 2.5. For improved accuracy, however, additional micromechanisms relevant for some fibers and/or matrices could be included, as highlighted in the following section.

2.3.5

Additional Fiber/Matrix Interaction Mechanisms

2.3.5.1 Matrix Microspalling When a fiber is pulled at an inclined angle with respect to its embedment orientation, the bearing pressure exerted by the exiting fiber may lead to spalling out of a matrix wedge on the order of micron to tens of micron size, as shown in Fig. 2.20. This is

38

2 Micromechanics and Engineered Cementitious Composites (ECC) Design Basis

Fig. 2.28 Matrix spalling caused by local bearing pressure exerted by inclined fiber pullout. Microspalling relaxes the fiber bridging stress

often reflected by low crackling sounds during the tensile loading of an ECC specimen, accompanied by matrix powder debris coming off the multiple cracks. The result of matrix microspalling is a sudden release of the tensioned fiber, as illustrated in Fig. 2.28, and effectively modifies the P(δ) relationship given by Eq. 2.15. The extent of modification is governed by the spall size s which in turn depends on the matrix tensile strength σ m and fiber inclination angle ϕ, diameter df, and a matrix spalling coefficient k [17, 24, 25].

2.3.5.2 Fiber Rupture The rupture of fibers is a direct consequence of the tensile stress in the fiber exceeding the fiber strength σ fu. As crack opening δ increases, increasing number of fibers will experience failure either during the debonding stage or in the sliphardening stage. Figure 2.29 shows the rupturing of a synthetic fiber in a cement matrix tested in a load-stage in an SEM (Courtesy: S. Akers). The effect of fiber rupture is the abrupt reduction of the fiber load P(δ, Le) in Eq. 2.5 to zero. A means to account for fiber rupture effect is by keeping track of which group of fibers has entered the rupturing stage in the integration process of Eq. 2.5, and discount that fiber group in the computation of the σ(δ) relation [17]. A mechanism discovered by Kanda and Li [26] relates to the reduction of fiber strength when the fiber is embedded in a mortar matrix. For this reason, σ fu should be interpreted as the in-situ fiber strength which is typically less than the manufacturer reported fiber strength by about 10%. The cause for this in situ strength reduction is likely related to damage on the fiber due to the rough matrix tunnel gripping the fiber. When fibers are pulled to failure at an inclined angle, the strength of the fiber is further reduced compared to the straight pullout case. Kanda and Li [26] found that this strength reduction follows an exponential relationship with the inclination angle ϕ: σ 0fu ¼ σ fu ef

0

ϕ

(2:16)

where f 0 represents a fiber/matrix interaction effect. Fiber strength reduction as a function of inclined angle is shown in Fig. 2.30, with the best fit of f 0 = 0.3 in

2.3 Micromechanical Model of ECC

39

Fig. 2.29 Fiber rupture during crack opening. (Courtesy of S. Akers)

2000.0

Fiber Strength (MPa)

Fig. 2.30 Fiber strength reduction due to inclined angle pull-to-failure. (Adapted from [26])

1500.0

1000.0

500.0

0.0 0.0

20.0

40.0 60.0 Inclined Angle f (deg.)

80.0

Eq. (2.16). The cause for the fiber strength reduction is not entirely clear, but a combination of slip-related fiber surface damage and kink-induced tension and compression has been suggested [26]. For fibers with high molecular alignment, compression at the fiber kink may result in premature local buckling failure. Note that the fiber kinking strength reduction effect is different from the fiber snubbing effect introduced in Eq. 2.10, although both are related to the inclination angle of fibers. The snubbing effect increases the fiber bridging force, while the fiber kinking effect reduces the effective fiber strength. This combination tends to promote fiber rupture. The in situ fiber strength effect and the fiber kinking strength reduction effect together lead to an enlarged group of fiber failures at a given composite crack opening δ and can have a significant influence on the σ(δ) relationship.

2.3.5.3 Cook-Gordon Effect Cook and Gordon [27] observed that the maximum tensile stress located at some distance from a blunt crack tip and parallel to the crack plane may trigger debonding

40

2 Micromechanics and Engineered Cementitious Composites (ECC) Design Basis

a

b =

+

Fig. 2.31 The Cook-Gordon effect results in (a) prestressing of the fiber segment α prior to intersection with the matrix crack, producing (b) an additional opening δcg when bridging is established

of a weak fiber/interface in a fiber composite, as illustrated in Fig. 2.31a. Thus, when a fiber intersects a matrix crack, a small segment of the fiber/matrix at the crack plane would have already been debonded, as shown in Fig. 2.31b. The resulting debond length α (the Cook-Gordon parameter) is expected to be proportional to the fiber diameter [1]. This free fiber segment prestressed prior to bridging of the matrix crack produces an additional crack opening δcg (Fig. 2.31b) given by: δcg ¼

4αP πd 2 Ef

(2:17)

and modifies the P(δ) relationship accordingly. Details can be found in [1, 17].

2.3.6

Linking P(d) to s(d) and Micromechanical Parameters

Equation (2.15) for the P-δ relation for the single straight fiber debond/pullout can be used in Eq. (2.5) to compute the σ(δ) relationship, which in turn can be used to check if the strain-hardening conditions (2.2) and (2.4) are satisfied. Conversely, Eqs. 2.2 and 2.4 together with Eqs. 2.5 and 2.15 can be used to determine the minimum fiber content to achieve strain-hardening. This is particularly useful for composite optimization for tensile ductility at minimum fiber content and composite cost. The computation procedure for the σ(δ) relationship is summarized in Fig. 2.32 [17]. For this purpose, numerical values are needed for the micromechanical parameters, and these are determined from single fiber pullout experiments. Details on single fiber pullout experiments are described in Sect. 2.4.1. Tables 2.2 and 2.3 summarize the micromechanical parameters and their values for an ECC containing PVA fibers – as mentioned above, these micromechanical parameters are unique for each fiber/matrix system. The parametric values in Tables 2.2 and 2.3 were used in computing the σ(δ) curves shown in Fig. 2.23. The resulting σ(δ) relation can be used to examine the conditions for strainhardening, i.e., Eqs. (2.1) and (2.3). The downlinking of σ(δ) to micromechanical

2.4 Experimental Determination of Micromechanical Parameters

For given d, check fiber status for each f and Le

Input Micromechanics Parameters

Start

Final s (d )

Modify crack opening accounting for Cook-Gordon effect: Eqn. (2.17)

Output s (d)

41

Calculate single fiber load for each f and Le and considering 2way pullout and matrix microspalling : Eqns. (2.12)-(2.16)

Calculate fiber bridging stress by averaging over full range of f and Le: Eqns. (2.5)-(2.11)

Fig. 2.32 Computational procedure for σ(δ) relation integrating the single fiber debond/pullout and other fìber/matrix interaction mechanisms Table 2.2 Typical micromechanical parametric values for PVA-ECC [17] Fiber parameters df Lf (μm) (mm) 39 12

Ef (GPa) 22

σfu (MPa) 1060

Interface parameters α f f0 (μm) 0.2 0.33 78

Matrix parameters σm Em (GPa) (MPa) 20 5

k 500

Table 2.3 Fiber/Matrix interfacial parameters for PVA-ECC with different fiber content [17] Matrix type 0.1 vol.% PVA 0.5 vol.% PVA 2 vol.% PVA

τ0 (MPa) 1.91 1.58 1.31

Gd (J/m2) 1.24 1.13 1.08

β 0.63 0.60 0.58

Note that in principle, the interfacial parameters τo, Gd, and β should not depend on fiber content. In practice, however, fiber/fiber interference becomes stronger as fiber content increases, causing reductions in the values of interfacial parameters

parameters offers the possibility of deliberate tailoring of fiber, matrix, and interface in order to meet the strain-hardening criteria with the least amount of fibers, thus optimizing the ECC composite.

2.4

Experimental Determination of Micromechanical Parameters

In order to compute the σ(δ) relation, the model described in Sect. 2.3 requires the input of micromechanical parametric values. Quantitative evaluations of micromechanical parameters are also necessary when tailoring of composite ingredients is carried out (Sect. 2.5). There are in general three sets of micromechanical parameters, namely, those related to fiber, those related to fiber/matrix interactions, and those related to matrix. Fiber properties, including fiber strength, Young’s modulus, diameter, length, are usually available from specification sheets from fiber manufacturers, although it is helpful to retest the fibers received to ensure

42

2 Micromechanics and Engineered Cementitious Composites (ECC) Design Basis

quality. For this purpose, and also for fiber/matrix interface determination, fiber manufacturers are usually able to provide continuous fibers for testing. Apart from fiber/matrix interfacial bond properties, there are other fiber/matrix interaction properties that need to be experimentally determined. As pointed out in Sect. 2.3.2.3, the snubbing coefficient f raises the bridging stress for inclined fiber pullout. In addition, fiber strength may be lowered when the fiber is embedded inside a cement matrix, and further lowered when pulled at an inclined angle (Sect. 2.3.5.2). Since the experimental procedures for such fiber/matrix interactions have been described when the mechanisms were introduced, they will not be repeated here. Instead, the following Sections will focus on the experimental determination of fiber/ matrix interfacial parameters and the matrix fracture toughness.

2.4.1

Determining Fiber/Matrix Interfacial Parameters from Measured P(d) Relation

The experimental methodology for determining fiber/matrix interfacial parameters of microfibers was developed by Katz and Li [28] and Redon et al. [19]. Figure 2.33 shows the method of preparation of a single fiber pullout specimen: (a) continuous fibers are tightened straight (but without stretching) in the mold with predrilled holes on the mold walls, (b) ECC matrix (without fibers) is cast into the mold in a direction normal to the plane of straight fibers, (c) slight vibration is applied to consolidate the ECC matrix around the fibers, and (d) after hardening, small single fiber specimen can be cut out as shown in Fig. 2.33 by means of a diamond saw. The thickness of the specimen (shown as around 0.8 mm) in this figure is chosen to ensure full debonding and sliding out of the fiber, since the fiber embedment length is equal to the specimen thickness. Care must be taken to ensure that a sharp cut is made in producing the single fiber specimen to avoid creation of a belly-button fiber end which could contaminate the test results.

Ut

Ut

Double sided adhesive tape Frame

Fibers

Casting direction Fibers A ECC

5 mm

Us

1

Ub

Ub 1

Us

Base plate

Specimen location

Specimen’s cutting lines

10 mm Le (embedment length): around 0.8 mm to ensure full debonding

Fig. 2.33 Preparation of a single fiber pullout specimen [19, 28]. Figure not drawn to scale

2.4 Experimental Determination of Micromechanical Parameters

Y X Z

43

XY Translator load-cell mount

Fiber free length = 1mm

Load-cell Specimen mount Fiber A: specimen glued Fiber B: specimen held by grips Fiber Superglue Fiber mounting plate

10 mm

10 mm !

~ 0.8 mm

Actuator

Fig. 2.34 Test setup of the single fiber pullout experiment [19, 29]

The test setup is shown in Fig. 2.34. A load-frame can be used together with a small capacity load cell with a 2 N range. Within the loading range, the error on load cell reading can be maintained below 1.25%. The actuator ( 80 mm stroke) reading is used to monitor load-point displacement. Although the specimen has a 1-mm free length of the protruded fiber segment which influences the displacement measurement, it is not necessary to make correction as the interface bond properties Gd and τo are measured using only the load-cell readings. The β measurement does require both load and displacement readings; however, calculation of this slip-hardening property utilizes a later portion of the test curve when fiber slippage dominates over elastic stretching of the free fiber segment. The single fiber pullout curve shown in Fig. 2.26 is repeated here as Fig. 2.35 for convenience, with specific points on the curve labeled for the purpose of interpretation for interface bond properties. Pa represents the maximum load when debonding has reached the end of the embedded fiber length. Pb represents the load after a sudden load drop but before sliding begins. At this stage, the load on the fiber is fully resisted by frictional forces on the interface. Subsequently, the load can increase or decrease depending on interfacial slip-hardening or softening. A straight unloading curve is expected when the coefficient of friction is held constant (i.e. when β = 0). Experimental data are interpreted via a fiber debond/pullout model [20] that allows the extraction of the three important bond properties Gd, τo, and β. Specifically, the one-sided debond/pullout model given in Eqs. 2.120 and 2.13 is used. Using the loads Pa and Pb in these equations, Gd and τo can be computed from [20]: Gd ¼

2ðPa  Pb Þ2 π2 Ef d f 3

(2:18)

Pb πd f Le

(2:19)

τ0 ¼

Because data from single fiber pullout test tends to be noisy, it may be more effective to use Eq. 2.12 directly to fit the maximum debond load Pa against fiber embedment length Le, using multiple specimens with different thicknesses (for a range of Le). That is,

44

2 Micromechanics and Engineered Cementitious Composites (ECC) Design Basis

= 0,

=

Single fiber pullout load (N)

Slip hardening,

> 0

debonded length Constant friction,

′ debonding

Slip softening < 0

Whole fiber slippage

= 0

(S) displacement (mm) , embedment length

Fig. 2.35 Typical test curve in a single fiber pullout test [19]. Prior to first peak (inset figure a), debonding can be modeled as a tunnel crack along the fiber/matrix interface. At Pa (inset figure b), debonding is complete, and sliding of fiber proceeds (inset figure c) after a sudden load drop to Pb corresponding to holding of fiber in the matrix by friction. If this frictional resistance does not change with the amount of sliding (β = 0), then a linear decay of force acting on the fiber takes place until the embedded fiber length is pulled out. The slip-displacement curve becomes nonlinear if slip hardening (β > 0) or slip softening (β < 0) takes place

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Gd Ef d f 3 Pa ¼ πd f τ0 Le þ π 2

(2:20)

Figure 2.36 illustrates this procedure. The y-intercept and the slope of the best fit linear line of Eq. 2.20 are used to extract the interfacial bond Gd and τo. The β value can be extracted from the initial slope of the experimentally determined P-S0 curve (Fig. 2.37), assuming a linear slip-hardening law, so that β¼

2.4.2

    df 1 ΔP  þ 1 Le πτ0 d f ΔS 0 S 0 !0

(2:21)

Determination of Matrix Parameters

The essential matrix (ECC without the fibers) parameters that affect composite properties are the fracture toughness Km, Young’s modulus Em and flaw size distribution c. The matrix strength σ m reported in Table 2.2 can be related to matrix flaw size distribution c and matrix toughness Km (see Sect. ▶ 5.3.2). The ASTM E399 test method can be adopted for measuring Km. This test method requires meeting a “small scale yielding” requirement which should be easily met in ECC matrix

Maximum debonding load,

Fig. 2.36 Maximum debond load Pa is expected to increase linearly with fiber embedment length Le [20]. The slope of this line yields τo, while the y-axis intercept yields Gd. By using multiple specimens with different Le, the inherently noisy single fiber pullout test can still provide meaningful data for interfacial bond properties

(N)

2.4 Experimental Determination of Micromechanical Parameters

45

0.3 Experiment Prediction 0.2

0.1

0.0 0.0

0.2

0.4

0.6

Fig. 2.37 Linear fit to the slip-hardening branch of the P-u relationship. The slope ΔP/ΔS0 yields the sliphardening parameter β [19]

1.0

0.8

Fiber embedment length,

1.2

(mm)

2.0

Load P (N)

1.5

b (from linear slip-hardening slope)

Pa

1.0

fiber ruptures as its tensile strength is exceeded during slip hardening Le

Pb 0.5

0.0 0.0

0.2

0.4

0.6

0.8

1.0

Fiber end displacement u (mm)

given that coarse aggregates are excluded in ECC formulations, so that the process zone size is expected to be small compared with specimen dimensions. Although a variety of specimen geometries are feasible, the notch beam geometry (Fig. 2.38) is the most convenient. Figure 2.39 presents the 28-day values of Km for ECC matrices that contain different amounts of fly ash [30]. It indicates that the matrix toughness generally decreases with fly ash content. This is expected due to the lower reactivity of fly ash compared to cement. The lowering of Km via fly ash addition can be utilized as a means to control the Jtip value, making it easier to satisfy the energy criterion (2.3). The Young’s modulus Em of ECC can be deduced from the uniaxial tension test (▶ Chap. 5). It is preferred to measure the tensile strain using a strain gage attached to the specimen, or in the minimum using the reading from the LVDTs. It is not

46

2 Micromechanics and Engineered Cementitious Composites (ECC) Design Basis

P 305 mm

76 mm 254 mm 38 mm

Fig. 2.38 Notched beam specimen and test-setup for matrix fracture toughness Km measurement [29]. The beam can be made from ECC without including the fiber

0.5

Km (MPa √m)

Fig. 2.39 ECC matrix fracture toughness (at 28 days age) decreases with fly-ash content, due to lower reactivity of fly-ash compared with cement. (After [30])

0.4

0.2

0.0 1

2

3

4

FA/C

desirable to use the machine displacement since that typically includes movements in the load-chain and is also potentially contaminated by slippage in the grip. The measured values of Em ranges from 2 GPa [31] to 48 GPa [32]. The lower end of this spectrum is associated with the ECC developed for fire-resistive function, while the high end is an ECC developed for impact cratering resistance. For general purpose ECC, Em falls in the range of 12–20 GPa [33, 34] depending on the composition. The flaw size range c that governs the initiation of multiple cracking is typically in the submillimeter to mm range. While still smaller flaws and pores may be expected, they do not generally play a direct role in the micromechanics of ECC, with the exception that the matrix toughness Km and Young’s modulus Em may be influenced by the porosity of the matrix material.

2.5 Material Tailoring

47

Fig. 2.40 Flaw size identification by sectioning a tensile specimen. Most of the large flaws are formed from air voids that are not bridged by fibers. (Adapted from [35])

The flaw size distribution of ECC has been studied using physical sectioning methods with a diamond saw, as shown in Fig. 2.40 [35]. This approach, however, has several limitations, including error introduced by the saw blade thickness that erodes away some of the specimen material during sectioning and the limited number of sections that can be practically investigated on a given tensile coupon specimen. An alternative approach would be to use X-ray computed tomography (μCT) which can capture 2D sections of the specimen, from which a 3D model can be reconstructed numerically to reveal the internal microstructure of ECC [36, 37]. This nondestructive approach, combined with appropriate image processing software, can be efficient and effective in determining the flaw size distribution in ECC. Figure 2.41 shows the 3D rendering of large flaws in two representative regions of an ECC specimen. The flaw size in these images is in the 0.2–1.1 mm range (Fig. 2.42). The variation of flaw size from one region to another is responsible for the variation in cracking strength of each of the multiple cracks that form sequentially during tensile loading. Figure 2.43 shows the multiple cracks observed on the specimen surface and the rendered air void flaws in the inside of the specimen in Region A.

2.5

Material Tailoring

One of the most powerful concepts behind ECC is the micromechanics design basis. In this section, we illustrate how the micromechanics theory detailed in Sect. 2.3 can serve this purpose.

48

2 Micromechanics and Engineered Cementitious Composites (ECC) Design Basis

Fig. 2.41 3D rendering of images of large flaws captured using CT-scan from two regions (a) Region A, and (b) Region B, of an ECC specimen. (Adapted from [37])

25

Number of flaws per cm3

Fig. 2.42 Distribution of flaw size obtained from CT-scan for the two regions identified in Fig. 2.41. The majority of the detectable flaws are in the 0.2–0.3 mm range. (Adapted from [37])

Region A Region B

20 15 10 5 0 0.0

0.4

0.6

0.8

1.0

Nominal radius (mm)

Equations 2.2 and 2.4 in conjunction with Eq. 2.5 can be used to strategically select or tailor ingredients of ECC. To illustrate, we show three examples below, one each on fiber, matrix, and interface tailoring. Additional examples of composite tailoring can be found in [38].

2.5.1

Fiber Tailoring

Figure 2.44 shows the computed σ(δ) of three fibers (at two volume percent) and their corresponding composite σ(e) relation [3, 39, 40].

2.5 Material Tailoring

49

Fig. 2.43 (a) Microcrack bands observed on specimen surface and (b) 3D rendering of air voids in Region A. Many smaller flaws were never activated in the multiple cracking process. (Adapted from [37])

The high modulus polyethylene fiber (PE) σ(δ) clearly has a high complimentary energy so that Eq. (2.3) is easily satisfied. As expected, this composite also shows a high ductility, with tensile strain capacity reaching 6% [3]. In contrast, the RMU-PVA fiber σ(δ) shows a high bridging stress σ o but a low complimentary energy and a correspondingly low strain capacity composite. This is due to the fact that PVA fibers with hydrophilic surface tend to bond extremely well to a cement matrix, so that a relatively high fiber load is needed to supply enough energy to break the chemical bond before fiber/matrix interface slippage could take place. The PE fiber, on the other hand, has a hydrophobic surface and a negligible chemical bond, so that relative slippage at low stress level allows the bridging fibers to absorb energy by interfacial frictional work. To correct for the poor complementary energy (Jb0 ) of the RMU-PVA fiber, a new version of PVA fiber (REC-15) was deliberately tailored for partial removal of the high chemical bond, through a proprietary surface coating of the fiber. As shown in Fig. 2.44, this modified fiber shows a dramatically enhanced Jb0 , resulting in a composite with an enhanced ductility ten times that of the composite based on the RMU-PVA fiber. The desire to consider alternative fibers is driven by considerations of cost and availability. Due to the continuous improvement of fiber technologies, including synthetic and plant fibers, the potential of lowering cost while enhancing performance of ECC is huge. The challenge lies in the appropriate tailoring of fiber properties, including both fiber strength and bonding properties to a cementitious matrix.

2.5.2

Interface Tailoring by Fiber Surface Coating

The attainment of the high tensile ductility of ECC containing the PVA-REC15 fiber shown in Fig. 2.44 is a result of deliberate tailoring of the interfacial properties Gd, τo and β [40]. Specifically, PVA fiber is hydrophilic and tends to have an excessively

50

2 Micromechanics and Engineered Cementitious Composites (ECC) Design Basis

Fig. 2.44 The effect of fiber types on σ(δ) relation and associated composite stress-strain relation. The computed σ(δ) relations are shown in the upper panel and experimentally determined σ(e) relationships are shown in the bottom panel. With high complementary energy Jb0 , PE-ECC shows high tensile ductility. The PVA (RMU 182) fiber has high strength. However, excessive chemical bond Gd and frictional bond τo reduces its Jb0 , leading to a composite with relatively low strain capacity. REC-15 is a PVA fiber tailored with a surface coating to moderate the chemical bond. As a result, the resulting σ(δ) relation has a much improved Jb0 over that of PVA (RMU 182) and the composite shows excellent tensile ductility

high chemical bond to cement matrix due to the presence of a pendant hydroxyl (-OH) group in PVA [41]. Single-fiber pullout test [20] indicated a typical value in the range of 3–5 J/m2. In comparison, the commonly used polypropylene (PP) fiber typically has negligible chemical bond (Gd = 0) in a cementitious matrix. Figure 2.45 shows the theoretically predicted influence of Gd on the σ(δ) relation and the corresponding Jb0 . This calculation suggests that the strain-hardening condition given by Eq. (2.4) can be more effectively met by reducing the chemical bond to no more than 2.5 J/m2 and achieving a higher Jb0 above 20 J/m2 and a desirable Jb0 /Jtip value above 4. One approach to reducing the chemical bond of PVA fibers is to limit the hydrophilic nature of the material by a surface coating. Figure 2.46 shows the effect of coating quantity on τo, Gd, and β. The model and method of extracting these parameters from single-fiber pullout curves are described in Sect. 2.3. The targeted ranges of interfacial properties indicated in Fig. 2.46 are the optimal ranges mentioned above. The measured interface properties for various oiling quantity are tabulated in Table 2.4. The general trend is that the interfacial bond properties significantly

2.5 Material Tailoring

51

Fig. 2.45 Computed effect of interfacial chemical bond Gd on σ(δ) relation and composite complementary energy Jb0 [40], providing guidance on the needed reduction in Gd

Fig. 2.46 Measured effects of surface coating content on interfacial properties [40]. As fiber surface coating increases, frictional bond τo, chemical bond Gd and slip-hardening coefficient β are all lowered. These charts suggest that coating content beyond 0.8% by weight of fiber allows the interfacial properties to enter into the target ranges desired for composite tensile ductility

decrease with the increase of surface coating quantity. For example, the average τ0 is reduced from 2.44 MPa for an uncoated fiber to 1.11 MPa for a 1.2% coated fiber. The drop of the chemical bond Gd is more dramatic. For untreated fibers, the average chemical bond Gd is 4.71 J/m2, which drops to 1.61 J/m2 at 1.2% coating content.

52

2 Micromechanics and Engineered Cementitious Composites (ECC) Design Basis

Table 2.4 Effect of surface coating quantity on interfacial properties and composite complementary energy Jb0 Oiling quantity (%) 0.0 0.3 0.5 0.8 1.2 a

τ0 (MPa) 2.44 0.49 2.15 0.19 2.14 0.15 1.98 0.13 1.11 0.13

Gd (J/m2) 4.71 0.58 3.16 0.66 2.96 0.75 2.18 0.39 1.61 0.60

β 2.21 0.71 2.31 0.19 1.82 0.23 1.18 0.34 1.15 0.17

Jb0 (J/m2) 3.64–6.63 5.17–13.8 7.68–13.7 12.5–20.7 24.2–38.1

Jb0 /Jtipa 0.73–1.33 1.03–2.76 1.54–2.72 2.50–4.14 4.84–7.62

Jtip ~ 5 J/m2 assumed for Jb0 /Jtip calculations

Fig. 2.47 Surface coating reduces chemical bond and damage on the fiber during pullout (a) Ruptured end of noncoated fiber; and (b) pulled out end of surface-coated fiber. Coat thickness is about 20–100 nm thick. Note the break in coating indicated by the arrow

The coating content also reduces the slip-hardening effects. The slip-hardening coefficient β for uncoated fibers reaches as high as 2.2. This drops to about 1.2 for 1.2% coated fibers. The reduction of interfacial bond and slip-hardening by fiber coating is expected to modify the σ(δ) relation and reduce the amount of fiber rupture. The computed complimentary energy Jb0 is found to increase as also reported in Table 2.4. The influence of surface coating on the pullout behavior of the fiber can be further appreciated by comparing the images in Fig. 2.47. Figure 2.47a shows the ruptured end of an uncoated PVA fiber, which shows severe delamination failure during the pullout process. When 0.8% surface coating is applied, the delamination effect is almost completely eliminated, allowing the full embedment length to slide out with little damage. The stress-strain curves and the corresponding crack patterns of all five sets of specimens with 0%, 0.3%, 0.5%, 0.8%, and 1.2% coating content are shown in Figs. 2.48, 2.49, and Table 2.5. The uncoated fiber composites exhibit limited ductile behavior, with an averaged strain capacity ecu below 1%. A few cracks can be observed (Fig. 2.49a), and the crack spacing ranges from 15 to approximately 40 mm. The 0.3% surface coated fiber composites show a marginally improved ecu of 1.6 0.33% (Fig. 2.48b). The crack pattern (Fig. 2.49b) shows relatively

2.5 Material Tailoring

53

Fig. 2.48 Effect of oiling agent content on tensile stress-strain curve of composites with: (a) 0%, (b) 0.3%, (c) 0.5%, (d) 0.8%, and (e) 1.2% surface coating content. As theoretically predicted, the composite tensile ductility dramatically increased at a coating content beyond 0.8%. At 1.2% surface coating content, the composite ductility becomes more robust with less variation

uneven crack spacing, reflecting unsaturated multiple cracking. The average crack spacing is 8 mm. For the 0.5% surface-coated fiber composites, the average ecu increases to 2.7 0.8% (Fig. 2.48c). The higher strain capacity is accompanied by an increase in the number of multiple cracks and a larger crack opening of 52 μm (relative to 43 μm for the ECC with uncoated fiber). One of the composites reaches a strain level of 3.8%, indicating that oil-coating variation is an important factor in attaining

54

2 Micromechanics and Engineered Cementitious Composites (ECC) Design Basis

Fig. 2.49 Effect of oiling agent content on multiple crack pattern of PVA-ECC: (a) 0% (ecu = 0.9%); (b) 0.3% (ecu = 1.9%); (c) 0.5% (ecu = 2.8%); (d) 0.8% (ecu = 3.6%); and (e) 1.2% (ecu = 4.7%). A larger number of cracks are associated with increased surface coating content and become saturated after about 0.8% coating Table 2.5 Effect of surface coating content on measured tensile properties Oiling quantity (%) 0.0 0.3 0.5 0.8 1.2

First crack strength σ fc (MPa) 3.11 0.23 2.63 0.43 2.35 0.21 2.90 0.10 2.92 0.06

First tensile strength σ cu (MPa) 4.89 0.07 4.72 0.17 4.09 0.22 4.62 0.36 4.41 0.15

Strain capacity ecu (%) 0.99 0.57 1.55 0.33 2.73 0.78 3.81 1.14 4.88 0.59

Crack spacing xd (mm) 27.00 12.00 7.50 2.80 3.50 1.10 2.50 0.33 2.80 0.52

Crack opening (μm) 43 20 44 7 52 10 71 9 88 12

2.5 Material Tailoring

55

strain-hardening behavior for this fiber. The average crack spacing for this set of specimens is 3.5 mm. The crack pattern of a 0.5% coated fiber composite is shown in Fig. 2.49c. This particular specimen has ecu of 2.8%. For the 0.8% coated fiber composites, ecu achieves an average value of 3.8 1.1% (Fig. 2.48d). One of the specimens reaches a strain level exceeding 5%, with a crack pattern approaching full saturation (Fig. 2.49d), and the average crack spacing is approximately 2.5 mm. Further increase of the surface coating to 1.2% improves the consistency of the composite behavior, leading to an average ecu of 4.9% (Fig. 2.48e). The increase in ecu is mainly contributed by the wider crack opening, which reaches an average value of 88 μm (Fig. 2.49e) because the crack spacing does not show further reduction when compared with the 0.8% coated composites. From the composite test results, it is evident that increasing the coating agent (at least within the range of this experimental investigation) leads to an increase in tensile strain capacity, accompanied by a larger crack width and reduced crack spacing. The strain capacity shows an almost linear increase from 1.5% to approaching 5%. The increase of the strain capacity of the 0.5% coated composites over that of the 0.3% coated composites appears to have derived from the more than doubling of the number of multiple cracks (crack spacing reduced from 7.5 to 3.5 mm). This suggests that the 0.3% coated composite may be in a transition from quasi-brittle to strain-hardening behavior, that is, the inequality in Eq. (2.4) is barely satisfied. In fact, the lower bound value of Jb0 /Jtip is only 1.03 for this case (Table 2.4). In contrast, the further increase in strain capacity of the 0.8% coated composites over that of the 0.5% coated composites appears to have derived mainly from the significantly enhanced crack opening (from 52 to 71 μm). The relatively smaller crack spacing reduction from 3.5 to 2.5 mm suggests that multiple crack saturation is being approached with the 0.8% coating content, and this is further confirmed by no further reduction in crack spacing of the 1.2% coated composites. As mentioned previously, the index Jb0 /Jtip should exceed 2.7 in order to achieve robust tensile behavior with saturated cracking [10]. Although this criterion was established on the experimental observation of PE-ECC composites, it is also consistent with the findings in this study. As shown in Table 2.4, the index Jb0 /Jtip increases with higher surface coating content and reaches 3 at about 0.8%, which is also the transition point of cracking saturation. The trends of composite properties discussed above and summarized in Fig. 2.50 are consistent with those for the fiber/matrix interface (Fig. 2.46). Figure 2.46 suggests that the surface coating content should be at least 0.8% to achieve the desired Gd and τ0. The experimental results on composite properties in Figs. 2.48 and 2.50 confirm that the 1.2% coated composite possesses the highest tensile strain capacity with the best multiple-crack saturation while the 0.8% coated composite already shows satisfying strain-hardening and multiple cracking behavior. Beyond 0.8% coating, the further reduction in interfacial bond properties appears to achieve additional strain capacity gain at the expense of crack opening increase, while crack spacing appears unchanged.

56

2 Micromechanics and Engineered Cementitious Composites (ECC) Design Basis

Fig. 2.50 Increase in surface coating content leads to (a) an increase in tensile strain capacity, (b) a reduction in crack spacing, and (c) an increase in crack opening. The higher tensile ductility is directly associated with a larger number of microcracks with larger crack opening. At a surface coating content of 0.8%, the crack width is approximately at 60–80 μm

The correlation between composite test results and single fiber test results can be further studied by examining the length of protruding fibers from a fracture surface of the composite by completely separating two halves of a specimen. Figure 2.51 confirms the expectation that more and longer embedded fibers can be pulled out in the composites with fibers having higher amount of coating. For example, the ECC with highly coated (1.2%) fibers shows a protruded fiber length averaging approximately 2 mm, while the composite with uncoated fibers reveals a majority of protruded fiber lengths below 1 mm, indicating a greater degree of fiber rupture. This verifies that the highly coated fibers are better protected from damage as depicted in Fig. 2.47b. However, it should be pointed out that for complete pullout, the protruded fiber lengths should vary between 0 and 6 mm, with an average of 3 mm for random fiber distribution because the fiber length is 12 mm. Hence, even for the 1.2% coated fiber, some of these fibers are expected to rupture in the composite, most likely during the slip-hardening stage. By reducing the interface properties Gd, τ0, and β, the higher surface coating content also reduces the bridging stiffness or the initial slope of the σ(δ) curve of the

2.5 Material Tailoring

57

Fig. 2.51 Micrographs showing protruded fibers on fracture surfaces of PVA-ECC specimens with: (a) 0%, (b) 0.5%, and (c) 1.2% surface coating. As surface coating content increases, less fiber rupture and more pullout were observed, consistent with the expectation of the effect of reducing the fiber/matrix interfacial bonds τo and Gd

resulting composites. This implies that larger crack openings are expected for a given load level during composite strain-hardening. This is consistent with the experimentally monitored crack width (Fig. 2.50c). While the discussion above focuses on tailoring of the fiber/matrix interface for strain-hardening in PVA-ECC, it is important to point out that a holistic approach is

58

2 Micromechanics and Engineered Cementitious Composites (ECC) Design Basis

necessary for truly optimal composite design. Tailoring of the fiber, matrix, and fiber/ matrix interface should be carried out in an integrative scheme. As a case in point, Li et al. [39] demonstrated that the optimal amount of sand in the matrix varies with the surface coating content of the fiber. This emphasizes the importance of treating ECC as a composite system in which the three phases interact with one another. The modification of one phase may necessitate the adjustments of other phases for truly optimal composite performance.

2.5.3

Matrix Tailoring

In uniaxial tension tests, the density of cracks or the crack spacing has been observed to vary significantly, at times even within different specimens of the same batch. To illustrate this, Fig. 2.52 shows an extreme case of tensile strain variability. Such high variability limits the usable range of tensile ductility of ECC in structural design, so that the full potential of the material is not realized. In this section, we discuss micromechanics guided matrix tailoring methodology to overcome this type of high variability in tensile ductility. The objective is to achieve robustness in composite tensile ductility. The density of multiple cracks, or inversely the average spacing of multiple cracks in ECC, is closely associated with the tensile strain capacity of the composite. This is so because the inelastic deformation of ECC derives from the number of multiple cracks and their opening magnitude in a representative volume element. In general, attaining a higher crack density is more desirable than wider crack opening, particularly from the viewpoint of maintaining material and structural durability (see ▶ Chap. 7). When fully saturated, the maximum crack spacing of strain-hardening fiber reinforced composites under uniaxial tension should in principle be no more than twice the minimum crack spacing [42, 43]. This minimum crack spacing is defined as the distance necessary to transfer load from the bridging fibers of a crack back into 7 6 Tensile Stress (MPa)

Fig. 2.52 An example of extreme variability in tensile ductility, with strain capacity varying from less than 1% to almost 3% [6]. This is a symptom of low margin in Jb0 /Jtip and σ o/σ fc of the composite and variability in composite flaw size and fiber bridging properties. The latter may be caused by poorly disbursed fibers

5 4 3 2 1 0 0

1

2 Strain (%)

3

4

2.5 Material Tailoring

59

Fig. 2.53 Unsaturated multiple cracking. Large crack spacing implies inefficient utilization of the reinforcing fibers and limits the tensile strain capacity [6]

the matrix through the fiber/matrix interfacial shear in order to create the next matrix crack, assuming uniform fiber distribution and homogeneous matrix strength. In practice, however, this may not be readily observed. Figure 2.53 illustrates a typical pattern of unsaturated multiple cracking, showing a wide distribution of crack spacing far exceeding twice the minimum crack spacing. The unsaturated multiple cracking could be traced to variability in fiber dispersion and in preexisting flaw size variation [6]. Control of fiber dispersion is discussed in ▶ Chap. 3. Control of flaw size can be attained through tailoring of the ECC matrix characteristics using artificial flaws. In ECC, cracks are initiated at preexisting flaws generated during composite processing. Flaws in ECC are observed to have typical sizes below 4 mm, and their existence considerably reduces the cracking strength from the intrinsic material strength. Figure 2.54 illustrates the effect of flaw size on the theoretical cracking strength of an infinite 2D ECC plate under uniaxial tension. The theoretical tensile strength of the composite without macrodefects is assumed to be 6.5 MPa. Using a cohesive crack model similar to that shown in Fig. 2.10, Wang [44] found that for flaw size of 1 mm, the cracking stress is reduced to 5.4 MPa, and for flaw size of 4 mm the cracking strength is further lowered to 4.8 MPa. As discussed in Sect. 2.3.1.1, one of the two criteria for multiple cracking in ECC is that the cracking strength must be below the fiber bridging capacity (Eq. 2.1). For the above calculation, and assuming a uniform fiber bridging capacity σ o of 5.5 MPa, only the population of flaws with size range above cmc = 1.7 mm will satisfy Eq. (2.1) and initiate multiple cracking. In other words, if the natural processinduced flaws were mostly below cmc, unsaturated multiple cracking would result. Saturated multiple cracking can only be reached when a sufficient number of large flaws exists. In cementitious matrix, however, the inherent flaws such as pores,

2 Micromechanics and Engineered Cementitious Composites (ECC) Design Basis

Fig. 2.54 With decreasing cracking strength as a function of initial flaw size, only flaws with size larger than cmc can be activated as multiple cracks prior to exhaustion of the fiber bridging capacity. For a given fiber bridging capacity, flaws below cmc will remain dormant and never become part of the multiple cracks. (After [44])

8 7 Cracking Strength (MPa)

60

Fiber bridging strength

6 5

cracking strength

4 3 2 1 0

0

1

2 3 Initial Flaw Size (mm)

4

5

weak boundaries between phases, and cracks induced by restrained shrinkage possess a random nature and strongly depend on material ingredient composition, processing details, and environmental effects. The number of cracks that can be activated before reaching peak bridging stress therefore may be limited and can vary significantly from one batch to another. Further, a higher toughness matrix (with higher Km) would shift the cracking strength up, so that a higher cmc will result. This will further reduce the population of flaws that can be initiated into multiple cracks, limiting the composite ductility and robustness. A practical approach to ensuring availability of appropriately sized flaws is by introducing artificial defects with prescribed size distribution. Figure 2.55 illustrates the concept of a matrix flaw tailoring scheme for saturated multiple cracking. In composites without explicit flaw size control, the distribution exhibits a random nature and spans over a large range. cmc is the critical initial flaw size that separates inert and active flaws (Fig. 2.55a). Only flaws larger than cmc can contribute to multiple cracking, as discussed above. The tailoring process superposes a large number of artificial flaws with a narrow size distribution to overwhelm the natural flaw system by providing a sufficiently large crack initiator pool (Fig. 2.55b). The artificial flaws can be any particles with weak bonds to the matrix or with low tensile strength. The effectiveness of the aforementioned matrix tailoring approach is presented below. Figure 2.56a shows the flaw size distribution in a normal cast PVA-ECC mix before and after adding artificial flaws [6]. The natural flaws were determined by specimen section sampling, and only large flaws exceeding 1 mm were counted. Low strength lightweight aggregates made from expanded shale were used as the artificial flaws (Fig. 2.56b). The aggregates have a graded size of 3.5 0.2 mm and the volume fraction is 7%. The superposition creates a concentration at the large size end of the flaw distribution. The effect of the tailoring on tensile ductility is clearly shown in Fig. 2.57, as the strain capacity of this mix increase from about 0.4% to 2.5% on average [45]. Such increase is achieved by developing more closely spaced microcracks. As shown in Fig. 2.58, near saturated multiple cracking prevails after adding artificial flaws, compared to the very uneven pattern seen previously.

2.5 Material Tailoring Fig. 2.55 (a) Natural flaw size distribution due to processing, and (b) with artificial flaws deliberately selected for their size above cmc. The introduction of artificial flaws can boost multiple cracking tendency and tensile strain capacity. (After [6])

61

a

p(c)

natural flaws

flaw size, c Size distribution of natural flaws inherent from processing

b

p(c)

artificial flaws

flaw size, c Size distribution of superimposed artificial flaws

a Probability Density

b

inherent flaws

1.5

artificial flaws 2cm

1.0

0.5

0.0

1

2

3 4 Flaw Size (mm)

5

Fig. 2.56 (a) Large flaw (>1 mm) size distribution in a normal PVA-ECC mix (gray histogram) and superposition of artificial flaws (white histogram) and, (b) low strength light-weight shale aggregates used as artificial flaws. (Adapted from [6])

Control of flaw size distribution also improves the robustness of ECC tensile behavior. As shown in Fig. 2.59a, the variation of strain capacity of the PVA-ECC presented in Fig. 2.52 diminishes drastically after adding 7 vol% of plastic beads with 4 mm diameter (Fig. 2.59b) as artificial flaws. These polypropylene (PP) beads are elliptical in shape with 2 and 4 mm for the short and long axis. The smooth

62

a

2 Micromechanics and Engineered Cementitious Composites (ECC) Design Basis

b

8

6 5 4 3 2 1 0

8 7

Tensile Stress (MPa)

Tensile Stress (MPa)

7

6 5 4 3 2 1

0

1

2

3

Strain (%)

4

5

0

0

1

2

3

4

5

Strain (%)

Fig. 2.57 Tensile behavior of PVA-ECC: (a) w/o artificial flaws and (b) with 7 vol% artificial flaws in the form of lightweight shale [45]. The two composites have identical composition except for the artificial flaws. While enhancing strain capacity and robustness, the composite strength was not compromised by the presence of artificial flaws

Fig. 2.58 Multiple-cracking pattern of PVA-ECC: (a) isolated bands of multiple cracking with natural flaws from processing, and (b) saturated multiple cracking when 7 vol% artificial flaws was added [45]

2.6 Fracture Mechanics of Steady State Crack Propagation and Tunnel Crack . . . 7

a

63

b

Tensile Stress (MPa)

6 5 4 3 2 1 0

0

1

2 3 Strain (%)

4

5

Fig. 2.59 (a) Robust tensile behavior of PVA-ECC with controlled flaw size distribution and tailored interface properties. Plastic beads with 4 mm diameter (b) were added at 7 vol%. The proportion otherwise is same as the mix in Fig. 2.52. The optimal content of artificial flaws is dictated by having enough of them for saturated multiple cracking, while not having so much as to lead to a significant reduction in compressive strength

surface and hydrophobic nature of PP makes for low bonding with the cementitious matrix. The successful use of this tailoring strategy has been further confirmed by Wang and Li [46] and Li and Li [47], who used artificial flaws to recover tensile ductility for ECCs designed for high early strength. The use of rapid setting matrices led to an imbalance in Km (and therefore σ fc) versus σ o, causing violation of Eq. (2.1). Artificial flaws return the composite to robust tensile ductility. Apart from flaw size distribution, the uniformity of fiber dispersion or distribution also plays a significant role in the mechanical properties of ECC, particularly in the ultimate tensile strength and ductility. Techniques in controlling and quantifying fiber dispersion can be found in [41, 48–50]. Because of the close association between the uniformity of fiber dispersion and the rheology and mixing sequence of ECC in the fresh state, this subject is taken up in ▶ Chap. 3 that focuses on processing of ECC. In general, high variation in tensile ductility or low strain capacity are indicative of poor fiber dispersion.

2.6

Fracture Mechanics of Steady State Crack Propagation and Tunnel Crack Propagation

2.6.1

Derivation of Eq. (2.3) for Steady State Crack Propagation

The path independent J-integral [51] is defined as ð  JΓ ¼

Γ

wdy  σ ij nj

@ui ds @x

 (2:22)

64

2 Micromechanics and Engineered Cementitious Composites (ECC) Design Basis

Fig. 2.60 The path independent J-integral for crack analysis

Γ

Γ

Γ Γ

d

Γ

Γ

Γ

Γ

Fig. 2.61 A convenient contour for evaluation of Eq. (2.22)

  Ðe where w eij ðx,yÞ ¼ 0 ij σ ij eij deij is the strain energy density, Г represents a contour path, and n is the outward normal vector at any point on this path (Fig. 2.60). For the problem where a flat crack is propagating steadily under a constant ambient uniaxial load σ ss and with opening δss, the contour shown in Fig. 2.61 can be conveniently utilized to evaluate Eq. (2.22). The flat crack is assumed to be bridged by fibers having a σ B(δ) constitutive relation and propagating against matrix fracture toughness Jtip. Using Eq. (2.22), and the horizontal paths Гe and Гf, it can be shown that 1 J Γe ¼ J Γf ¼ σ ss δss 2

(2:23)

Similarly, for the vertical paths, J Γa þ J Γd ¼ J Γg

(2:24)

so that J tip ¼ σ ss δss 

ð δss

σ ðδÞdσ ss

(2:25)

0

which is Eq. (2.3). As an alternative derivation of Eq. (2.25), one can consider the energy exchange in a body (of thickness t) containing a steadily advancing flat crack

2.6 Fracture Mechanics of Steady State Crack Propagation and Tunnel Crack . . .

a

65

2c

A-A

y

∆a

x 2c + 2∆a

B-B

b

∆a

Fig. 2.62 Consideration of energy exchange for a long steady-state flat crack in a plate subjected to ambient tensile traction of σss leading to Eq. 2.26. (After [52])

(Fig. 2.62) [52]. Extension of the crack by a length Δa is equivalent to replacing a strip of material with width Δa, far ahead of the crack tip by a strip of material far behind the crack tip. The elastic strain energy stored in the strips are identical. However, during crack extension, work done on the body by boundary tractions amounts to σ ss δss tΔa. Energy Gtip tΔa is dissipated by material breaking down at the crack tip as it advances. Similarly, Ð δ energy is absorbed by the fiber bridges (non-linear springs) of the amount 0 ss σ ðδÞdσ ss tΔa . This results in an energy balance equation: Gtip tΔ a ¼ σ ss δss tΔ a 

ð δss

σ ðδÞ dσ ss tΔ a

(2:26)

0

which is identical to Eq. 2.25, when Jtip is interpreted as Gtip by assuming that the break down zone size of the cement matrix is small.

2.6.2

Derivation of Eqs. (2.12) and (2.120 ) for Single Fiber Debond P(u) Relation

To analyze the debonding process, the model shown in Fig. 2.63 with a propagating tunnel crack of length a is used. For simplicity, the fiber (with diameter df, crosssectional area Af and Young’s modulus Ef) and matrix (with Young’s modulus Em) are both assumed to undergo unaxial deformation. Along the debonded interface, the relative slippage between the fiber surface and the matrix tunnel surface is resisted by interfacial friction τo. Based on force equilibrium of a fiber segment at x, under a load σ = P/Af on the fiber exit point, the stress in the fiber σ f at point x within the debond zone can be written as

66

2 Micromechanics and Engineered Cementitious Composites (ECC) Design Basis

Fig. 2.63 The fiber debonding model

Fiber Matrix

a

x

=

Debonded interface

x  4τ0 a σ f ð xÞ ¼ σ  1  a df

(2:27)

Thus, the fiber stress diminishes linearly from the front end towards the embedded end of the fiber, with the load transferred to the matrix via interfacial friction. Correspondingly, by considering force equilibrium at a matrix cross-section at x, the stress build-up in the matrix σ m can be expressed as σ m ð xÞ ¼

Vf

x 4τ0 a 1 a df 1  Vf

(2:28)

The relative slippage between the fiber and matrix along the debonded interface, i.e., δt (x) = uf (x)  um (x) can be written as δt ðxÞ ¼

 ðx 

σ f ð x0 Þ σ m ð x0 Þ σx x  4τ0 a 0  x 1 ð1 þ η Þ dx ¼ Em Ef 2a d f Ef 0

where η is a stiffness ratio constant given by η ¼ E

(2:29)

E V

f f . ð1V f Þ The relative displacement u at the fiber exit point (x = a) is then

u ¼ δt ðaÞ ¼

m

σa 2τ0 a2  ð1 þ η Þ Ef Ef df

(2:30)

Equation (2.30) represents a P-u relationship except that it carries the unknown debonded length a. To determine the tunnel crack length, it is necessary to utilize linear elastic fracture mechanics. Consider an incremental extension δa of the tunnel crack, energy balance requires δW  δU el  δF ¼ Gd δa

(2:31)

where δW represents external work done on the elastic body (Fig. 2.64) during crack extension, and δUel represents the change in elastic energy storage. Two energy dissipation mechanisms are present in this problem: fracture energy Gdδa and

2.6 Fracture Mechanics of Steady State Crack Propagation and Tunnel Crack . . . Fig. 2.64 Determination of the debond zone length a

67

Tunnel crack front

Fiber

Debonded zone a Matrix

,

, ,

P ,

′

Fig. 2.65 Free body diagrams for calculating external work. u0 is the global displacement. The force P applied to the fiber end is resisted by the composite stress σ

frictional energy δF on the debonded zone. Gd is the fiber/matrix interface chemical bond resisting tunnel crack advance. Considering the work done via surface tractions on the free bodies shown in Fig. 2.65, 1 We ¼ 2

ð

1 uf ðxÞτ0,f dAi,f þ 2 Ai,f

ð

1 um ðxÞτ0,m dAi,m þ Af u0 σ 2 A i ,m ð 1 1 δt ðxÞτ0 dAi ¼ A f u0 σ  2 2 Ai

(2:32)

where u0 is the global displacement of the body relative to the fiber exit point and is given by u0 ¼

σa 2τ0 a2 σV f Le  þ Ef ð1 þ ηÞ Ef d f Ec

(2:33)

Treating friction dissipation as a surface traction and hence absorbing the δF term in Eq. (2.31) into the work term,

68

2 Micromechanics and Engineered Cementitious Composites (ECC) Design Basis

  ð 1 1 0 δW  δU ¼ δW ¼ δ Af u σ  δt ðxÞτ0 dAi 2 2 Ai el

(2:34)

Equation (2.34) utilizes the concept that the change in elastic strain energy during incremental crack extension in an elastic body is always equal to half the external work done. Thus, energy balance during tunnel crack extension Eq. (2.31) can now be expressed as ð 1 1 Af σδu0 ¼ δ δt ðxÞτ0 dAi þ Gd πd f δa 2 2 Ai

(2:35)

Combining Eq. (2.35) with Eq. (2.33) leads to the desired form 4τ0 að1 þ ηÞ þ σ¼ df

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 8Gd E f ð1 þ ηÞ df

(2:36)

expressing the equilibrium tunnel crack length a in terms of applied load σ on fiber end, i.e., Eq. (2.120 ). By substituting the σ-a relation in Eq. (2.36) into the σ-u-a relation in Eq. (2.30), we obtain sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2Ef ð1 þ ηÞ σ ¼ 2 ðτ0 u þ Gd Þ df

for u  uo

(2:37)

where 2τ0 L2e ð1 þ ηÞ Le þ uo ¼ Ef d f Ef

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 8Gd E f ð1 þ ηÞ df

(2:38)

is the fiber exit point displacement when debonding reaches the end of the embedded fiber. Equation (2.37) expresses the fiber bridging stress as a function of the exit point displacement u during debonding. The fiber force is then sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Ef d 3f ð1 þ ηÞ PðuÞ ¼ π ðτ0 u þ Gd Þ 2

for u  uo

giving Eq. (2.12).

2.7

Summary and Conclusions

The design basis of Engineered Cementitious Composites (ECC) takes on a holistic view of the interactions between fiber, matrix, and fiber/matrix interface phases of the composite. The design basis is formulated in terms of strength and fracture

References

69

criteria for crack initiation and steady state flat crack propagation. Such formulation relies on the application of fracture mechanics at various length scales, including tunnel crack propagation along the fiber/matrix interface, the initiation of a crack from a defect site modeled as a spherical void, and the steady state propagation of a bridged crack. The result is a set of equations that, when satisfied, govern the existence of multiple cracking and tensile ductility. Because this set of equations are expressed in terms of measurable physical parameters, their satisfaction can be ensured by deliberate choice of material ingredients or tailoring/modifying them to suit. Interestingly, the success of studying and modeling fracture phenomena at the micro- and mesolength scales has the potential to obviate the need of fracture mechanics at the structural scale. This is because the macroscale tensile ductility of ECC suppresses the brittle fracture failure mode. This observation appears supported by a variety of large scale structural element tests (▶ Chap. 6). The micromechanics of ECC takes the guess work out of ECC design. Instead of the traditional trial-and-error approach, micromechanics provides a systematic tool for narrowing down the range of micromechanical parameters desirable to achieve ECC performance. Illustrations of the effectiveness of the use of micromechanics are demonstrated with fiber surface coating for fiber/interface tailoring and in the choice of artificial flaw size for enhancing the magnitude and robustness of tensile strain capacity. As expected, the use of micromechanics pervades throughout this book.

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35. Tosun-Felekoglu, K., Felekoglu, B., Ranade, R., Lee, B.Y., Li, V.C.: The role of flaw size and fiber distribution on tensile ductility of PVA-ECC. Compos. Part B Eng. 56, 536–545 (2014) 36. Fan, S., Li, M.: X-ray computed microtomography of three-dimensional microcracks and selfhealing in engineered cementitious composites. Smart Mater. Struct. 24(1), 1–14 (2015) 37. Lu, C., Leung, C.K.Y., Li, V.C.: Flaw distribution and cracking strength in Engineered Cementitious Composites (ECC). Cem. Concr. Res. 107, 64–74 (2018) 38. Li, V.C.: Tailoring ECC for special attributes: a review. Int. J. Concr. Struct. Mater. 6(3), 135–144 (2012) 39. Li, V.C., Wang, S., Wu, C.: Tensile strain-hardening behavior or polyvinyl alcohol engineered cementitious composite (PVA-ECC). ACI Mater. J. 98(6), 483–492 (2001) 40. Li, V.C., Wu, C., Wang, S., Ogawa, A., Saito, T.: Interface tailoring for strain-hardening polyvinyl alcohol-engineered cementitious composite (PVA-ECC). ACI Mater. J. 99(5), 463–472 (2002) 41. Horikoshi, T., Ogawa, A., Saito, T., Hoshiro, H.: Properties of polyvinyl alcohol fiber as reinforcing materials for cementitious composites. Int. RILEM Work. High Perform. Fiber Reinf. Cem. Compos. Struct. Appl. 1, 145–153 (2006) 42. Aveston, J., Kelly, A.: Theory of multiple fracture of fibrous composites. J. Mater. Sci. 8(3), 352–362 (1973) 43. Wu, H.-C., Li, V.C.: Stochastic process of multiple cracking in discontinuous random fiber reinforced brittle matrix composites. Int. J. Damage Mech. 4(1), 83–102 (1995) 44. Wang, S.: Micromechanics Based Matrix Design for Engineered Cementitious Composites. University of Michigan, Ann Arbor (2005) 45. Wang, S., Li, V.C.: Tailoring of pre-existing flaws in ECC matrix for saturated strain hardening. In: Framcos2004, Vail, Colorado, pp. 1005–1012 (2004) 46. Wang, S., Li, V.C.: High-early-strength engineered cementitious composites. ACI Mater. J. 103(2), 97–105 (2006) 47. Li, M., Li, V.C.: High-early-strength engineered cementitious composites for fast, durable concrete repair-material properties. ACI Mater. J. 108(1), 3–12 (2011) 48. Li, M., Li, V.C.: Rheology, fiber dispersion, and robust properties of Engineered Cementitious Composites. Mater. Struct. 46(3), 405–420 (2012) 49. Zhou, J., Qian, S., Ye, G., Copuroglu, O., Van Breugel, K., Li, V.C.: Improved fiber distribution and mechanical properties of engineered cementitious composites by adjusting the mixing sequence. Cem. Concr. Compos. 34(3), 342–348 (2012) 50. Felekoʇlu, B., Tosun-Felekoʇlu, K., Gödek, E.: A novel method for the determination of polymeric micro-fiber distribution of cementitious composites exhibiting multiple cracking behavior under tensile loading. Constr. Build. Mater. 86, 85–94 (2015) 51. Rice, J.R.: A path independent integral and the approximate analysis of strain concentration by notches and cracks. J. Appl. Mech. 35(2), 379 (1968) 52. Leung, C.K.Y.: Design criteria for pseudoductile fiber-reinforced composites. J. Eng. Mech. 122(1), 10–18 (1996)

3

Processing of Engineered Cementitious Composites (ECC)

Contents 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Self-Consolidating Casting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Fiber Dispersion Control and Characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Sprayable ECC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 Extrusion of ECC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

74 74 82 89 93 98 99

Abstract

Engineered Cementitious Composites have unique tensile ductility and autogenous crack width control, characteristics attractive to a variety of construction applications. For different construction approaches, such as on-site casting, off-site precasting, shotcreting, or structural member extrusion, the fresh property requirements can be distinctively different. For example, while self-consolidation behavior is desirable for casting, this behavior does not satisfy the requirements for shotcreting. Hence, it is necessary that the fresh properties of ECC be designed to suit the specific application methodology. Control of fresh properties, however, must not interfere with the hardened properties of ECC. In particular, the high tensile ductility must be properly maintained. One of the essential challenges of processing ECC material is the uniform dispersion of fibers in the matrix. Even at a moderate fiber volume content of two percent, balling and nonuniform dispersion of fibers can result in poor hardened properties and high variability of tensile strain capacity, if the material composition and mixing procedure are not properly designed and controlled.

© Springer-Verlag GmbH Germany, part of Springer Nature 2019 V. C. Li, Engineered Cementitious Composites (ECC), https://doi.org/10.1007/978-3-662-58438-5_3

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This chapter describes the accumulated knowledge of fresh property control of ECC that leads to enhanced uniformity of fiber dispersion. As well, techniques for achieving processing requirements for self-consolidating casting, shotcreting, and extrusion are presented. The presented information should be helpful for successful processing of ECC in the laboratory as well as the production of ECC in the field.

3.1

Introduction

In ▶ Chap. 2, the micromechanical theory behind the selection and/or tailoring of ingredients that leads to mix compositions of ECC with tensile strain-hardening properties is presented. To produce ECC specimens or structural members, the mix ingredients must be processed. This chapter deals with the processing of fresh ECC. Three types of construction processes are described, useful for different types of applications. The most common is casting of ECC into formworks, both for on-site and precast constructions. It is generally desirable to achieve selfconsolidating performance, since it eliminates the laborious vibration work that depends on skilled workmanship. In addition, shotcreting of ECC can be particularly useful for tunnel lining construction and for repair works. ECC has also been extruded into prismatic members. In all cases – casting, shotcreting, and extrusion – mixing of ECC in a mixer is an important step. A particular challenge in mixing ECC is fiber dispersion uniformity since a high aspect ratio and as much as two percent by volume of fiber is employed. As pointed out in ▶ Chap. 2, the number of fibers crossing a one square centimeter surface in ECC can exceed one thousand, e.g., using a PVA fiber with 40 μm diameter. Homogeneous mixing, with uniformly dispersed fibers, is necessary to ensure robust hardened properties of ECC and efficient use of fibers. The reliability of structural members can be strongly influenced by fiber dispersion uniformity. Section 3.2 describes several approaches to achieving self-consolidating casting, in laboratory and field scales. Section 3.3 presents the means to enhance fiber dispersion and quantification of fiber dispersion uniformity. Section 3.4 reviews the state-of-the-art on shotcreting with ECC. Section 3.5 discusses a method of extrusion of ECC elements.

3.2

Self-Consolidating Casting

3.2.1

The Chemical Admixture Approach

ECC can also be made self-consolidating similar to self-consolidating concrete. However, major differences between ECC and concrete have significant impact on the fresh property behavior; these include the absence of coarse aggregates and the

3.2 Self-Consolidating Casting

75

inclusion of fibers in ECC. In addition, the typical use of a relatively low waterbinder ratio also negatively impacts on the workability of ECC. Self-consolidating ECC has the specific characteristics of good workability, no segregation of ingredients (cohesiveness between particles and fibers, and water), and consistency with time between the mixing and casting stages. The last is also known as stability of the fresh mix with respect to time. In order not to interfere with the ingredient make-up of ECC dictated by micromechanics for composite tensile ductility in the hardened state, one route to controlling the fresh rheology of ECC is via the use of chemical admixtures that affects mainly the fresh paste behavior [1–4]. This ensures achieving fresh and hardened property targets without conflicting with the requirements on mix composition dictated by the micromechanical criteria (Eqs. ▶ 2.2 and ▶ 2.4). Instead, fresh property of ECC will be tuned by constitutive rheological control of cement paste through a suitable combination of chemical admixtures of superplasticizer (SP) and viscosity modifying admixture (VMA). The SP, such as melamine formaldehyde sulfonate (MFS), is typically a polyelectrolyte that serves as an electrostatic dispersant of cement particles suspended in the mixing water. That is, the cement particles are coated with the polyelectrolyte causing the like polarity of nearby suspended particles to repel each other, thus preventing agglomeration (Fig. 3.1 top). Over time, however, the reduction of the repulsive layer leads to the re-aggregation of cement particles, resulting in a rapid rise in viscosity and loss of workability. If a VMA, such as a hydroxypropyl methylcellulose (HPMC), is used in addition to SP, steric stabilization can be established. Further, HPMC also tends to increase Electrostatic layer formation

Repulsive layer reduction  aggregated particles

SP

SP

HPMC Chain

HPMC + SP

Electrostatic layer formation

Steric layer preservation

Fig. 3.1 The combination of VMA and SP leads to effective electrostatic dispersion and steric stabilization of cement particles suspended in a water medium. (Adapted from [1–4])

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the suspension medium viscosity (using the remaining HPMC after coating of all cement particles). Steric stabilization is useful in delaying the gradual loss of electrostatic repulsion over time. It works by means of the long polymeric chains of the HPMC on the cement particles that physically maintain space between particles (Fig. 3.1 bottom). Although there are now commercially available admixtures that combine both electrostatic and steric actions, such as polycarboxylates, Kong et al. [1–4] suggested the use of superplasticizer and viscosity agent separately for better control of the rheological properties of ECC. They also suggested that the combined action is more effective if the cement particles are first coated with HPMC before the superplasticizer is added. An optimal rheology of fresh cement paste is defined as one that provides high deformability as well as good cohesiveness (minimum sedimentation of suspended solids in water) and slow increase of viscosity over time. Conceptually, a minimum amount of superplasticizer is needed to fully coat the solid particles as indicated by the zeta potential reaching a steady state value (Mix 2 in Fig 3.2a). With this amount of superplasticizer, the mix viscosity will usually be too low (below ηcrit) for maintaining cohesiveness between the solid particles and water. An optimal amount of viscosity agent is then determined to bring the paste viscosity back to a level above ηcrit where good cohesiveness is achieved (Mix 2 in Fig. 3.2b). Although a smaller amount of superplasticizer and viscosity agent (Mix 1) can lead to the same viscosity, such a

a

b

c

Mix 1 Mix 1 Viscosity

Mix 1

Mix 2

Mix 2

Mix 2 0

0

Concentration of SP (%) + HPMC

0

Concentration of HPMC (%)

Time

Fig. 3.2 Concept behind constitutive rheological control of cement paste: (a) Mix 2 has the minimum amount of SP (W2,SP) for complete coating of cement particles, which results in a low viscosity. (b) To restore the viscosity to a level above ηcrit to prevent particle sedimentation, a higher amount of HPMC (W2,HPMC) is needed. (c) This prevents the re-aggregation of particles that could lead to rapid rise in viscosity as in the case of Mix 1. (Adapted from Kong et al. [1–4])

3.2 Self-Consolidating Casting

a

77

b

c 70 mm (2.8 in.) 60 mm (2.4 in.) 100 mm (4 in.)

Fig. 3.3 Slump flow test of stabilized mortar at (a) 20 min, Γm = 9.7, and (b) 60 min, Γm = 8.9. (c) Half slump cone with D0 = 100 mm

Table 3.1 Mix compositions with optimal amount of SP and HPMC Cement 1

Water 0.40

Sand 0.6

Fly ash 0.15

SP 0.0054

HPMC 0.001

mixture will not be able to maintain cohesiveness over time due to re-agglomeration of solid particles when they are not fully coated with superplasticizer (Fig. 3.2c). It is not desirable, however, to use excessive amount of superplasticizer that could lead to a tendency of hydration delay. Through experiments, Kong et al. [1–4] demonstrated the translation of desirable paste rheology into desirable mortar (ECC without the fibers) rheology that in turn drives the desirable self-consolidating fresh properties of the ECC composite. Figure 3.3 shows the deformability of the mortar at 20 min (Fig. 3.3a) and 60 min (Fig. 3.3b) after mixing, using a half size inverted cone (100 mm) on a flow table (Fig. 3.3c). The mortar deformability is quantified by the flow index Γm ¼ ðD=D0 Þ2  1

(3:1)

where D = (D1 + D2)/2, D1 is the maximum diameter of the fresh material spread out like a pancake on a flat Plexiglas surface, D2 is the spread diameter perpendicular to it, and D0 is the base diameter of flow cone. The small reduction in flow diameter is acceptable, especially considering the long time-gap between the two slump flow tests. The optimal combination of SP and HPMC for the mix shown in Table 3.1 based on constitutive rheological control of cement paste is responsible for this stabilization effect. Mortar viscosity, fiber type, and mixing shear energy have strong effects on fiber dispersion in an ECC mix. Typically, a higher viscosity (up to a limit) aids in separation of fibers by a higher shear force in the fresh material during the mixing process, resulting in higher fiber dispersion uniformity. A higher mortar viscosity also prevents segregation of material ingredients. A hydrophilic fiber (such as PVA) tends to enhance wetting of the fiber surface by cement paste due to the presence of the hydroxyl group, thus improving fiber dispersion uniformity. In contrast,

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hydrophobic fiber (such as PP or PE) does not provide such a physicochemical force to improve fiber dispersion. A high shear energy provided by the mixing equipment aids in fiber dispersion. Fresh ECC composite deformability can be characterized by the same slump flow test as described for mortar (using the same Eq. (3.1)), except that a full-size flowcone with base diameter of 200 mm is utilized. Figure 3.4 shows the spread of the pancake-like ECC. No edge bleeding or separation of ingredients is observed. In addition to deformability measurement, ECC self-consolidation is also characterized by the index L = 2H/H0, where H0 is the initial height of the fresh ECC mix (Fig. 3.5) in a box apparatus and H is the height of the ECC mix that flows through the gate separating the two compartments of the box. The gate detail in the box apparatus is shown in the insert of Fig. 3.5. Fig. 3.4 Slump flow test of ECC showing a good spread (Γ =11.7) with ingredient cohesiveness. The mix composition is given in Table 3.1, with 2% by volume of PVA fiber of 12 mm length

Fig. 3.5 Box test shows the self-consolidating behavior of fresh ECC, with L = 0.94. Insert shows gate details. The fresh ECC must pass through without segregation or trapping of ingredients at the gate

3.2 Self-Consolidating Casting

79

A Γ-value of 8–12 and an L-index of 0.73–1 are desirable as suggested by experience in self-consolidating concrete casting [5, 6]. The ECC shown in Figs. 3.4 and 3.5 shows a D1 = 72.3 cm, D2 = 70.5 cm and H = 16 cm, H0 = 34 cm, corresponding to Γ = 11.7 and L = 0.94 near the higher end of the recommended values, suggesting good self-consolidation behavior.

3.2.2

Liquefaction Approach

One disadvantage of the chemical admixture approach introduced in Sect. 3.2.1 above is that the viscosity modifier, HPMC, may introduce excessive amounts of air voids that could lead to a reduction in compressive strength. Further, a planetary mixer with adequate shear force and rotating speed is needed to achieve the desirable self-consolidating behavior of the fresh ECC. To overcome the concern of excessive air voids and achieve ECC mixing with conventional concrete drum mixers, not designed for delivering large shear forces, Fischer et al. [7] and Lepech and Li [8] introduced an alternative approach for self-consolidation, based on the concept of soil liquefaction. The liquefaction approach relies on achieving a densely packed, cohesionless, and well-dispersed particle system consisting of cement, mineral admixtures, and sand but without HPMC. Liquefaction of the mix is achieved by the high pore pressure introduced by agitation of the mixer, causing free-flow of the mixture inside the drum, and self-consolidation behavior during placement. This approach requires an adequate amount of water in the mix but has been demonstrated to be able to maintain a relatively low w/b ratio suitable for ECC composite strength and ductility property targets. The liquefaction approach is particularly suitable for mixing ECC in conventional gravity-based drum mixers. Despite the lack of blending effect introduced by coarse aggregates in conventional concrete that help break up coagulated cement and sand particles within the rotating drum, the desirable deformability based on slump flow test, fiber dispersion uniformity, and composite strain-hardening have been demonstrated in PVA-ECC. The key to the liquefaction approach is the Alfred grain size distribution curve (Eq. (3.2)) [8] that has been successfully used in ceramics design [9]:
CPFT ¼ 100

Dq  Dqs DqL  Dqs

 (3:2)

where CPFT is the cumulative percent of particles finer than a particle with a diameter of D; Ds is the diameter of the smallest particle in the distribution; DL is the diameter of the largest particle in the distribution; and q is the distribution modulus. As determined by Funk and Dinger [9] through analytical combination of polydisperse particle systems, optimal packing distribution is achieved with a distribution modulus equal to 0.37. The Alfred distribution curve is shown as the solid line in Fig. 3.6.

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Normalized Particle Fraction (%)

Particle Size (mil) 0.04 100 80 60

0.4

4

40

0.1

1.0

M45 M46 M47 M48 Optimum

40 20

0 0.001

0.01 Particle Size (mm)

Fig. 3.6 Alfred particle-size distribution curve for optimal packing and liquefaction [8] Table 3.2 ECC mixture proportions by weight. (Source: Lepech and Li [8]) Mixture designation M45 M46 M47 M48 a

Cement 1.0 1.0 1.0 1.0

Fly ash 1.2 1.2 1.2 1.2

Sand 0.8 1.2 1.4 1.6

Water 0.56 0.58 0.59 0.6

HRWRa 0.012 0.012 0.012 0.012

Fiber, volume % 0.02 0.02 0.02 0.02

High-range water reducer

Several mixes (M45-M48) were designed and tested for their fresh properties [8]. Table 3.2 shows these mix designs that differ mainly in the amount of sand. All proportions are given with materials in the dry state; therefore, water was proportionally added to each experimental mixture to return the additional sand to the saturated surface-dry (SSD) state. PVA fibers of 2% by volume and 8 mm in length were used in these experiments. The particle size distributions of these mixes are also shown in Fig. 3.6. The size distributions of the ingredients that go into these mixes are shown in Fig. 3.7. As shown in Table 3.3, M46 with an improved distribution curve shows improved deformability over that of M45. However, the deformability of M47 and M48 with higher sand content and better distribution curves are not improved over that of M46. Lepech and Li [8] suggested that a possible reason could be the inaccurate characterization of the assumed silica sand continuous distribution curve that was based on given discrete size distribution. They also observed a drier appearance in M47 and M48 despite an elevated content of water to ensure that the additional sand particles are in a saturated surface-dry condition. These mixes show Γ-values (11.25–18.4) that match or exceed the selfconsolidation requirement of Γ = 8–12 considered suitable for self-consolidating concrete, demonstrating the effectiveness of the liquefaction approach.

3.2 Self-Consolidating Casting

81

Normalized Particle Fraction (%)

Grain Size (mil) 0.04 100

0.4

4.0

40

400

80 60 40

US Silica F-110

20

Fly Ash (Normal)

Cement

0 0.001

0.01

1

0.1

10

Grain Size (mm)

Fig. 3.7 Grain size distribution of solid ingredients in ECC [8]

Table 3.3 Measured deformability of ECC mixes [8] Mixture designation M45 M46 M47 M48

3.2.3

Mean 18.4 20.2 16.6 11.25

Γ SD 1 1.3 1 1

Count 6 6 6 6

Full-Scale Field Mixing and Casting

Self-consolidating ECC based on the liquefaction approach has been successfully cast in the field for a bridge deck link-slab [10]. For field mixing and casting of ECC using a regular transit mixing truck, three objectives are sought: (1) high fluidity of the mix must be achieved throughout the mixing process; (2) the mortar matrix should be nearly homogeneous after only a short mixing time and immediately prior to fiber addition; and (3) the mixing sequence should allow for as short a mixing time as possible to keep pace with ongoing operations at commercial concrete batching plants. Batching of ECC up to three cubic meters was successfully tested based on an optimized mixing sequence shown in Table 3.4. The elapsed time shown in Table 3.4 is the recommended time for execution of each of these activities at the time of batching. Approximately 10% of mixing water was reserved for drum washing purposes. After all dry materials were added, this reserved mixing water was charged to wash dry material residue from the screw fins high within the mixing drum and to move all materials to the bottom of the drum (Step 5). During the course of this washing, the remainder of the reserve mixing water was added into the truck to maintain the correct water-

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Table 3.4 Mix sequence used for batching ECC with a transit mixing truck [10] Activity no. 1 2 3 4 5 6 7 8 Total a

Activity Charge all sand Charge approximately 90 to 95% of mixing water, all HRWRa, all hydration stabilizer Charge all fly ash Charge all cement Charge remaining mixing water to wash drum fins Mix at high rpm for 5 min or until material is homogenous Charge fibers Mix at high rpm for 5 min or until material is homogenous

Elapsed time, minutes 2 2 2 2 4 5 2 5 24

Note: HRWR = High-range water reducer

cement ratio (w/c). This step proved critical in getting all materials well mixed within the mixing drum. As expected, due to the absence of large aggregate to blend materials within the mixing drum, additional mixing time is needed between charging of the matrix materials and the fibers. This 5 to 10 min of mixing time (Step 8) provides further agitation and time for the high-range water-reducer (HRWR) to liquefy the material. To reduce batching time at the concrete plant and make use of travel time to the site, the mortar mixing time (Step 6) can take place in transit. After arriving at the job site, the fibers can then be added. Once the fibers are charged into the drum, the composite is mixed (at high RPM) on site for an additional 5 min for proper dispersion. In Step 2, a hydration stabilizer was added to maintain fresh mix flowability during the required (e.g. 60-min) transit mixing time. The deformability factor Γ was observed to decrease by less than 15% during this time period. Figure 3.8 shows the tensile stress-strain curve for ECC-M45 based on coupon specimen test and using the mix procedure described above. The 28-day tensile strength over 4 MPa and strain capacity over 2% meets the need of field applications in general, and for the bridge deck link-slab in particular. The compressive strength for this mix reached 68 MPa at 28 days. Figure 3.9 shows self-consolidation field casting of ECC into the form-work of a bridge deck link-slab. For this application, a total of 30 cubic meters of ECC was mixed and casted [10].

3.3

Fiber Dispersion Control and Characterization

Apart from self-consolidation behavior for placement in formwork, the promotion of uniform fiber dispersion in the fresh mix is also an important goal of ECC processing. Uniform fiber dispersion enhances composite properties and their

83

7

1015

6

870

5

725

4

580

3

435 290

2 7 day 28 day

1

Tensile Stress s (psi)

Tensile Stress s (MPa)

3.3 Fiber Dispersion Control and Characterization

145 0

0 0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Tensile Strain e (%) Fig. 3.8 Tensile Stress-Strain curve for ECC-M45 mixed in a transit mixing truck [10]

Fig. 3.9 Self-consolidating casting of ECC into bridge deck link-slab in Michigan. A standard transit mixing truck was used for large scale ECC mixing

robustness, resulting in lower property variability. As a result, a larger portion of the stress-strain curve can be utilized in structural design, resulting in more efficient use of fibers in ECC. In this section, methods of quantification and promotion of fiber dispersion uniformity are reviewed.

3.3.1

Fiber Dispersion Uniformity Control by Means of ECC Mortar Viscosity Control

Control of ECC mortar plastic viscosity can be utilized as a tool to enhance fiber dispersion uniformity. A higher mortar viscosity generates a higher shear force in the mixing process, resulting in the breaking up of fiber bundles. This concept has been verified experimentally using VMA in small amounts [11, 12].

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Specifically, the addition of a VMA up to 0.04% of cement weight was found to increase the plastic viscosity from about 2 Pa.s to about 40 Pa.s, when measured with a viscometer (Fig. 3.10a). Measurement using a Marsh Cone (Fig. 3.10b) also revealed an increase in flow time from about 10s to 40s. In the simple flow time test, the Marsh Cone was filled with the ECC mortar, and the time taken for the complete flow-out of the mortar from the unplugged Marsh Cone was monitored. The increase in Marsh Cone flow time and plastic viscosity with the amount of VMA addition and their linear correlation with each other are shown in Fig. 3.11. The impact of the addition of VMA on ECC ductility is dramatic. Figure 3.12 shows relatively low tensile strain capacity of less than 1.5% when the VMA/C ratio is below

Fig. 3.10 (a) Viscometer and (b) Marsh Cone flow time apparatus. (Source: Li and Li [11])

a

b 120 mm

300 mm

Marsh Cone Flow Time (s)

20 mm

25 mm

ECC_0.04%

40 ECC_0.025%

30

ECC_0.03%

ECC_0.02%

20

y = 2.3737x + 5.9715 R2=0.9546

ECC_0.015% ECC_0.01%

10 ECC_0

0 0

2

4

6

8

10

12

14

16

Plastic Viscosity (Pa.s)

Fig. 3.11 Plastic viscosity and Marsh Cone flow time increase with the amount of VMA. The amount of VMA added is indicated by the label on each data point. (Source: Li and Li [11])

3.3 Fiber Dispersion Control and Characterization 4.0 Tensile Strain Capacity (%)

Fig. 3.12 The influence of VMA content on tensile strain capacity of ECC. (Source: Li and Li [11]). A jump in tensile strain capacity is observed when the VMA/Cement ratio exceeded 0.015%

85

3.0

2.0

1.0

0.0 0

0.01

0.02

0.03

0.04

0.05

VMA/Cement Ratio (%)

0.015% but jumps to about 3% when the VMA/C ratio is larger than 0.02%, corresponding to a viscosity higher than about 7 Pa.s or Marsh Cone flow time of 25 s in Fig. 3.11. To determine if the significant enhancement of strain capacity was related to improved fiber dispersion uniformity, fiber dispersion was characterized by a dispersion index, α (Eq. (3.3)). In this technique, images of the weakest cross-section of an ECC coupon specimen were obtained using fluorescence microscopy (Fig. 3.13). Under an incident light with an appropriate spectrum (wavelength of 370–390 nm), the fluorescence images appear as bright dots of PVA fibers on black background of the matrix (Fig. 3.14). sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P ðxi  xÞ2 Ψð x Þ ¼ = x n α ¼ exp½ΨðxÞ

(3:3)

In Eq. (3.3), ψ(x) is the coefficient of variation, xi is the number of fibers in the unit area i, x is the average number of fibers in one unit area, and n is the number of unit areas in a cross-sectional cut of the ECC specimen (Fig. 3.12). α equals 1 for perfectly uniform fiber dispersion and approaches 0 when the coefficient of variation of fiber dispersion becomes larger. Note that the value of α is sensitive to the size of the unit area but can be used in a relative manner to describe the trend of dispersion uniformity. Figure 3.15 summarizes the correlation between Marsh Cone flow time (or viscosity), fiber dispersion uniformity (as measured by α) and tensile strain capacity. The fiber dispersion coefficient increases as a function of Marsh Cone flow time until about 25 s, after which it stabilizes at about 0.8. The tensile strain capacity is found to first increase and then stabilize at a value of 3% when the fiber dispersion coefficient reaches 0.8.

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Sample

x2 Mercury Lamp

UV Filter

Beam Splitter Emission filter

Image Output

CCD Camera

Fig. 3.13 Fluorescence image technique [11]

12.7 mm

76.2 mm Fig. 3.14 Fluorescence image of a sample specimen showing fiber dispersion [11]

Figure 3.16 shows the improvement in the robustness of the composite tensile property. At low VMA content especially at or below 0.015%, the tensile strain is not only low but also shows high variability. These data show unequivocally that fiber dispersion uniformity plays an important role in achieving high composite ductility and robustness. Although VMA is used as a viscosity agent in this study, it is likely that any means of achieving a higher mortar viscosity should contribute to driving fiber uniformity and composite ductility and property robustness.

3.3.2

Fiber Dispersion Uniformity Control by Mixing Sequence

An alternative means to achieving a higher viscosity for fiber dispersion enhancement is by adjusting the mixing sequence. Zhou et al. [13] suggested holding back some amount of water to increase the plastic viscosity to the desired level when fiber was added. Only after the fibers have been uniformly mixed is the rest of the water added. Figures 3.17 and 3.18 show the difference between the standard laboratory

Tensile Strain Capacity (%)

4.0

1.0

Tensile Strain Capacity (%)

Fig. 3.15 Correlation between March Cone flow time, tensile strain capacity, and fiber dispersion coefficient of ECCs with various amounts of VMA [11]. A Marsh Cone flow time exceeding 25 s leads to a higher value of fiber dispersion coefficient and tensile strain capacity

Fiber Dispersion Coefficient

3.3 Fiber Dispersion Control and Characterization

87

3.0 2.0 1.0 0.0 0

0.2 0.4 0.6 Fiber Dispersion Coefficient

0.8

1.0

0

10

20 30 40 Marsh Cone Flow Time (s)

50

0

10

0.8 0.6 0.4 0.2 0.0

4.0 3.0 2.0 1.0 0.0 20

30

40

50

Marsh Cone Flow Time (s)

mixing sequence and the proposed mixing sequence. Specifically, the adjusted mixing sequence involves (1) part of water, with the w/b ratio of 0.27 resulting in a mix with the desired viscosity range as suggested by Yang et al. [12], was mixed with solid materials and superplasticizer at low speed for 1 min and then at high speed for 2 min; (2) PVA fibers were added and mixed at high speed for 2 min; and (3) the remaining water was added and mixed at high speed for another 2 min. The influence of the simple adjustment of mixing sequence on the tensile strain capacity of ECC is dramatic. Figure 3.19 shows the change in tensile ductility in two different mixes of ECC. Analyses of fiber distribution in specimen cross-section show a strong correlation between enhanced fiber dispersion and increase in tensile strain capacity using the adjusted mixing procedure (Fig. 3.20).

Tensile Stress (MPa)

3

6 c 5 4 3 2 1 0 0 6 e 5 4 3 2 1 0 0 6 g 5 4 3 2 1 0 0

5

6 d 5 4 3 2 1 0 0

1 2 3 4 Tensile Strain (%)

5

6 f 5 4 3 2 1 0 0

1 2 3 4 Tensile Strain (%)

5

Tensile Stress (MPa) 5

6 b 5 4 3 2 1 0 0

1 2 3 4 Tensile Strain (%)

Tensile Stress (MPa)

6 a 5 4 3 2 1 0 0

Processing of Engineered Cementitious Composites (ECC)

1 2 3 4 Tensile Strain (%)

Tensile Stress (MPa)

Tensile Stress (MPa)

Tensile Stress (MPa)

Tensile Stress (MPa)

88

1 2 3 4 Tensile Strain (%)

5

1 2 3 4 Tensile Strain (%)

5

1 2 3 4 Tensile Strain (%)

5

Fig. 3.16 Tensile stress-strain curves of ECC mixes with different amounts of VMA (a) 0%, (b) 0.01%, (c) 0.015%, (d) 0.02%, (e) 0.025%, (f) 0.03%, (g) 0.04% [11]

3.4 Sprayable ECC

89

Fig. 3.17 Standard mixing sequence [13]

3.4

Sprayable ECC

There are applications such as repair work or tunnel lining construction when shotcreting of ECC is desirable. A sprayable ECC for wet-mixture shotcreting is defined as one that can be conveyed through a hose and pneumatically projected at a high velocity from a nozzle onto a substrate surface. For such applications, the requirements for fresh properties are different from self-consolidating casting (Sect. 3.2). While workability for mixing aimed at uniform fiber dispersion remains important, the following fresh property performances are critical for shotcreting of ECC: (a) Initial high deformability: The fresh ECC should have good pumpability from the mixer to the spraying nozzle through a flexible hose. (b) Thickness build-up on spraying: Once the fresh ECC is sprayed onto a vertically placed or overhead substrate, the material should be able to build up in thickness without falling off under gravity. (c) Optimal rest time: The moment just after mixing to the moment of spraying defines a rest time, during which the fresh mix needs to undergo a significant drop in deformability. This rest time should be long enough to accommodate the required time for pumping the material through the hose and any other time delays but should be short enough to meet the requirement (b) above. In most cases, the optimal rest time could be between 15 to 60 min. (d) Pumping pressure must be limited to below the capacity of the pump equipment. To achieve the above performance, a two-stage design for rheological control [14] is desired. The fresh ECC mix must have an initial viscosity low enough for good

90

3

Processing of Engineered Cementitious Composites (ECC)

Fig. 3.18 Adjusted mixing sequence [13] by holding back some amount of mixing water leads to a higher viscosity for fiber dispersion control 4 Tensile Strain Capacity (%)

Fig. 3.19 Adjusted mixes M1A and M2A shows dramatic increase in tensile ductility over the corresponding mixes M1 and M2 based on conventional mixing sequence [13]

3

2

1

0 M1

M1A

M2

M2A

3.4 Sprayable ECC 3 Tensile Strain Capacity (%)

Fig. 3.20 A strong correlation of enhanced tensile strain capacity and improved fiber dispersion coefficient resulting from adjustment in mix sequence [13]

91

R2 = 0.98

2

1

0 0.55

0.60

0.65

0.70

0.75

0.80

Fiber Distribution Coefficient

pumpability (without overloading the pump motor), defined as Stage 1. This is followed by a rapid rise in viscosity to ensure adhesion to the substrate and cohesion of the composite without ingredient segregation, defined as Stage 2. Similar to self-consolidating ECC, a combination of chemical admixtures of superplasticizer (SP) and viscosity agent (e.g., an HPMC) is necessary to achieve performance (a) and (d) in Stage 1. This works with the same principle of modulating the flocculation between cement particles to achieve the desired fluidity. However, in contrast to self-consolidation ECC, the sequence of adding the two chemicals to the cement paste should be reversed. For sprayable ECC, the addition of HPMC comes after the addition of SP, so that the electrosteric effect of HPMC is suppressed in favor of the medium viscosity increase effect (Sect. 3.2.1). The change in sequence prevents the deformability of the ECC mix from remaining high over an excessive amount of time and hinders the required performance specified in (b) and (c). In addition to SP/HPMC sequence change, the rest time and rapid rise in viscosity in Stage 2 can be controlled by the addition of reactive particles, such as calcium aluminate cement (CA) particles. The chemical reaction of CA with water tends to increase viscosity, but the small particle size (at about 5.5 μm, smaller than that of cement particles at about 12 μm) tends to enhance fluidity by freeing the water between cement particles. When small amount of CA is used, the particle size effect dominates initially, resulting in a viscosity below that of the cement paste without CA. This is followed by a rapid rise in viscosity to above that of the cement paste. At higher amount, the reactivity effect becomes dominant at all times, causing excessively high viscosity for Stage 1. Hence, the amount of CA must be properly controlled so that a low viscosity is attained in Stage 1, while a rapid rise in viscosity is attained in Stage 2. To enhance pumpability and limit the pumping pressure, a shorter fiber length is preferred. These concepts for fresh property design of sprayable ECC were demonstrated by Kim et al. [14]. A mix containing ordinary Portland cement with 5% of cement weight replaced by CA was adopted (Table 3.5); 2% by volume of PVA fibers of

92

3

Processing of Engineered Cementitious Composites (ECC)

Table 3.5 Mix proportion of a sprayable ECC. (Source: Kim et al. [14]) Cement 0.95

Water 0.46

Sand 0.80

Fly ash 0.30

HPMCa 0.0005

HRWRAb 0.0075

CAc 0.05

Vfd 0.020

Note: All numbers are mass ratios except for Vf a Hydroxypropylmethylcellulose b High-range water-reducing admixture c Calcium aluminate cement d Fiber-volume fraction

Deformability Index, Γ

CA/C = 0.05

2

1 No CA 0

0

15

30

45

60

Rest Time after mixing (mins)

Fig. 3.21 Two stage deformability of ECC matrix was enhanced with the use of CA [14]

8 mm long were used in this mix, which satisfies the strain-hardening criteria based on the micromechanics considerations (▶ Chap. 2). The matrix material of the sprayable ECC shows high deformability better than that without CA (Fig. 3.21) up to about 25 min rest time, after which the deformability falls to a level below or about the same as the matrix without CA. Note that these deformability values are substantially lower than mixes designed for self-consolidation (Sect. 3.2). Demonstration of sprayability was performed based on a pump-out test and a spray test, using a spiral pump with a manufacturer specification of a maximum allowable pump pressure of 4 MPa. The spray tests involve both fill-up test that sprays the ECC with an air pressure of approximately 700 kPa onto an almost vertically positioned wood box of 356  362 mm2 bottom area and 51 mm depth and a spray-on test that measures the thickness on vertical and overhead surfaces. The pump out test measures the pumping pressure without the nozzle attached. Pumping pressure was registered at less than 1 MPa. The fill-up test was successful after a rest time of 15 min (Fig. 3.22). Spray-on tests attained 45 mm thickness on a vertical surface (Fig. 3.23) and 25 mm thickness on an overhead surface (Fig. 3.24). When compared with steel FRC often used in shotcreting, very low rebounds were

3.5 Extrusion of ECC

93

Fig. 3.22 Fill-up test shows good adhesion and cohesion of sprayable ECC [14]

observed in spraying ECC. It is most likely due to the smaller size of sand and low bending stiffness of the PVA fiber in ECC. The tensile stress-strain curve of the sprayable ECC was found to exhibit a strain capacity of 1.5 to 2% and ultimate tensile strength of 4–4.5 MPa (Fig. 3.25), comparable to those of ECC applied by casting. Sprayable ECC has been applied to dam repair, retaining wall repair, irrigation channel repair, viaduct repair, and tunnel lining construction ([15], see also ▶ Chap. 9). Figure 3.26 shows shotcreting of sprayable ECC in the repair of a damaged concrete dam wall.

3.5

Extrusion of ECC

The extrusion process is particularly suitable for prismatic elements such as pipes. Extrusions of PE-ECC [16] and PP-ECC [17] have been successfully demonstrated. Given the high tensile ductility of ECC, extruded elements can have thinner walls and can be used without the need for steel reinforcement as typically required for extruded concrete elements. The extrusion process demands unique fresh ECC behavior, including the need for good workability during mixing, fluidity for passage of the material through the extrusion die, and adequate stiffness for easy handling without distortion of prismatic element shape by its self-weight as the material comes out from the extruder. The extrusion of PE-ECC pipe was performed with an extruder designed using the principle of soil consolidation under pressure [16, 18, 19] (Fig. 3.27). In this process, the ECC can be mixed with excess water that is later squeezed out from specially designed outlet holes along a drainage section of the extruder, as the material undergoes increasing amount of consolidation while traveling down the

94

3

Processing of Engineered Cementitious Composites (ECC)

Fig. 3.23 Spray-on test to vertical surface for: (a) spraying sequence onto vertical surface; and (b) 45 mm thickness of sprayed ECC layer [14]

length of the extruder. The consolidation pressure causes de-watering of the fresh material in a zone close to the draining section where the consolidated fiber reinforced composite material acts as a filter, allowing only water to pass. The length of the consolidated fiber reinforced composite pipes is increased as the water is squeezed out. In this manner, the fresh ECC is transformed from a fiber/particle

3.5 Extrusion of ECC

95

Fig. 3.24 Spray-on test to overhead surface for: (a) spraying ECC onto overhead surface; (b) sprayed layer of ECC; and (c) 25 mm thickness of sprayed ECC layer [14]

Tensile Stress (MPa)

5 4 3 2

Sprayed ECC Cast ECC

1 0

0

0.5

1.0

1.5

2.0

2.5

3.0

Strain (%)

Fig. 3.25 Uniaxial tensile stress versus strain curves of sprayable ECC at 28 days [14]

suspension into a compacted fiber reinforced material with a low water/cement ratio and low porosity. The resulting tight packing enhances the mechanical bonding between the fiber and the matrix and stability of pipe shape as it emerges from the extrusion dye even before hydration is completed.

96

3

Processing of Engineered Cementitious Composites (ECC)

Fig. 3.26 Shotcreting of sprayable ECC for repair of the Mitaka Dam in Japan, in 2003 [15]

pressurized inlet

extruder pipe

core

draining section CL

seal

fresh material

consolidated material

Fig. 3.27 Consolidation principle of ECC pipe extrusion [16]

The consolidated material is moved forward by a back and forth motion of the core of the extruder. When the core is moved forward, the consolidation pressure on the cross section of the consolidated section combined with the friction resistance between the pipe and the core exceeds the frictional resistance between the consolidated pipe and the extruder pipe. This simple mechanical operation causes the consolidated pipe to move out in front of the draining section accompanied by the flowing of more fresh material forward to the zone near the draining section. By applying suitable consolidation pressure and moving of the core at adequate time intervals, a continuous production process is established. Table 3.6 shows the composition (before extrusion) of an ECC mix. Figure 3.28 shows an ECC pipe being extruded.

3.5 Extrusion of ECC

97

Table 3.6 Mix composition a PE-ECC mix used in extrusion process Reactive powder (C + SF) 1 (0.975 + 0.025)

Sand 0.5

Water 0.365

SP 0.01

Viscosity agent 0.0012

Fiber (% volume) 1.43

Fig. 3.28 Extrusion of ECC pipe

Mix proportions (by weight) used in extrusion. The following abbreviations are used: C: cement, SF: solid (dry) silica fume, SP: super plasticizer, MHEC: methylhydroxyethylcellulose. The water content refers to the fresh state, i.e., before extrusion. The mechanical behavior of extruded PE-ECC pipes has been established by a typical crushing test configuration with line loads p per length along opposite generatrices. The data from crushing tests can be represented as stress versus deformation plot by converting the line load on the pipe to stresses using a linear elastic analysis. Denoting the outer diameter of the pipe d0 and the inner diameter di, the stress fcr, can be expressed as

f cr

di 1þ 6 p d0 ¼  2 π d0 di 1  d0

(3:4)

If the material behaves in a perfectly linear elastic brittle manner, then, according to the theory of curved beams, fcr coincides with the material tensile strength ft, when p corresponds to the ultimate loading capacity of the pipe. The PE-ECC pipe specimen was tested after an initial curing in 100% RH in room temperature for 24 h followed by water curing at 50  C for 1 week. The extruded ECC pipes have higher load capacity and a much higher ductility and deformation capacity than typical extruded FRC pipes (Fig. 3.29a). Unlike normal concrete or FRC pipes that fail in quarters under the crushing test configuration, the PE-ECC tends to ovalize showing a significant amount of damage tolerance (Fig. 3.29b).

98

a

3

Processing of Engineered Cementitious Composites (ECC)

25

b (MPa)

20 15 10 5 0

0

2

4 6 8 Vertical deformation

10

Fig. 3.29 (a) Test curve of a 100 mm diameter PE-ECC extruded pipe showing high strength and ductility [16], and (b) Ovalization and multiple cracking of tested pipe section

3.6

Conclusions

As has been demonstrated, a variety of processing methods are available for ECC. The choice of processing method, including self-consolidating casting, spraying (shotcreting), and extrusion, depends on the application. In each case, the fresh properties must be appropriately adjusted to suit the application method. The factors that govern fresh properties include water, sand, mineral additive, chemical additive, and fiber contents. Apart from the amount, the type of sand (particle size, roundness and sphericity), mineral additive (shape and size), chemical additive (superplasticizer, viscosity modifying agent, calcium aluminate), fiber (length, surface hydrophilicity), and mixing sequence have strong influence on fresh properties. The challenge is to design for fresh properties without interfering with the desired hardened properties in ECC. Most influencing factors affect both fresh and hardened properties. So, it is necessary to be strategic in their adjustments. In principle, however, superplasticizer and viscosity modifying agent, and mixing sequence, do not affect hardened properties, unless they alter the fiber dispersion uniformity. Fiber dispersion uniformity is of critical importance to the robustness of composite hardened properties. In particular, the variability of tensile strain capacity can be highly affected by fiber agglomeration. However, this variability can be largely controlled by optimizing the fresh matrix viscosity. Specifically, the use of optimal amount of VMA and the sequence of mixing have been shown to be effective approaches. Polymeric fiber dispersion can be quantified using florescence microscopy that allows objective quantification of fiber dispersion uniformity.

References

99

References 1. Kong, H.-J., Bike, S., Li, V.C.: Development of a self-compacting engineered cementitious composite employing electrosteric dispersion/stabilization. J. Cem. Concr. Compos. 25(3), 301–309 (2003) 2. Kong, H.-J., Bike, S., Li, V.C.: Constitutive rheological control to develop a self-consolidating engineered cementitious composite reinforced with hydrophilic poly(vinyl alcohol) fibers. J. Cem. Concr. Compos. 25(3), 333–341 (2003) 3. Kong, H.J., Bike, S.G., Li, V.C.: Effects of strong polyelectrolyte on rheological properties of concentrated cementitious suspensions. J. Cem. Concr. Res. 36(5), 851–857 (2006) 4. Kong, H.J., Bike, S.G., Li, V.C.: Electrosteric stabilization of concentrated cement suspensions impacted by a strong anionic polyelectrolyte and a non-ionic polymer. J. Cem. Concr. Res. 36 (5), 842–850 (2006) 5. Nagamoto, N., Ozawa, K.: Mixture proportions of self-compacting high-performance concrete. In: High-Performance Concrete: Design, Materials, and Advances in Concrete Technology, vol. SP-172. ACI International (1997) 6. Okamura, R.H., Ozawa, K.: Mix-design for self-compacting concrete. Concr. Lib. JSCE. 25, 107–120 (1995) 7. Fischer, G., Wang, S., Li, V.C.: Design of Engineered Cementitious Composites (ECC) for processing and workability requirements. In: Brandt, A.M., Li, V.C., Marshall, I.H. (eds.) Proceedings, BMC-7, Warsaw, Poland, pp. 29–36 (2003) 8. Lepech, M.D., Li, V.C.: Large scale processing of engineered cementitious composites. ACI Mater. J. 105(4), 358–366 (2008) 9. Funk, J.E., Dinger, D.R.: Particle packing, part VI—applications of particle size distribution concepts. Interceram. 43(5), 350–353 (1994) 10. Lepech, M.D., Li, V.C.: Application of ECC for bridge deck link slabs. RILEM J. Mater. Struct. 42(9), 1185–1195 (2009) 11. Li, M., Li, V.C.: Rheology, fiber dispersion, and robust properties of engineered cementitious composites. RILEM J. Mater. Struct. 46(3), 405–420 (2013) 12. Yang, E.H., Sahmaran, M., Yang, Y., Li, V.C.: Rheological control in the production of engineered cementitious composites. ACI Mater. J. 106(4), 357–366 (2009) 13. Zhou, J., Qian, S., Ye, G., Copuroglu, O., van Breugel, K., Li, V.C.: Improved fiber distribution and mechanical properties of engineered cementitious composites by adjusting mixing sequence. J. Cem. Concr. Compos. 34(3), 342–348 (2012) 14. Kim, Y.Y., Kong, H.J., Li, V.C.: Design of Engineered Cementitious Composite (ECC) suitable for wet-mix shotcreting. ACI Mater. J. 100(6), 511–518 (2003) 15. Rokugo, K., Kanda, T., Yokota, H., Sakata, N.: Applications and recommendations of high performance fiber reinforced cement composites with multiple fine cracking (HPFRCC) in Japan. Mater. Struct. 42, 1197–1208 (2009) 16. Stang, H., Li, V.C.: Extrusion of ECC-material. In: Reinhardt, H., Naaman, A. (eds.) Proc., High Performance Fiber Reinforced Cement Composites 3 (HPFRCC 3), pp. 203–212. Chapman & Hull (1999) 17. Takashima, H., Miyagai, K., Hashida, T., Li, V.C.: A design approach for the mechanical properties of polypropylene discontinuous fiber reinforced cementitious composites by extrusion molding. J. Eng. Fract. Mech. 70(7–8), 853–870 (2003) 18. Krenchel, H., Fredslund-Hansen, H., Stang, H.: Method and apparatus for producing bodies of consolidated particulate material, and product produced thereby, 1995. International patent application, PCT/DK95/00296 19. Pedersen, C.: New production processes, materials and calculation techniques for fiber reinforced concrete pipes. PhD thesis, Department of Structural Engineering and Materials, Technical University of Denmark, Series R, no. 14 (1996)

4

Mechanical Properties of Engineered Cementitious Composites (ECC)

Contents 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Direct Tension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Flexure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4 Shear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 Compression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.6 Fatigue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.7 Creep . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.8 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

102 102 115 120 124 127 130 132 135

Abstract

The mechanical properties of Engineered Cementitious Composites (ECC) serve multiple purposes. The compressive strength and tensile stress-strain relation are fundamental characteristics of the material. The tensile strain capacity defines the tensile ductility of a given mix composition and processing/curing method. The crack pattern (crack spacing and crack width distribution) is a critically important indicator of durability of the material. Appropriate test methods must be used for proper material characterization. This is particularly important in light of the fact that tensile test is not commonly used for concrete material. The tensile and compressive properties can be used as representative material qualities of ECC. The flexural properties of ECC serve as a first indicator of structural performance, especially since beams are common structural elements. The simple test setup for flexural test (compared with that of tensile test) also makes it ideal for quality control of ECC when used in large quantities in field applications.

© Springer-Verlag GmbH Germany, part of Springer Nature 2019 V. C. Li, Engineered Cementitious Composites (ECC), https://doi.org/10.1007/978-3-662-58438-5_4

101

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Mechanical Properties of Engineered Cementitious Composites (ECC)

This chapter covers the fundamental mechanical properties of ECC in tension, compression, and flexure. Other properties covered include shear, fatigue, and creep. Together, they provide the needed database for design of structures under complex loading, including high frequency fatigue, high strain rate, and sustained loading.

4.1

Introduction

ECC is a family of materials rather than a single material, as emphasized in ▶ Chap. 1. The wide range of property values achievable for meeting different demands for different structures or structural elements are made possible with material ingredient tailoring. Mechanical property characterization is an important part in the micromechanics-based tailoring and composite design and development of ECC. To fully take advantage of the unique behavior of ECC in structural design, it is necessary to characterize its mechanical properties to be used in the design process. This is particularly important given that structural failure is more associated with brittle fracture failure of concrete, and ECC offers tensile properties not typically available in normal concrete. As a result, new testing methodology becomes necessary. In addition, the ductility in tension also translates into major differences in flexural, shear, and fatigue behavior in ECC when compared with normal concrete. This chapter provides an overview of these and other relevant properties; however, instead of being exhaustive, it aims to present a flavor of the wide range of mechanical properties achievable to date with ECC. The fundamental mechanical properties covered in this chapter are useful to understanding the enhanced resilience of structural members (▶ Chap. 6). As the most significant performance gain with ECC over concrete and tensionsoftening FRCs is achieved under tension, the behavior of ECC under direct tension and flexure is more elaborately discussed in this chapter, along with descriptions of test setups and procedures.

4.2

Direct Tension

Determining the tensile response of ECC involves measuring the uniaxial tensile stress as a function of uniaxial tensile strain of the material. Such direct characterization of the tensile stress-strain response distinguishes it from the indirect tension response obtained from the experiments such as the Brazilian test for measuring splitting-tensile strength or four-point bending (FPB) test for determining the modulus of rupture of concrete and FRCs. However, unlike these indirect tension tests, the direct tension test method is not yet universally standardized, in spite of the recent efforts of the research community to reach a consensus on a standard protocol. (Standards are available in China and in Japan.) To provide sufficient guidance, this section describes current best practices for the direct tension tests, along with the

4.2 Direct Tension

103

typical direct tensile response of an ECC specimen and a review of the range of currently achievable tensile properties.

4.2.1

Specimen Geometries

The brittleness of the cementitious matrix of ECC poses certain challenges for the design of specimens for the direct tension tests. For testing ECC or any other material under direct tension, its specimen, regardless of its shape, must be gripped and pulled uniaxially in opposite directions. The act of gripping inevitably causes local stress concentrations in the gripped portion of the specimen. The problem of stress concentration is further exacerbated by the rough and uneven surface of cementitious materials including ECC. If the specimens are improperly designed, these stress concentrations can cause excessive cracking in the grip region leading to premature failure or misalignment of the uniaxial loads at the two ends of the specimen. The specimen geometries discussed below, along with the test setups in Sect. 4.2.2, for direct tension tests are aimed at reducing these stress concentrations in order to mitigate the effects of “out-of-gauge premature failure” of the specimen. In relation to the above discussion, it should be mentioned that the tensile ductility of ECC aides in reducing the effects of stress concentration. Unlike concrete and strain-softening FRCs, ECC is damage tolerant (similar to metals) and is able to redistribute and diffuse the stress concentrations through multiple microcracks. Therefore, even if an ECC specimen shows a few cracks in the grips during a direct tension test, it may still be acceptable provided the final failure of the specimen occurs within its gauge length. Two types of planar specimen geometries are typically used for conducting the direct tension tests on ECC specimens, namely, dogbones (sometimes also called dumbbells in the literature) and coupons. Figure 4.1 shows these two geometries. In the dogbone geometry (JSCE [1]), the stress in the gauge region (3.200 long), across which the tensile displacement is measured, has a cross-sectional area only half of that in the grip region. For an applied tensile loading, the dogbone geometry, therefore, ensures higher stresses in the gauge than the grip region in spite of the stress concentrations in the grip region. As a result, most of the cracking occurs in the gauge of the dogbones. On the other hand, the coupon geometry has a constant crosssection throughout the specimen length and does not allow stress amplification in the gauge. As a result, the coupons tend to show greater degree of cracking in the grips compared to dogbones. Thus, dogbones may be more suitable, compared to coupons, for determining the tensile behavior of ECC under direct tension loading, if excessive cracking in the grips is a concern. In spite of the above limitation, the coupon geometry offers several advantages such as the ease of manufacturing the mold, simple grip fixtures, more random distribution of fibers, almost no restrained shrinkage cracks, and versatility for use in functionality studies such as self-healing or self-sensing. Due to a larger crosssectional area, coupons show a wider fiber orientation distribution compared to dogbones and may therefore provide a better representation of the material behavior

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a

13.0

0.50 Side View Plan View

2.4

Grip Region

1.2

3.2 Gauge Length

b

1.6

3.4

12.0

0.50 Side View Plan View

3.0

Cut-out Region

Grip Region

1.5

2.0

0.5

4.0 Gauge Length

Fig. 4.1 Planar ECC specimen geometries for direct tension tests (All dimensions in inches) (a) Dogbone (JSCE [1]) focuses stresses onto the narrower section along the gauge length, thus avoiding failure at the grips, (b) Coupon provides a larger section for better fiber distribution uniformity and simpler geometry that avoids shrinkage stress build-up during specimen curing

in structural applications. The restraints provided by the changes in the crosssectional area at two sections of the dogbone geometry tend to promote residual tensile stress and possibly shrinkage microcracks as the specimen undergoes curing in the mold. Liberal oiling of the specimen mold helps to minimize the stress due to restrained shrinkage. The constant cross-sectional area of coupons minimizes this type of restrained shrinkage microcracking tendency and is also useful for resonance frequency measurements in self-healing studies (Sect. ▶ 10.3) and for electrical impedance measurements in self-sensing studies (Sect. ▶ 10.5). Thus, both the dogbones and coupons have their advantages and limitations, and the choice ultimately depends on the factors discussed above. The small cross-section at the gauge region of the planar dogbone specimens may limit the orientation distribution of the fibers (typically 0.500 long) in ECC. Such

4.2 Direct Tension

105

Side View 18.0

3.0

Plan View

5.0

Grip Region

6.0

3.0

6.0 Gauge Length

Fig. 4.2 Large dogbone geometry. The larger cross-section (compare to the dimension shown in Fig. 4.1a) allows closer to 3-D distribution of fibers and resembles that in a structure. (All dimensions in inches)

artificial unidirectional orientation may not capture the true material behavior in structural applications with randomly distributed fibers. To account for the threedimensional distribution of fibers, large dogbone specimens with gauge crosssection of 300  300 (Fig. 4.2) can be used for direct tension characterization of ECC.

4.2.2

Test Setup

The setup for the direct tension test using a planar dogbone specimen is shown in Fig. 4.3a. While the dogbone in this figure is gripped by hydraulic wedge grips on the plan view-faces (refer to Fig. 4.1a), it is also possible to grip the dogbone along its slanting side edges. An example of this alternative method of gripping is shown in Fig. 4.3b. Although a large dogbone is shown in Fig. 4.3b, similar grips of smaller size can be used for the planar dogbones as well. The aluminum plates, visible in Fig. 4.3a, are glued to the grip region (Fig. 4.1a) of the dogbones to achieve smooth gripping surfaces, thereby minimizing the stress concentrations. The coupon specimens are gripped similarly to the planar dogbone specimens. The direct tension tests are conducted under displacement control. The displacement across the gauge length is typically measured using two Linear Variable Differential Transducers (LVDTs) mounted parallel to the side edges of the specimen as shown in Fig. 4.3a. The average of the displacements recorded by these LVDTs is divided by the gauge length to compute tensile strain. Taking the average of the two

106

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Mechanical Properties of Engineered Cementitious Composites (ECC)

Fig. 4.3 Direct tension test setup

LVDT readings eliminates error caused by any rotational movement of the specimen during the test. Most direct tension tests are run at quasi-static strain rates of 105/s to 104/s; higher rate tests can be run with the same setup with faster data acquisition and grip modifications. The load for calculating the stress is measured by a load cell built into the test system. In this manner, this direct tension test setup enables the measurement of the tensile stress-strain relation of ECC, while minimizing the stress concentrations in the grip region. More than one type of end support conditions for the grip fixtures has been used in the literature for the tensile test setup described above. The majority of the end conditions can be classified into three different types: fixed-fixed, fixed-hinge, and fixed-hinge/roller. These end support conditions are illustrated in Fig. 4.4. The end conditions shown in Fig. 4.3a represent the fixed-fixed end condition as both specimen ends have little freedom to move or rotate independently of the test system’s grips. Although the fixed-fixed support condition is the simplest to achieve in practice, it may also cause unintentional in-plane and out-of-plane moments in the specimen during the direct tension experiment. The unintended moments are induced by the misalignment of the specimen ends and their inability to readjust due to the fixed-fixed support. Often, the misalignment is caused by the roughness and/or unevenness of the specimen surface, but it can also be caused by the misalignment of the test system’s grips. Hinge support such as that recommended in JSCE [1] (pp. Testing Method:6–10) releases the moment at the hinged end, whereas the hinge/roller support used in Zhou

4.2 Direct Tension Fixed-fixed (Figure 4.3a)

107 Fixed-hinge (JSCE, 2008)

Fixed-hinge/roller (Zhou et. al., 2010)

Fig. 4.4 Various types of support conditions used in direct tension tests. The fixed-hinge arrangement is most often used. The nonzero moment induced on the fixed end can be accommodated by the noncatastrophic ductile response of ECC

et al. [2] can, in theory, release the moment at both ends by providing both rotational and translational degrees of freedom at one end (Fig. 4.4). However, the damage tolerance of ECC can itself diffuse these moments through matrix cracking and redistribution of stresses. The choice of the end support, therefore, depends on the trade-off between the practicality of the experiment versus the necessity to minimize the effects of moment generated microcracking.

4.2.3

Stress-Strain Behavior

A typical stress-strain curve of ECC obtained from direct tension test is shown in Fig. 4.5. The visual condition of the ECC specimen at five different stages (a) through (e) of this stress-strain curve is documented in Fig. 4.6. As the load increases from zero, the tensile stress inside the composite increases linear-elastically until the elastic limit (EL) is reached. EL is slightly less than the first crack strength σfc. Between EL and σfc, the largest crack-like internal flaw or a weakness in the ECC specimen initiates microcrack extension as the stress intensity factor at this site equals the local matrix fracture toughness. This extension is typically stable due to fiber bridging and requires increasing load to maintain (Fig. 2.12a). As the tensile stress reaches σfc, a flat matrix microcrack almost instantaneously propagates throughout the specimen cross-section. The steadystate flat crack propagation is a direct result of satisfying the energy criterion for multiple cracking (Sect. ▶ 2.3.1.2). This causes a slight drop in tensile stress as the load

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a

b 6

σult

(e) (d)

Stress (MPa)

5 4

(b)

σfc 3

30 mm

σmc

(c)

EL (a)

2 1 0 0%

1%

2%

3%

4%

εult

5%

Strain

Fig. 4.5 Typical direct tension stress-strain response of ECC: (a) stress-strain curve (b) saturated multiple cracking in a dogbone specimen. During strain-hardening, increasing amount of microcracks are formed while load capacity continues to increase until the tensile strain capacity is exhausted. This occurs when one of the multiple cracks forms a large crack due to loss of fiber bridging capacity on that crack plane

Fig. 4.6 Evolution of multiple cracking in an ECC specimen under direct tension. (Note: (a) through (e) correspond to various stages of the stress-strain curve in Fig. 4.5a. Microcracks are initiated at different loads due to a distribution of flaw sizes in the ECC matrix)

transfer capacity of the matrix at that composite section is suddenly lost. However, the fiber bridging capacity is not exceeded at the matrix cracking stress (due to satisfaction of the strength criterion discussed in Sect. ▶ 2.3.1.1), and the tensile stress not only regains but exceeds σfc with increasing tensile strain. The tensile stress increases until

4.2 Direct Tension

109

another micro-crack is triggered at the next largest flaw. A new flat crack is formed and the process repeats until the fiber bridging capacity (σ0) is exceeded by the applied tensile stress at the weakest bridged section among all the cracked sections of the ECC specimen being tested. As a result, the damage localizes at the weakest bridged section and the tensile stress reduces monotonically following the bridging stress-crack opening (σ-δ) relation of that section. The maximum tensile stress experienced by the specimen during this experiment is called the direct tensile strength or ultimate tensile strength (σult), and the corresponding strain value is called the tensile strain capacity (εult) as shown in Fig. 4.5. The smallest size flaw triggered into a micro-crack just before σult has the critical flaw size (cmc) as introduced in Sect. ▶ 2.5.3. σmc in Fig. 4.5a is the stress at which this flaw is triggered. The micromechanics-based design of ECC thus facilitates multiple microcracking of the matrix, while maintaining the composite integrity through fiber-bridging, under tension. A typical crack pattern observed in an ECC dogbone during the direct tension test is shown in Figs. 4.5b and 4.6e. This crack pattern has an average crack width of about 45 μm, which is typical of most ECCs. This particular crack pattern is “saturated” as the matrix microcracks are evenly distributed and, more importantly, the crack spacing (1.2 mm) is almost as small as theoretically possible. The theoretical crack spacing is the minimum distance (fiber embedment) needed to transfer the tensile stress from the fibers to the matrix and back to the fibers, which is governed by the fiber/matrix interfacial bond (constrained by the fiber strength). If the fiber strength is not exhausted, greater bond results in smaller crack spacing, provided that there are enough flaws available to be triggered (refer to Sect. ▶ 2.5.3). The direct ultimate tensile strength (σult) of various versions of ECC reported in literature, designed to meet different structural requirements, ranges from 1 to 3 MPa (e.g., fire-resistive ECC [fc0  3 MPa] or ECCs made with PP/natural fibers and/or high recycled material content) to 4–6 MPa (e.g. M45-ECC [fc0  50 MPa] – most common for structural applications) to 13–17 MPa (ultra-high strength [fc0 > 150 MPa] ECC for impact and blast resistance). The pseudo strain-hardening index (PSHstrength), equal to the ratio σult/σfc [3], is a measure of the stress margin available between σfc and σult for forming microcracks. As mentioned in Sect. ▶ 2.3.1.2, the PSHstrength for saturated multiple cracking, as observed in Fig. 4.5b, is typically greater than 1.3. In spite of their different strengths, the common feature of all these different versions of ECC is their tensile ductility or strain capacity, which should be consistently greater than 2%. The tensile stress-strain behavior of ECC exhibits age dependence (Fig. 4.7). In particular, the change in the tensile strain capacity reflects the age-dependent evolutions of the matrix fracture toughness and fiber/matrix interaction properties, which are both influenced by the continued hydration with time [4]. Initially, until the age of about 10 days, the fiber/matrix interfacial bond grows rapidly, causing an increase in the fiber-bridging capacity (σ0). Although the matrix fracture toughness also increases, the rate of increase is slower than that of σ0 which enhances tensile ductility by improving the margin between σ0 and the matrix cracking strength (σfc). The fiber/matrix bond, which is dominated by the chemical bond in PVA-ECC, attains close to its maximum value at the age of 10–14 days [5]. However,

Mechanical Properties of Engineered Cementitious Composites (ECC)

a 6

b Tensile Strain Capacity (%)

4

Tensile Stress (MPa)

110

5 4

90 days

3 2

24 hours

1

0 0

1

2 Strain (%)

3

4

5

4 3 2 1 0

1

10 Age (day)

100

Fig. 4.7 Age dependence of ECC’s (a) stress-strain curves and (b) tensile strain capacity. The tensile ductility [4] changes with continuously maturing matrix and fiber/matrix interface with age. After about 10 days, excessive increase in matrix fracture toughness can lead to a drop in composite tensile ductility. For structural design, it is recommended to use tensile strain capacity value beyond 56 days to be conservative on safe design

the matrix fracture toughness continues to increase significantly beyond 14 days due to continued hydration and reduction of porosity, causing the σ0/σfc, and therefore tensile ductility, to reduce. Finally, the matrix fracture toughness also plateaus at the age of about 90 days, resulting in the stabilization of the tensile strain capacity of ECC thereafter. Thus, the influence of continued hydration on the microstructure and microscale properties of ECC is responsible for the age dependence of tensile strain capacity of ECC. For structural design, it is recommended to use the long-term strain-capacity so as to be conservative for safety. For characterizing the tensile behavior of ECC, the direct tension test should be used instead of the splitting-tensile strength (STS) test. The STS test, as standardized in ASTM C496 [6], was originally designed to determine the tensile strength of normal concrete, which is a brittle material. However, unlike normal concrete, ECC shows an extremely ductile behavior that causes a change in the failure mode of the split-cylinders from almost pure tensile cracking to a combination of multiple tensile cracking and compressive crushing. The difference in failure patterns of concrete and ECC split-cylinders is shown in Fig. 4.8. This change in the failure mode of the split-cylinders causes a nonconservative estimation of the tensile strength of ECC [7] using the STS test, and therefore, the direct tension test is necessary to characterize such strain-hardening materials under tension. Similar to the STS test, the FPB test alone cannot be used to characterize the fundamental tensile behavior of ECC. While the FPB tests may be used for quality control due to ease of experimentation only after it has been ascertained that the material actually shows strain-hardening under direct tension, the FPB test by itself cannot be used as a composite design tool to characterize and compare various materials. This is because the modulus of rupture and maximum mid-point deflection (results of the FPB tests) depend on both the tensile and compressive properties of the material and therefore do not purely capture the tensile response of the material. Furthermore, it is also incorrect to conclude that a certain FRC possesses tensile

4.2 Direct Tension

111

Fig. 4.8 Comparison of cracking patterns in (a) normal concrete (Source: http://y2u.be/6lkZIrLp_mE) and (b) ECC split-cylinders (400 diameter). For ductile ECC, the final failure mode is a combination of multiple tensile cracking and crushing. As a result, the measured tensile strength overestimates the true tensile strength

ductility based only on the multiple cracking and/or deflection-hardening observed in a flexure test, as the moment capacity of a section can increase beyond the yield point through the movement of the neutral axis even in the absence of tensile strain-hardening of the material. This could happen due to stabilization of a crack propagating from the tensile towards the compression zone of the beam, allowing additional cracks to form. Thus, while all strain-hardening materials exhibit flexural deflection-hardening, all deflection-hardening materials do not necessarily strain-harden under direct tension [8].

4.2.4

Measurement of Crack Width

The measurement of crack widths can be done in at least two different ways. The first method involves direct observation of individual cracks using an optical microscope and measurement of individual crack width of each crack along a line coinciding with the specimen’s longitudinal centerline. Given the variation of width along each crack, and plausible joining and branching along the crack length, it is recommended to use three lines parallel to the specimen axis to determine the crack widths. This method provides complete statistical information of the crack width distribution, including average crack width, maximum crack width, and the standard deviation. However, this direct method of crack width measurement is time intensive. The second method estimates the average crack width by multiplying the tensile strain capacity of the dogbone specimen by the gauge length divided by the total number of cracks observed within the gauge length along the specimen centerline. This can be supplemented by the actual observation of only the maximum crack width, which provides a rough estimate of the standard deviation. While the average crack width is useful for material characterization, as it is a material property of ECC, the maximum

112

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Mechanical Properties of Engineered Cementitious Composites (ECC)

crack width is critical (along with the average crack width) for determining the durability of ECC structural elements. This method of crack width measurement is quicker and less labor intensive but may lead to over-simplification of the crack pattern. Alternatively, semi-automated measurement of crack pattern and crack width distribution can be achieved with the use of digital image correlation (DIC) [9]. The ECC specimen is first sprayed with black and white paint to create a random speckle pattern (Fig. 4.9a). High resolution photos are then taken of the AOI on the specimen surface before and during uniaxial tensile loading (Fig. 4.9b) at 5 s intervals. The movement of small regions of pixels between the undeformed and the deformed states is tracked (by matching their grey scale distribution) and used to compute the local strains. Various correlation functions are used in the matching process [10]. 2D image correlation analysis can be conducted using a commercial software such as Vic2D. In this manner, strain maps can be generated at various loading stages (Fig. 4.10). Based on the strain map, the axial strain variation along the center line can be computed as shown in Fig. 4.11. The peak strains thus recorded reflects the deformation jumps at the location of the cracks. By multiplying the peak strains to the distances between adjacent peaks, the width of cracks along the centerline can be estimated. An example of the crack width distribution deduced in this manner is shown in Fig. 4.12 [11]. The DIC method of measuring crack width on ECC specimens has several advantages over other approaches. These include (1) noncontacting monitoring avoids interference with deformation development on the specimen caused by Fig. 4.9 (a) Dogbone specimen with random speckle pattern, (b) Specimen being uniaxially tensionloaded showing the Area of Interest (AOI) and Center Line

4.2 Direct Tension

113

Fig. 4.10 Strain maps reflecting microcrack patterns generated from DIC at four loading stages with imposed overall strains of (a) 1.0%, (b) 2.0%, (c) 3%, and (d) 4%. Often bands of microcracks are formed, as blank space filled in at higher imposed strain levels, and finally become saturated prior to final failure with the opening of a single crack. (Adapted from [9])

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Mechanical Properties of Engineered Cementitious Composites (ECC)

Fig. 4.11 Strain-distribution along center line obtained from DIC at a particular loading state. The positive peaks reflect displacement jumps due to crack openings. The negative peaks are likely a result of numerical errors in the image analysis. (Adapted from [9])

15

Strain (%)

10

5

0

-5

0

20 40 60 80 100 Distance along gage length (mm)

Number of cracks

6 1.4

4

1.1

0.8

2 0.6 0.3

0 0

20

40

60 80 100 120 140 Crack width (µm)

Fig. 4.12 Crack width distribution at different loading stages indicated by the imposed overall uniaxial strain on the specimen. The crack widths were computed using data sets like that shown in Fig. 4.11. Crack widths in ECC are found to follow a log-normal distribution curve. As expected, the peaks of the log-normal curves shift to higher crack width values with increasing imposed strains (0.3%, 0.6%, 0.8%, 1.1%, and 1.4%). (Adapted from [11])

instrumentation, (2) provides a large field of view and reasonable resolution (about 10 μm), (3) allows measurement of crack width distribution and crack pattern development while the specimen is under load in the machine, thus avoiding partial closing of cracks upon unloading, (4) less subjective compared with manual measurement of crack width, and (5) automated thus allowing higher efficiency particularly when working with a large set of specimens.

4.2.5

Strain-Rate Sensitivity

Structures can be loaded at different strain rates (Fig. 4.13). For most circumstances, loading rates at or below 104/s are considered quasi-static loading. Under earthquake loading and impact loading, the strain rate can reach 101/s and 101/s, respectively. Under blast loading, the strain rate can be still higher, at 102–103/s. Most materials, including concrete, have strain-rate sensitivity. This means that the

4.3 Flexure

115 Seismic strain rates

Load Conditions Strain Rates -1 (s )

Creep

10

-8

10

-7

Static

10

-6

10

-5

Seismic

10

-4

10

-3

10

-2

High strain rates Impact

10

-1

10

0

10

Blast

1

10

2

10

3

Fig. 4.13 Strain rates experienced under different types of loading [12]. The tensile properties of ECC can be influenced by high strain rates. In general, the tensile strength increases while the strain capacity of ECC tends to decrease unless properly designed for

mechanical properties change with the rate of loading. For ECC, it is particularly important to understand any changes in their tensile strength and strain capacity under high loading rates. The source of rate sensitivity of ECC can come from the rate sensitivity of the fiber, matrix, or fiber/matrix interface [13]. The rate sensitivity of the matrix may be reflected in increase of its fracture toughness Km as a function of strain rate. The rate sensitivity of the fiber can be reflected in increase of the fiber stiffness and strength as a function of strain rate as is expected for most polymeric material. The higher fiber strength σf leads to higher fiber bridging capacity. The interfacial chemical bond Gd and frictional bonds τo have been found to also increase with increasing strain rate [14]. Their excessive increase, however, can lead to a reduction of composite tensile strain capacity, caused by violation of the energybased strain-hardening criterion (▶ Chap. 2). Changes in ECC tensile properties can be summarized by changes in Dynamic Increase Factor (DIF) that measures the ratio of the property at different strain rates normalized by that at quasi-static loading rate (Fig. 4.14). The first crack strength of ECC shows an increase with strain rate, consistent with the increase in Km as preexisting flaws require higher tensile stress to initiate cracking. The ultimate tensile strength σult of ECC also increases with strain rate due to the higher bridging capacity across cracks, as a result of increase in fiber strength and fiber/matrix interface properties. The increase in σult is particularly pronounced at strain rates above 101/s, based on Hopkinson bar tests [15]. The tensile strain capacity generally shows a decrease with strain rate. Control of fiber/matrix interface [13] is key to maintaining ECC’s tensile ductility under high loading rate (Sect. ▶ 6.4.1).

4.3

Flexure

4.3.1

Flexural Stress-Deflection Behavior of ECC Beams

The flexural behavior of an ECC beam is typically determined using the FPB test. This test is also known as the third-point bending test as the middle two loads are applied at one-third of the span length from both sides. Such loading provides a constant moment in the middle third of the simply supported beam’s

116

a

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Mechanical Properties of Engineered Cementitious Composites (ECC)

b

3

8

Tensile strength DIF

Cracking strength DIF

7 2

1

6 5 4 3 2 1

0 -5 10

Cracking strength DIF

c

10

-3

-1

10 10 -1 Strain rates (s )

10

3

0 -5 10

10

-3

-1

10 10 -1 Strain rates (s )

10

3

3

2

1

0 -5 10

10

-3

-1

10 10 -1 Strain rates (s )

10

3

Fig. 4.14 Dynamic increase factors of tensile properties of ECCs as a function of strain rates. (a) First crack strength generally shows an increase with strain rate, (b) ultimate tensile strength generally shows an increase with strain rate, with high rate of increase at high impact loading rates, and (c) strain capacity can decrease unless properly controlled [14]. (Adapted from [16])

span. Several geometries of beams, ranging from thin plates (similar to coupons mentioned above with very large span-to-depth ratio) to the beams of size 400  400  1400 (span length of 1200 ) standardized in ASTM C1609 [17] for testing the flexural performance of FRC, have been investigated in the literature. The flexural strength of ECC beams is expected to be size independent – a direct result of ECC’s tensile ductility that suppresses the fracture mode, so that the size effect associated with brittle or quasi-brittle fracture failure cannot be present. This has been experimentally verified [18] using a broad range of beam sizes. However, change in the beam behavior may occur due to difference in fiber orientation distributions influenced by the beam’s dimensions [19]. The flexural responses of PVA-ECC and PE-ECC are shown in Fig. 4.15. They show deflection hardening behavior, i.e., the flexural load (stress) continues to rise after damage is initiated in the beams. As expected, the flexural strength increases with age, but the deflection at peak load is reduced. This is consistent with the

4.3 Flexure

b

20 90 days 15 10 24 hours 5 0 0

5 10 Deflection (mm)

15

Flexural Stress (MPa)

Flexural Stress (MPa)

a

117

15

10 2% PE-ECC

5 1% Steel FRC

0 0

2

4 6 8 Deflection (mm)

10

Fig. 4.15 Typical flexural response of ECC beams (a) PVA-ECC at two ages [4] (b) PE-ECC & Steel FRC [20]. Age leads to higher strength but lower flexural ductility. For ECC, deflection hardening is guaranteed regardless of beam dimensions

Fig. 4.16 Crack patterns in ECC beams (beam depth = 400 ) under FPB. (a) High strength ECC [7], (b) PE-ECC [20]. Deflection hardening is accompanied by multiple cracks which extends to over 80% of beam height, shifting the beam neutral axis up towards the top beam surface. The distributed tensile deformation also causes spreading of compressive strain on the upper side of the beam. In contrast, the concentrated strain on the compression side of normal concrete or FRC beams often leads to brittle spalling

increase in direct tensile strength and decrease in tensile strain capacity with age, as discussed in Sect. 4.2.3. Typical crack patterns observed in ECC beams (not reinforced with any conventional steel reinforcement) under FPB are shown in Fig. 4.16. As observed in this figure, ECC beams exhibit saturated flexural cracking perpendicular to the principal tensile stress field with the crack tips reaching up to about 85% of the total beam depth in the constant moment region of the beam (between the two vertical black lines). These flexural cracks are similar to those observed in a well-detailed reinforced concrete with conventional steel reinforcement but are spaced much closer. The average beam deflections near the modulus of rupture are very high up to 2.5% of the span length. Such flexural ductility and multiple cracking are direct results of the extreme tensile ductility of ECC. The flexural/tensile strength ratio of ECC has been investigated [20] using classical beam bending theory. By modeling ECC’s uniaxial tensile and compressive

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Mechanical Properties of Engineered Cementitious Composites (ECC)

behaviors as bilinear functions, the moment-curvature (M-ϕ) relation of the ECC beam was computed. The M-ϕ relation was further translated into the flexural stressdeflection relation, and the modulus of rupture (MOR) of the ECC beam (peak flexural stress) was thus estimated. The key results of this analytical investigation are shown in Fig. 4.17. The measured values of MOR/σfc, σult/σfc, and εult for a PE-ECC are also indicated in this figure. As observed in Fig. 4.17a, the MOR/σfc ratio increases linearly as a function of the σult/σfc ratio. In this case, it is evident that when σult is increased and when σfc is held constant, the result would be an increase in the MOR/σfc ratio as well as increase in the MOR value. However, when σfc is decreased and σult is held constant, the result would be an increase in the MOR/σfc ratio but a decrease in the MOR value. To design for high MOR in a structural element, therefore, it is desirable to design ECC with high σult and avoid excessively low σfc. The MOR/σfc ratio (Fig. 4.17b) can be much in excess of unity, which represents an elastic-perfectly brittle material. The MOR/σfc ratio increases with the material’s tensile ductility and overshoots 3 (MOR/σfc ratio = 3 represents an elastic-perfectly plastic material), which is achievable only if the material undergoes tensile strainhardening. However, the rate of increase of MOR/σfc ratio decreases significantly beyond εult equal to 1%. A closer investigation reveals that the initial high slope, Δ(MOR/σfc)/Δ(ε ult), is associated with a significant increase in the size of the microcracking zone. At εult equal to 1%, the size of the microcracking zone approaches about 90% of the beam depth and does not significantly increase thereafter causing the flattening of the (MOR/σfc)-εult curve. This suggests that, beyond εult of 1%, the MOR of an ECC beam does not significantly change as a result of increasing tensile strain capacity of the material; on the other hand, the MOR/σfc continues to increase at a constant rate with increasing σult/σfc (Fig. 4.17a). Hence, as a strain-hardening material, ECC can achieve an MOR over three times that of the first crack strength, demonstrated both theoretically and experimentally in Fig. 4.17.

a

b

9

4

8

PE-ECC

6

MOR/

MOR/

7

5 PE-ECC

4

3

2

3 2

1 1

2

3

4

0

0.02

0.04

0.06

0.08

εult (mm/mm)

Fig. 4.17 Computed variation of flexural/first crack strength ratio with (a) ultimate tensile strength and (b) tensile strain capacity [20]. Higher fiber bridging capacity and higher composite strain capacity lead to a higher σult and a higher MOR. The corresponding flexural and tensile properties of a PE-ECC are also shown

4.3 Flexure

4.3.2

119

Quality Control Based on Beam Test

The tensile properties of ECC, particularly the tensile strain capacity, may show significant variation between specimens of a given batch, if the criteria for robust tensile ductility [21] are not satisfied. Even when these criteria are met, the coefficient of variation in tensile ductility typically varies between 10% and 20% due to inherent variability in a number of factors influencing the mix processing. Although the first crack strength and the ultimate tensile strength also show variability, their spread is usually less than that of the tensile strain capacity. Thus, it is important, especially in field applications, to exercise good quality control over the material properties. Good processing control of ECC (▶ Chap. 4) can improve fiber dispersion uniformity and enhance robustness of composite mechanical properties. Due to the ease of experimentation of a FPB test relative to a direct tension test, and recognizing the forward mapping from the material properties to the structural response (Sect. 4.3.1), inverse methods have been developed to back-calculate the tensile properties of ECC from the flexural load-deflection response of ECC beams. One such method is presented in Qian and Li [22, 23]. Using moment-area theorems and the symmetrical trapezoidal curvature diagram under FPB, it can be shown that the beam deflection (u) at the load points in an FPB test is given by Eq. 4.1, where εt is the tensile strain at the bottommost plane of the beam at mid-span, c is the distance of the neutral axis from the bottommost plane of the beam at mid-span, and L is the span length of the beam. u  0:1

e  t L2 c

(4:1)

In Eq. 4.1, L is constant but c is dependent on the material properties. However, as observed in Maalej and Li [20], the size of the microcracking zone in an ECC beam, which governs the distance of the neutral axis (c) from the bottom of the beam, does not grow significantly beyond the tensile strain capacity of 1%. If c is approximately constant, then from Eq. 4.1, u is linearly proportional to εt, and in the limit, the deflection capacity, umax, of the beam is proportional to the material tensile strain capacity, εult. The above result is proven numerically [22] through forward computation of flexural stress-deflection relation based on a large set of material properties. Through such analysis, a “master curve” is further constructed to predict the tensile strain capacity εult of PVA-ECC based on the beam deflection capacity umax in an FPB test. These predictions were verified using direct measurement of tensile strain capacity through direct tension tests. The direct tensile strength of ECC can also be estimated based on the FPB test [21], utilizing the normalized MOR versus εult plot in Fig. 4.17b and the predicted εult. However, the conservative assumption of an elastic-perfectly plastic behavior is made in this study, so that, instead of MOR/σfc, MOR/σte is plotted against εult for a variety of material properties to compute the master curve. Here, the effective tensile stress capacity, σte, is assumed equal to the first crack strength (σfc) as well as the

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4

Mechanical Properties of Engineered Cementitious Composites (ECC)

ultimate tensile strength (σult) of ECC. Thus, knowing umax and MOR in an FPB test, εult and σult of ECC can be estimated and used to perform quality control in the field. Researchers at Japan Concrete Institute (JCI) [24] and the Technical University of Denmark (DTU) [25] have also developed similar inverse methods. The JCI method assumes an elastic-perfectly plastic material model as that used in Qian and Li [22, 23] and utilizes similar sectional analysis as that performed in Maalej and Li [20], to predict the material properties based on the FPB test results. However, the JCI method requires the use of LVDTs to measure the beam curvature, whereas the Qian and Li approach only requires the load point deflection measured by the stroke displacement. The DTU method is more rigorous, utilizing a hinge model with both tensile strain hardening and softening effects to accurately invert for the direct tension properties based on the FPB test. However, this method requires slightly advanced mathematical computations that may limit field applications. In spite of its experimental and mathematical simplicity, Qian and Li [22, 23] provide an effective method for material quality control in the field. It should be emphasized that the quality control method discussed here is intended as a simple-to-carry-out methodology to ensure the meeting of design specification for ECC used in the field. This implies that the ECC is already properly designed in the laboratory to show tensile strain-hardening. The FPB beam test should not be used for material development purpose. More specifically, it should not be used to qualify a material for being a strain-hardening material or not. As pointed out earlier, an ECC will always exhibit a deflection-hardening response in a beam test. However, a material that shows deflection-hardening does not guarantee a material that exhibits tensile strain-hardening in a direct tension test.

4.4

Shear

The performance of ECC and reinforced-ECC (R/ECC) structural elements under shear have been investigated for a variety of applications. The behavior of concrete under shear, similar to under tension, is brittle, which significantly increases the probability of catastrophic failure of concrete [even reinforced-concrete (R/C)] structural elements subjected to high shear forces, such as corbels, short columns, shear keys, etc. Selected laboratory investigations comparing the performance of ECC, normal concrete, and other materials in shear-intensive beams are presented in this section. The shear behavior of ECC has been experimentally investigated [26] using Ohno shear beams [27]. In this study, two different types of ECC were investigated. PE-ECC containing 2% by volume of polyethylene fibers was designed for high tensile ductility. DRECC containing 7% by volume of hooked steel fibers was designed for high tensile strength. In addition to these two ECCs, R/C, FRC, and plain concrete (PC) beams were also investigated in this study. The geometry of the Ohno shear beam is shown in Fig. 4.18a. The loads in this test setup are applied such that a constant shear of magnitude P/3 is experienced by the shear panel being tested. The R/C panel was designed with adequate shear reinforcement as specified in the

4.4 Shear

121

b A-A

A Shear panel

185

170

210 A 185

50 50 50

150

540 50 50 50

160

170 2P/3

25

Flexural Reinforcement

135 P/3

50

150

Flexural Reinforcement

210 P/3 50

2P/3 330

160

Average Shear Stress (MPa)

a

10 8 6

PE-ECC

4 2 0

0

0.01 0.02 0.03 Average Shear Strain (mm/mm)

c

All dimensions are in mm

Fig. 4.18 Shear performance of various materials determined by Ohno shear beam test [26]. (a) Beam geometry and loading configuration, (b) shear stress–shear strain response, and (c) diagonal multiple cracking pattern of ECC under shear. Even without steel reinforcement, the two ECC specimens demonstrated superior load carrying capacity, ductility, and crack width control under shear loading

ACI building code, whereas all other beams did not contain any shear reinforcement; however, flexural reinforcement was provided to preclude flexural failure and enforce a shear failure of the panel. The results of the Ohno shear beam tests in the form of shear stress-strain responses of the panels are shown in Fig. 4.18b. Both ECC panels performed well in comparison with the PC, R/C, and FRC panels. The DRECC designed for high strength and moderate ductility failed at an ultimate shear stress of 9.89 MPa, which was about 300% more than the PC and about 81% higher than the R/C system. The increase over the FRC systems was 226%. On the other hand, the PE-ECC system that was designed for high strain capacity and only moderate load carrying capacity sustained a maximum stress of 5.09 MPa, which was about twice that of the PC system and only slightly lower (about 7%) than the RC specimen, despite having no shear reinforcement. In other words, ECC by itself can carry high shear load even without reinforcing steel. The ductile shear performance of ECC panels compared to other materials is revealed by comparing the strain capacities of various specimens. While the first crack strains of all the panels are comparable (about 0.1%), the ultimate strain capacities are decidedly different. PC being a brittle material shows no ductility under shear and fails after the first crack at 0.1% shear strain. FRC shows slight improvement in the strain capacity due to the fiber-bridging of cracks and fails at 0.6% strain; however, much of this “strain” capacity is attributable to the large crack opening which develops rapidly after the first crack. The R/C panel records a strain

122

4

Mechanical Properties of Engineered Cementitious Composites (ECC)

of 1.95% at the peak which is due almost entirely to the opening of one or two large cracks in the concrete and plastic deformation of the wire mesh crossing them. The peak strain of DRECC panel was about 0.7%, which is six times that of the PC panel. The PE-ECC panel showed the most ductile behavior as designed and resulted in a peak strain of about 2.6%, which is over 20 times the failure strain of PC and exceeds the strain capacity of the R/C panel. Unlike R/C and FRC, no large cracks develop in either ECCs, so that the measured deformations were real strain due to distributed microcracking. Thus, the structural ductility under shear mirrors the tensile strain capacity of the corresponding materials, which is expected as the shear response of the Ohno beams is effectively a diagonal tensile response (Fig. 4.18c) that remains ductile for ECC. The performance of ECC panels in terms of shear strength and ductility described above underlies the potential of reducing or eliminating transverse steel reinforcement in structural members. The shear behavior of R/ECC beams has been investigated [28]. Shimizu et al proposed a method to compute the shear contribution of ECC based on the uniaxial tensile properties of ECC. Correlations between the fiber volume fraction and the tensile strength and that between the tensile strength and the shear capacity of the ECC beam were determined in this study. In another study, Kanda et al. [29] reported the response of R/ECC and R/C Ohno shear beams subjected to cyclic shear loading, simulating the response of coupling beams in buildings under seismic loading. In this study, the influence of three experimental parameters: (a) material type, R/ECC or R/C, (b) shear-span-to-depth ratio, 1 or 0.5, and (c) transverse reinforcing ratio, 0% or 1%, on the behavior of shear panels was investigated. The transverse reinforcement ratios are chosen such that the failure mode is shear-tension for 0% and shear-compression for 1%. The experimental results of the cyclic loading tests in the form of the stress-strain envelopes (obtained by joining the outermost points of the hysteresis curves) are shown in Fig. 4.19. The influence of the first parameter, the material type, can be observed by comparing RC-1-0 and ECC-1-0 curves for shear-tension failure mode and by comparing RC-1-1 and ECC-1-1 for shear-compression failure mode. Under shear tension failure mode, loading capacity is increased by 50% and strain capacity is enhanced over 200% by using R/ECC instead of R/C. Under shear compression failure mode, loading capacity is again increased by 50%, while there is no influence of the material type on the strain capacity. Thus, ECC enhances the shear performance more significantly when the failure mode is tension-related (which is typically the catastrophic mode of failure) than when it is compression-related. The effects of the second parameter, combining transverse reinforcement with ECC, are revealed by contrasting ECC-1-1 with ECC-1-0 or ECC-0.5-1 with ECC-0.5-0 in Fig. 4.19. In both cases, shear loading capacity is remarkably increased by 36–108% while ultimate displacement is not significantly varied. Beams without transverse reinforcement, ECC-1-0 and ECC-0.5-0, showed rather ductile behavior. Hence, this observation suggests that combining transverse reinforcement with ECC is effective in enhancing shear load resistance, although ECC beams behave in ductile manner even without transverse reinforcement.

4.4 Shear

123 10

: Trans. reinforcement yielding : Peak point

Shear Stress (MPa)

8

ECC-0.5-1 ECC-1-1

6 ECC-0.5-0 4

RC-1-1

2

ECC-1-0 RC-1-0

0

0

5

15

10

20

3

Rotation Angle (x10 rad.)

Fig. 4.19 Shear stress-strain (rotation angle) envelope curve [29]. The first number 0.5 or 1 indicates shear span/depth ratio and the second number 1 or 0 indicates the transverse reinforcement ratio in percent. This study shows the effectiveness of ECC in load carrying capacity and prevention of brittle failure even when transverse reinforcements are absent

The effects of the third parameter, shear-span-to-depth-ratio, are revealed by contrasting ECC-1-1 with ECC-0.5-1 or ECC-1-0 with ECC-0.5-0. With or without transverse reinforcement (second index = 1 or 0), shear strength of shorter spans (first index = 0.5) is enhanced by 41–116% relative to that for the longer spans (first index = 1). The strain capacity of shorter span specimens is slightly smaller than that of the longer span specimens. Nevertheless, the behavior is still extremely ductile considering the prevailing notion that the brittleness increases in shorter R/C spans. Therefore, ECC is effective in preventing brittle shear behavior in very short-span beam even without transverse reinforcement. In addition to the above cyclic shear tests, Kanda et al. [29] also explored the feasibility of developing bolted ECC panel joints (Fig. 4.20), building upon the excellent damage tolerance of the material under shear loads. While the concrete panels used in this study for comparison failed in a brittle manner in the joint region, the ECC panels showed no localized damage in the joint region but failed at the panel base support under compression. Furthermore, the peak shear load sustained by the ECC panels was almost twice that of the concrete panels. Thus, the feasibility of dry-jointing ECC panels with high shear load capacity needed for structural wall assembly was demonstrated in this study. Inspired by the proven feasibility of dry-jointing ECC panels, Qian and Li [30, 31] investigated the use of ECC in other similar shear-intensive applications, such as the stud connections between steel and concrete and embedded anchors. They showed that stud connections with ECC exhibit more ductile failure mode and a higher ultimate strength and slip capacity compared with connections with other

124

4

Mechanical Properties of Engineered Cementitious Composites (ECC)

Fig. 4.20 ECC panels bolted together (dry-joint) with steel connection. Despite the high stress concentration at the bolts under shear loading of the panels, brittle fracture was prevented by the ductile shear behavior of ECC [29]

concrete materials, in addition to a much-improved structural integrity. The superior ductility of ECC is reflected by the microcrack development near the shear studs, suppressing the localized fracture mode typically observed in other concrete materials. Similarly, Qian and Li [31] demonstrated experimentally that the tensile ductility of ECC, compared to the brittle behavior of normal concrete, leads to significant enhancement of pullout load and displacement capacities of an anchored steel bolt. See also Sect. ▶ 9.5.2. for a broader discussion on steel/ECC interaction. Details of resilience of R/ECC structural members subjected to shear loading can be found in ▶ Chap. 6.

4.5

Compression

The compressive behavior, mainly compressive strength, of ECC is typically measured using cylinder and cube specimens (similar to concrete and FRC) following ASTM C39 [32] and C109 [33] standards, respectively. Although, a stress-rate for loading is specified in these two standards for mainly determining the peak strength of the material, these rates are often converted to equivalent strain/displacement rates (utilizing the elastic modulus of the material) to determine the complete stress-strain behavior of ECC under uniaxial compression. The compressive strengths of different versions of ECC vary widely from 10–30 MPa for low strength ECC designed for fire-proofing and nonstructural repair, to 40–70 MPa (elastic modulus of about 18–20 GPa) for typical ECC usable in most structural applications, to 150 MPa and above for ultra-high strength ECCs (elastic modulus of about 50 GPa) for specialized applications such as impact and blast resistance. The highest compressive strength reached in ECC to date is 205 MPa, with over 3% tensile strain capacity [34]. The variation in compressive strength of the specimens belonging to the same batch of ECC is low with reported coefficients

4.5 Compression

b

70 60

N5

50

N4

40

Stress (MPa)

Stress (MPa)

a

125

N3 N2

30 20

150

100

50 N1

10 0

200

0

0.3

0.6 Strain (%)

0.9

1.2

0 0

0.5

1.0 Strain (%)

1.5

2.0

Fig. 4.21 Compressive behavior of ECC. Residual compressive load capacity is retained after peak load by bridged subparallel closely spaced axial cracks. (a) Normal strength ECC (cylinder); N1, N2,.., N5 are different strength ECCs [35], (b) ultra-high strength ECC (cube) fc0  170 MPa [7]

of variation typically less than 5%, and very rarely beyond 10%, although greater variation in the tensile properties is possible as mentioned in Sect. 4.3.2. Typical stress-strain behavior of ECC under compression is shown in Fig. 4.21. For normal strength ECC, the prepeak curve is linear and elastic until about 40–50% of the peak. The curve for the ultra-high strength ECC is linear till about 80% of the peak, which is typical of VHSC/UHPCs of similar strength. After this phase of nearperfect linear elasticity, the rising stress-strain curve of ECC becomes increasingly nonlinear and inelastic accompanied by the formation of subparallel, closely spaced vertical cracks. These cracks are stabilized through fiber-bridging in ECC resulting in a more ductile response up to and near the peak, instead of a sharp peak typically observed in concrete and FRCs. At the peak, axial splitting of the matrix occurs due to the joining of multiple microcracks. However, the postpeak stress does not drop to near zero but to a residual stress value which is partly determined by the tensile stress bridged across the vertical splitting crack through fiber-bridging. For the tests shown in Fig. 4.21, the residual stress after the drop is about half the peak load in both normal and ultra-high strength ECCs. Thereafter, the increasing compressive displacement causes the vertical cracks to open wider resulting in decreasing fiberbridging capacity, and therefore, decreasing compressive stress. The cylindrical specimen continues to compress with increasing diameter without disintegrating (Fig. 4.22). Overall, ECC shows extremely ductile behavior under compression due to effective crack stabilization and fiber-bridging effects throughout the entire loading. The compressive ductility of ECC is in sharp contrast with concrete’s brittle behavior under compression. Concrete’s compressive stress-strain curve before the peak is modeled as a parabola [37] followed by a steep linear decay of compressive strength in the postpeak region. The ACI 318 building code assumes the maximum usable strain capacity of concrete as 0.3% for design purpose. Due to the absence of the stabilizing effect of the bridging fibers, concrete’s stress-strain curve does not

126

4

Mechanical Properties of Engineered Cementitious Composites (ECC)

Fig. 4.22 The compression failure mode of (a) ECC is associated with subparallel closely spaced microcracks that are bridged, providing residual load capacity beyond peak [4], and (b) high strength concrete that explodes after reaching peak load and no residual load capacity [36]

exhibit the residual branch of ECC’s stress-strain curve and can fail catastrophically beyond the compressive strain of 0.3%. As a result, over-reinforced sections are not permitted in the structural design of reinforced concrete structures, which may lead to unnecessary increase in structural member dimensions. On the other hand, ECC’s post-peak behavior under compression is reliably ductile and shows significant residual strength well beyond 0.3% strain, which can be potentially utilized for designing more balanced sections with smaller dimensions. At peak load, the compressive strains in ECC typically range from 0.25% to 0.6% (depending on compressive strength and fiber/matrix bond) with significant residual load capacity up to 1% strain. The compressive strength of ECC, similar to other cementitious materials, is an age-dependent property. As observed in Fig. 4.23 the compressive strength of ECC (mix proportions given in [4]) made with Type I cement increases rapidly till the age of 14 days. The rate of increase of strength decreases thereafter and a relative plateau is achieved beyond 90 days. Such behavior is not unique but typical of cementitious materials containing significant amount of pozzolanic material ([38], p. 106). The rapid rise of compressive strength till 14 days is attributable to the primary hydration of the Type I cement, whereas a combination of primary and secondary hydration of

4.6 Fatigue

127

Fig. 4.23 Age dependence of ECC’s compressive strength [4]. The compressive strength and rate of strength gain are dependent on the composition of the ECC matrix. The data shown are for a normal strength ECC. Very high strength ECC with 28-day compressive strength of 205 MPa [34] and high early strength ECC with 4-day compressive strength of 23 MPa [40] have been developed

fly ash in ECC explains the subsequent increase in compressive strength. Thus, the age dependence of compressive strength of ECC is directly related to the rate of hydration of ECC’s cementitious ingredients. It is possible to increase the rate of strength gain in ECC by utilizing fast-setting Type III cement to replace Type I cement in ECC. Wang and Li [39] and Li and Li [40] reported the development of high early strength-ECC (HES-ECC). HES-ECC can achieve a compressive strength of about 23 MPa within 4 hours after casting (55 MPa at 28 days), along with tensile strain capacity greater than 2.5% [40] and flexural strength of 10 MPa. These fast hardening properties make HES-ECC ideal for use in concrete repair applications.

4.6

Fatigue

Similar to other materials, the fatigue performance of ECC is characterized by an S-N curve, which relates the amplitude of the cyclic stress (S) to the logarithm of the number of cycles to failure (N). The experimental fatigue data (Fig. 4.24) have been derived from beams of size 400  400  1600 made of PVA-ECC, PE-ECC, and FRC [41]. Cyclic loading (at 8 Hz under FPB) with multiple levels of stress amplitudes ranging from 50% to 90% of the average monotonic MOR of the respective material was applied. Some of the beam specimens (shown with horizontal arrows in Fig. 4.24) undergoing the lowest stress levels did not fail at two million cycles, at which point the cyclic loading was discontinued in this study. The deflection hardening behavior of the ECC beams under pseudo-static, monotonic flexure loading was similar to that shown in Fig. 4.15 with a distributed cracking pattern (Fig. 4.16), whereas the FRC beam showed deflection-softening with all the damage concentrated in only one crack. The insights into the fatigue behavior of ECC and the damage evolution at various stress levels are discussed below. ECC exhibits a bilinear S-N relation (Fig. 4.24) which resembles that of the metallic materials [42], whereas FRC exhibits a linear S-N relation, which is similar

128

4

Mechanical Properties of Engineered Cementitious Composites (ECC)

Fatigue Stress Level, S

1.2 1.0 0.8 0.6 FRC

0.4

PVA-ECC

0.2

PE-ECC 0.0

0

1

2 3 4 5 Cycles to Failure, Nu (log)

6

7

Fig. 4.24 Fatigue performance of ECC beams [41]. (Note: Fatigue stress level, S, is the cyclic stress amplitude normalized by the average MOR of the beams of the respective materials under monotonic loading.) Both ECCs show a bi-linear S-N curve, whereas the FRC shows a linear S-N curve. At high stress amplitude, ECC outperforms FRC. However, under low stress amplitude, FRC outperforms ECC

to that of other brittle and quasi-brittle cementitious materials, such as concrete and polymer cement mortars. ECC exhibits longer fatigue life at high stress levels (>70% of the monotonic MOR); however, the fatigue life of ECC becomes equal to or even shorter than FRC at low stress levels. This implies that the fatigue life advantage of using ECC over FRC and concrete in a structure would diminish if the cross-section of the structure is scaled according to the monotonic strength (which keeps the stress levels low). The evolution of damage, measured by the total crack mouth opening displacement (CMOD), with normalized number of cycles (normalized by the fatigue life, Nu) observed in both PVA-ECC and FRC beams is compared in Fig. 4.25. While the total CMOD of the ECC beam is the sum of multiple crack openings within a gauge length of 100 mm at the mid-span of ECC beam, the total CMOD of the FRC beam mainly represents opening of a single crack (as no multiple cracking is observed in the FRC beam) plus negligible elastic strains. In general, ECC beams sustained greater damage (with higher total CMOD) than the FRC beams at all stress levels. Comparing the ECC beams with each other, the damage appears to be proportional to the fatigue stress, that is, the total CMOD increases with S (Fig. 4.25a). Greater CMOD at higher S is a direct result of increased number of cracks in ECC beams at higher stress levels, as observed in Fig. 4.26. In contrast, the damage is independent of the fatigue stress in FRC beams. This contrast in the damage evolution of ECC and FRC beams reflects the cracking (damage tolerance) sensitivity of each material to the applied stress. At higher S, the multiple cracking in the ECC specimen provides a shielding effect on the eventual fatigue failure crack. In contrast, at lower S, both ECC and FRC develop only a single crack, and the fatigue resistance of the beams depends solely on the fatigue resistance of the fiber bridges acting on the single crack. The number of cracks in ECC beams is indeed related to the fatigue stress amplitude. Initiation of a crack requires the stress intensity factor to equal the matrix

4.6 Fatigue

b

2.0

PVA-ECC

III

1.5

Total CMOD at σmax (mm)

Total CMOD at σmax (mm)

a

129

II S=0.90

1.0

S=0.85

I

S=0.75

0.5 0.0 0.0

S=0.60 S=0.50

0.2

0.4

0.6 N/Nu

0.8

1.0

FRC 0.8 0.6

S= 0.70

0.4 S= 0.60

0.2

S= 0.90 S= 0.80

0.0 1.0

0.0

0.2

0.4

0.6

0.8

1.0

N/Nu

Fig. 4.25 Damage evolution at different fatigue stress levels [41]. The total CMOD for PVA-ECC refers to the total crack mouth opening displacement of all microcracks. For PVA-ECC (a), most cracks are formed in Phase I, with increasing crack opening in Phase II. Damage localization occurs in Phase III, leading to failure at one of the multiple cracks. For FRC (b), only one crack exists and Phase I is absent

Fig. 4.26 Multiple cracking in PVA-ECC beams at different fatigue stress levels [41]. At higher stress range (a), the multiple cracks shield the eventual fatigue failure crack. At lower stress range (b), only a single crack emerges similar to that of an FRC

fracture toughness. Greater applied stress is therefore needed to achieve the critical stress intensity factor for smaller flaws, which happens only when the amplitude of the fatigue stress is increased. At smaller fatigue stress, the material surrounding the flaw behaves elastically almost indefinitely, and only the existing cracks further extend and open with increasing number of cycles. Thus, ECC loses its multiple cracking ability at smaller fatigue stress and, in the limit, approaches the FRC behavior if the fatigue stress amplitude is so low that it only triggers a single crack. In this regard too, ECC behavior is analogous to ductile metals which can also fail catastrophically under low fatigue stress (below yield limit) in the presence of a crack. Three distinct phases of damage evolution in ECC beams can be identified in Fig. 4.25a. Almost all of the cracks in the PVA-ECC beam are formed in the first

130

4

Mechanical Properties of Engineered Cementitious Composites (ECC)

phase, particularly in the first loading cycle [41]. Both the length and the width of the cracks formed in the first phase steadily increase during the second phase. As no new cracks are formed in this phase, the rate of increase in CMOD with the number of cycles is almost constant. In the third phase, the damage localizes quickly at the weakest bridged crack resulting in the sudden increase in slope of the CMOD-N/Nu curve. The FRC beam also undergoes these three phases; however, the first phase is extremely shortened due to the formation of only one crack in the FRC beam. The influence of fiber type (PE versus PVA) on the behavior of ECC under fatigue was also investigated [41]. As the crack opening increases with greater number of fatigue cycles, the bridging fibers lose their bridging ability by either rupturing or pulling out. While the PE fiber has higher strength but lower bond with the cementitious matrix, the PVA fiber has lower strength but greater bond with the cementitious matrix. Therefore, as the crack opening increases with increasing number of fatigue cycles, the fiber-bridging degradation is dominated by fiber rupture in PVA-ECC and by fiber/matrix bond degradation in PE-ECC. An analytical method to predict the fatigue life of ECC beams under flexure, by modeling the fiber-bridging degradation, is proposed by Suthiwarapirak and Matsumoto [43]. This study utilizes a simplified phenomenological approach, which captures the influence of fiber-bridging degradation under fatigue on the tensile stress-strain and stress-crack opening relation of ECC. The fiber-bridging degradation law in this study utilizes empirical coefficients obtained by curve-fitting the experimental results discussed above; however, the degradation law once determined in this way can be potentially used as a material property to predict the flexural fatigue behavior of ECC beams of any dimensions. The micromechanics of ECC fatigue behavior has been studied by Kakuma et al. [44], based on a fiber-bridging model originally derived for FRC under fatigue [45]. This model explicitly considers the influence of fatigue damage on the single fiber pullout behavior and utilizes scale-linking (similar to that used for monotonic analysis) to predict the fiber-bridging law and its degradation with increasing number of fatigue cycles. The model satisfactorily predicted uniaxial tensile stressstrain response of ECC as a function of the number of fatigue cycles.

4.7

Creep

All cementitious materials are known to creep, i.e., exhibit increase in strain, when subjected to a sustained stress on the order of days and months. The most widely accepted mechanism is the slow movement of physically adsorbed water and the breaking and reformation of bonds in the gel structure of calcium silicate hydrates at the nano-scale (see, for example, Mehta and Monteiro [46]). Furthermore, microcracking occurs as a result of local increase in stress, causing nonlinearity of the creep behavior. Thus, creep deformation of cementitious materials under sustained load is caused by the movement of water and associated changes in the microstructure of the cementitious matrix.

4.7 Creep

131

The experimental investigations of the time-dependent behavior of ECC under sustained compressive loads are reported by Rouse and Billington [47]. In this study, the influence of fine aggregates (sand) and fibers on the compressive creep behavior of ECC specimens, both sealed (basic creep) and unsealed (drying creep + basic creep), was experimentally determined. In cementitious materials in general (not just ECC), the cement paste is the primary source of the time-dependent phenomena such as creep. Furthermore, the fine aggregates have greater stiffness than the cement paste and provide greater dimensional stability. Due to these two reasons, ECC specimens with sand in their matrix showed significantly lesser creep than the specimens without sand. From the results reported in Rouse and Billington [47], the inclusion of fibers seems to significantly increase the compressive creep in ECC, i.e., the matrix specimens with the same overall composition as ECC but without fibers showed significantly lower creep strain than the ECC specimens (with fibers). A possible (not investigated further) physical explanation hypothesized in this study is that ECC specimens may have greater internal permeability/porosity (due to mixing of fibers) than their matrix counterparts allowing easier movement of moisture within the cement paste, which may lead to increased creep. The time-dependent behavior of ECC under sustained tensile loads is reported by Boshoff and van Zijl [48], with further details and constitutive models for creep reported in Boshoff [49]. At the macroscale, cracked dogbone specimens of ECC preloaded to 1% strain were subjected to 8 months of sustained loading at multiple tensile stress levels. The time-dependent total strain (shrinkage + creep) is plotted in Fig. 4.27a for the cracked dogbone specimens. The negative contribution from shrinkage is significant only for the specimens subjected to low sustained stress (30% and 50% of the average ultimate tensile strength – which was 2.8 MPa for this ECC). All the curves in Fig. 4.27a begin at 0,0; however, the initial rise in strain is too quick (within 5 hours) to be observed in these plots. The major contribution to creep in the cracked ECC specimens comes from the creep of bridging fibers at multiple cracks, which leads to significant increase in crack width over time

b Creep Strain [% / MPa]

Time-dependent Strain [%]

a 80%

2.5 1.5

70%

0.5

50% 30%

-0.5 0

50

100

150

Time (Days)

200

300

0.10 0.08 0.06 0.04

0.02 0 0

50

100

150

200

Time (Days)

Fig. 4.27 Evolution of time-dependent tensile strain in ECC specimens [48]. (a) Cracked dogbones (preloaded to 1% strain) under sustained load of 30%, 50%, 70%, and 80% of tensile strength. (b) Uncracked dogbones under sustained load of 50% of tensile strength

132

4

Mechanical Properties of Engineered Cementitious Composites (ECC)

Fig. 4.28 Photographs showing increase in crack width over time in tensile creep tests [49]. The specimen was preloaded to 1% to create multiple microcracks and subsequently placed under sustained load at 80% of ultimate strength. The source of creep was traced to movement at the fiber/matrix interface which allows the multiple microcracks to open

(Fig. 4.28). Along with creep contribution from fiber-bridging, the formation of a limited number of new cracks during the sustained load phase was also reported to contribute to the creep of the cracked ECC specimens. Similar to the cracked specimens, the uncracked dogbone specimens were also subjected to sustained tensile load. However, the investigation was performed for only one sustained load level of 50% of the average ultimate tensile strength (below the matrix cracking strength), and the creep strain evolution of multiple specimens to form a band of values is presented in Fig. 4.27b. As the matrix contribution is most dominant in the uncracked specimens, unrestrained shrinkage was recorded and subtracted from the total strain to obtain the creep strain only. From these results, the creep strain of the matrix appears to be insignificant compared to that of fiberbridging in ECC. In order to understand the influence of creep on fiber-bridging at the microscale, Boshoff and van Zijl [48] also conducted single fiber pullout tests under sustained loads. It was observed that the main source of creep in fiber-bridging is the creep of the fiber/matrix interfacial bond, as no significant creep was observed in the fibers. As a sustained pullout load of about 50% of the peak pullout load (for a given embedment length) was applied, all fibers were observed to completely pull out within only 80 h of load application. The creep rate was found to be higher for fibers that were predebonded (prior to the sustained loading) than for fully bonded fibers. Thus, enhancing the fiber/matrix bond can be an effective method to control creep in microcracked ECC.

4.8

Summary and Conclusions

ECC represents a family of materials (▶ Chap. 1) with properties tuned to their intended applications. Various ECCs are tuned to be processed in different manners, including self-consolidating and spraying application (▶ Chap. 3). Other ECCs are

4.8 Summary and Conclusions

133

Table 4.1 Four broad classes of ECC and their corresponding properties ranges Density ρ (kg/m3) Young’s modulus E (GPa) First crack strength σfc (MPa) Ultimate tensile strength σult (MPa) Tensile strain capacity (%) Compressive strength fc0 (MPa) Compressive strain capacity εult (%) Flexural strength MOR (MPa) Intended applications References

FR-ECC 550 4–6

LW-ECC 930–1800 8–12

Normal-ECC 1800–2100 15–23

HS-ECC 2300–2400 41–48

0.8–1

2–4

3–5

8–10

1–1.5

2–5

4–8

14–17

1–3

2–4

2–8

3–8

2.5–3.5

20–40

30–80

120–205

–

–

0.4–0.5

0.3–0.4

–

–

10–16

28–32

Fire-proofing of steel structures [50, 51]

Lightweight applications [5, 52]

Structural use

Impact and blast resistant structures [7, 34, 55]

[5, 53, 54]

tuned for specific functions, such as self-healing, self-sensing, self-thermal-adaptive, or self-cleaning and air-purifying (▶ Chap. 10). Specific versions of ECC are designed for fire-resistive purpose or for impact and blast resistive applications. In most cases, the mechanical properties are designed to match the expected type and magnitude of loading of the specific application. For this reason, while ECC has a common characteristic of being ductile in tension, their density ρ, Young’s modulus E, and compressive strength fc’ can have a wide range, as indicated for four broad classes of ECCs: fire-resistive (FR-ECC), light-weight (LW-ECC), normal-ECC, and high-strength (HS-ECC) (Table 4.1). As might be expected, lower density is associated with lower Young modulus and compressive strength. Fire-resistive ECC intended to protect steel structure as a sprayable coating has a low density of 550 kg/ m3 and a low compressive strength of about 3 MPa, while high strength ECC intended for impact and blast resistant structures that may experience both high compressive stress and tensile stress has a density of about 2350 kg/m3 and a high compressive strength of about 200 MPa. Except for the low end of FR-ECC, all four classes of ECC have tensile strain capacities in excess of 2%. Figure 4.29 summarizes the range of compressive strength versus tensile strain capacity of these four broad classes of ECC. An Ultra High Strength Concrete (UHPC) material is included in this plot for comparison. The emphasis on tensile ductility when designing ECCs is due to the recognition that the bottleneck of mechanical properties of concrete in general is the rapid exhaustion of tensile capacity. The high tensile ductility of ECC further translates into advantages under shear loading or flexural loading. In general, the shear strength and ductility of ECC is on the same order of magnitude of the tensile strength and

134

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250

Compressive Strength (MPa)

Ductal/UHPC 200

HS-ECC

150

100

Normal-ECC

50

FR-ECC

LW-ECC

0 0

1

2

3

4

5

6

7

8

Tensile Ductility (%)

Fig. 4.29 The tensile strain capacity of ECC generally exceed 2%, while the compressive strength ranges from 3 MPa to over 200 MPa. Their properties are intentionally tuned to match demands of specific applications. Although a dense matrix can lead to challenges in tensile ductility, high strength ECC with high tensile ductility has been successfully designed

ductility. This is due to the fact that shear loading can be represented by a combination of diagonal tension and compression loading. Further, the flexural strength (MOR) is appropriately 3–4 times that of the first crack strength, whereas the MOR of normal concrete is about equal to the first crack strength. The MOR of high strength ECC is competitive with flexural strength of wood. Thus, the elevation of tensile properties of ECC directly translates into elevation of shear and flexural properties. The translation of the advantages of ECC properties into resilience and durability of reinforced ECC (R/ECC) structures is discussed in ▶ Chaps. 6 and ▶ 7, respectively. When ECC is used together with steel reinforcement, it creates synergies that exploit the tensile strain capacity of ECC. Specifically, both steel and ECC strain harden beyond their elastic limits. The compatible deformation between ECC and steel extends from the elastic stage into their strain-hardening stage, leading to significant enhancement of structural response not feasible with other normal strength or high strength cementitious materials. The higher creep of ECC compared with concrete under sustained load should be properly designed for in structures. This is especially the case if the sustained load is in tension and the ECC has been damaged to create microcracks. While self-healing of the microcracks (▶ Chap. 10) may alleviate some of the concerns of tensile creep, precaution must be taken in the structural design stage for long term structural response. Similarly, low amplitude fatigue loading of ECC structures may lead to single crack failure that limits the unique advantages of ECC. More research is

References

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needed to understand and control the behavior of structures under these types (sustained tension and low amplitude fatigue) of loading.

References 1. Japan Society of Civil Engineers: Recommendations for design and construction of high performance Fiber reinforced cement composites with multiple fine cracks (HPFRCC). Concrete Engineering Series, vol. Concrete L. (2008) 2. Zhou, J., Qian, S., Sierra Beltran, M.G., Ye, G., Breugel, K., Li, V.C., van Breugel, K., Li, V.C.: Development of engineered cementitious composites with limestone powder and blast furnace slag. Mater. Struct. 43(6), 803–814 (2010) 3. Kanda, T., Li, V.C.: Interface property and apparent strength of high-strength hydrophilic fiber in cement matrix. J. Mater. Civ. Eng. 10(1), 5–13 (1998) 4. Wang, S.X., Li, V.C.: Polyvinyl alcohol fiber reinforced engineered cementitious composites: materials design and performances. In: Int’l Workshop on HPFRCC Structural Applications, pp. 65–73 (2005) 5. Wang, S.: Micromechanics Based Matrix Design for Engineered Cementitious Composites. University of Michigan, Ann Arbor (2005) 6. ASTM C496: Standard test method for splitting tensile strength of cylindrical concrete specimens, C496/C496M-11. ASTM (2011) 7. Ranade, R., Li, V.C., Stults, M.D., Heard, W.F., Rushing, T.S.: Composite properties of highstrength, high-ductility concrete. ACI Mater. J. 110(4), 413–422 (2013) 8. Stang, H., Li, V.C.: Classification of fiber reinforced cementitious materials for structural applications. In: 6th RILEM Symposium on Fiber-Reinforced Concretes (FRC) – BEFIB 2004, pp. 197–218 (2004) 9. Ohno, M., Li, V.C.: A feasibility study of strain hardening fiber reinforced fly ash-based geopolymer composites. Constr. Build. Mater. 57, 163–168 (2014) 10. M, S., Orteu, J., Schreier, H.: Image Correlation for Shape, Motion and Deformation Measurements: Basic Concepts, Theory and Applications. Springer, New York (2009) 11. Ranade, R., Zhang, J., Lynch, J.P., Li, V.C.: Influence of micro-cracking on the composite resistivity of Engineered Cementitious Composites. Cem. Concr. Res. 58, 1–12 (2014) 12. Kim, D.-J., Naaman, A.E., El-Tawil, S.: High performance Fiber reinforced cement composites with innovative slip hardending twisted steel fibers. Int. J. Concr. Struct. Mater. 3(2), 119–126 (2009) 13. Yang, E.-H., Li, V.C.: Tailoring engineered cementitious composites for impact resistance. Cem. Concr. Res. 42(8), 1066–1071 (2012) 14. Yang, E.-H., Li, V.C., Dancygierb, A.N., Yankelevskyb, D., Katzb, A., Bentur, A.: Impact resistance of engineered cementitious composites. In: International Symposium on Interaction of the Effects of Munitions with Structures (ISIEMS) (2007) 15. Secrieru, E., Mechtcherine, V., Schröfl, C., Borin, D.: Rheological characterisation and prediction of pumpability of strain-hardening cement-based-composites (SHCC) with and without addition of superabsorbent polymers (SAP) at various temperatures. Constr. Build. Mater. 112, 581–594 (2016) 16. Yu, K., Li, L., Yu, J., Wang, Y., Ye, J., Xu, Q.F.: Direct tensile properties of engineered cementitious composites: a review. Constr. Build. Mater. 165, 346–362 (2018) 17. American Society for Testing and Materials: C 1609/C 1609M-05 Standard Test Method for Flexural Performance of Fiber-Reinforced Concrete (Using Beam With Third-Point Loading) 1. ASTM. American Society for Testing and Materials, West Conshohocken (2010) 18. Lepech, M., Li, V.C.C.: Preliminary findings on size effect In ECC structural members in flexure. Brittle. Matrix. Compos. 7, 57–66 (2003)

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19. Kanakubo, T., Shimizu, K., Kanda, T.: Size effect on flexural and shear behavior of PVA-ECC. In: Protect Workshop, p. Paper No. 54 (2007) 20. Maalej, M., Li, V.C.: Flexural/tensile strength ratio in engineered cementitious composites. J. Mater. Civ. Eng. 6(4), 513–528 (1994) 21. Li, V.C., Kanda, T.: Multiple cracking sequence and saturation in fiber reinforced cementitious composites. J. Mater. Civ. Eng. 2, 65–69 (1998) 22. Qian, S., Li, V.C.: Simplified inverse method for determining the tensile strain capacity of strain hardening cementitious composites. J. Adv. Concr. Technol. 5(2), 235–246 (2007) 23. Qian, S., Li, V.C.: Simplified inverse method for determining the tensile properties of strain hardening cementitious composites (SHCC). J. Adv. Concr. Technol. 6(2), 353–363 (2008) 24. Kanakubo, T., Shimizu, K., Katagiri, M., Kanda, T., Fukuyama, H., Rokugo, K.: Tensile characteristics evaluation of DFRCC – round robin test results by JCI-TC. In International RILEM Workshop on High Performance Fiber Reinforced Cementitious Composites in Structural Applications, pp. 27–36 (2005) 25. Ostergaard, L., Walter, R., Olesen, J.F.: Method for determination of tensile properties of engineered cementitious composites (ECC). In Construction Materials: Proceedings of ConMat’05 and Mindess Symposium, p. 74 (2005) 26. Li, V.C., Mishra, D.K., Naaman, A.E., Wight, J.K., Lafave, J.M., Wu, H.-C., Inada, Y.: On the shear behavior of engineered cementitious composites. Adv. Cem. Based Mater. 1, 142–149 (1994) 27. Arakawa, T., Ono, K.: Shear tests of reinforced concrete beams by a special type of loading (structure). Trans. Archit. Inst. Japan. 57, 581–584 (1957) 28. Shimizu, K., Kanakubo, T., Kanda, T., and Nagai, S.: Shear Behavior of PVA-ECC Beams, in Proc., Int’l RILEM Workshop HPFRCC in Structural Applications. In: Fischer, G., and Li, V.C. (eds.) published by RILEM SARL, pp. 443–451 (2006) 29. Kanda, T., Watanabe, S., Li, V.C.: Application of Pseudo strain hardening cementitious composites to shear resistant structural elements. In FRAMCOS-3, pp. 1477–1490 (1998) 30. Qian, S., Li, V.C.: Influence of concrete material ductility on shear response of stud connections. ACI Mater. J. 103(1), 60–66 (2006) 31. Qian, S., Li, V.C.: Headed anchor/engineered cementitious composites (ECC) pullout behavior. J. Adv. Concr. Technol. 9(3), 339–351 (2011) 32. ASTM. C39: “Standard Test Method for Compressive Strength of Cylindrical Concrete Specimens. American Society for Testing and Materials, West Conshohocken, PA (2015) 33. ASTM C109: Standard Test Method for Compressive Strength of Hydraulic Cement Mortars (Using 2-in. or [50-mm] Cube Specimens) 1. American Society for Testing and Materials, West Conshohocken, PA (2011) 34. Ranade, R.: Advanced Cementiitious Composite Development for Resilient and Sustainable Infrastructure. University of Michigan, Ann Arbor (2014) 35. Zhou, J., Pan, J., Leung, C.K.Y.: Mechanical behavior of fiber-reinforced engineered cementitious composites in uniaxial compression. J. Mater. Civ. Eng. 27(1), 04014111 (2015) 36. Imperial College, London, UK. https://expeditionworkshed.org/workshed/compression-failurehigh-strength-concrete-cylinder/. Assessed 20 Aug 2018 37. Hognestad, E., Hanson, N.W., McHenry, D.: Concrete stress distribution in ultimate strength design. ACI J. 27(52–28), 455–479 (1955) 38. Mindess, S., Young, J.F., Darwin, D.: Concrete. Pearson, Upper Saddle River (2002) 39. Wang, S., Li, V.C.: High-early-strength engineered cementitious composites. ACI Mater. J. 103 (2), 97–105 (2006) 40. Li, M., Li, V.C.: High-early-strength engineered cementitious composites for fast, durable concrete repair-material properties. ACI Mater. J. 108(1), 3–12 (2011) 41. Suthiwarapirak, P., Matsumoto, T., Kanda, T.: Multiple cracking and fiber bridging characteristics of engineered cementitious composites under fatigue flexure. J. Mater. Civ. Eng. 16(5), 433–443 (2004)

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42. Bannantine, J.A., Comer, J.J., Handrock, J.L.: Fundamentals of Metal Fatigue Analysis. Prentice-Hall, Englewood Cliffs (1989) 43. Suthiwarapirak, P., Matsumoto, T.: Fiber bridging degradation based fatigue analysis of ECC under flexure. JSCE J. Appl. Mech. 6, 1179–1188 (2003) 44. Kakuma, K., Matsumoto, T., Hayashikawa, T., He, X.: An analytical study on the stress-strain relation of PVA-ECC under tensile fatigue. In: Proceedings of FraMCoS-7, pp. 1683–1690 (2010) 45. Matsumoto, T.: Journal of applied mechanics crack bridging law in discontinuous fiber reinforced composites under cyclic loading. JSCE J. Appl. Mech. 10, 923–933 2007 46. Mehta, P.K., Monteiro, P.J.M.: Concrete: Microstructure, Properties, and Materials, 4th edn. McGraw Hill, New York (2014) 47. Rouse, J.M., Billington, S.L.: Creep and shrinkage of high-performance fiber-reinforced cementitious composites. ACI Mater. J. 104(2), 129–136 (2007) 48. Boshoff, W.P., van Zijl, G.P.A.G.: Tensile Creep of SHCC, pp. 87–95 (2007) 49. Boshoff, W.P.: Time-Dependent Behavior of ECC. Stellenbosch University, South Africa (2007) 50. Zhang, Q., Li, V.C.: Development of durable spray-applied fire-resistive Engineered Cementitious Composites (SFR-ECC). Cem. Concr. Compos. 60, 10–16 (2015) 51. Zhang, Q., Li, V.C.: Ductile fire-resistive material for enhanced fire safety under multi-hazards – a feasibility study. In: Structures Congress 2014, pp. 1148–1158 (2014) 52. Wang, S., Li, V.: Lightweight engineered cementitious composites (ECC). In: High Performance Fiber Reinforced Cement Composites (HPFRCC4), pp. 379–389 (2003) 53. Li, V.C.: Engineered cementitious composites (ECC) – material, structural, and durability performance. In: Nawy, E. (ed.) Concrete Construction Engineering Handbook, p. 78. CRC Press, Boca Raton (2008) 54. Wang, S., Li, V.: Polyvinyl alcohol fiber reinforced engineered cementitious composites: material design and performances. In Proceedings, Int’l Workshop on HPFRCC Structural Applications, Hawaii, pp. 65–73 (2005) 55. Yu, K.-Q., Yu, J.-T., Dai, J.-G., Lu, Z.-D., Shah, S.P.: Development of ultra-high performance engineered cementitious composites using polyethylene (PE) fibers. Constr. Build. Mater. 158, 217–227 (2018)

5

Constitutive Modeling of Engineered Cementitious Composites (ECC)

Contents 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Phenomenological Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Multiscale Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

140 142 163 173 174

Abstract

As research in ECC advances from material development to structural applications, the need for accurate constitutive models that capture ECC’s response under load becomes increasingly apparent. When combined with finite element method, constitutive models of ECC can be utilized to simulate structural response. Such simulations are useful to develop a better understanding of how the unique properties of ECC, such as tensile ductility and crack width control, can be translated into advantageous structural performances. Ultimately, high fidelity numerical simulation of ECC structural behavior can lead to a reduction in the amount of experimentation needed to gain confidence in full-scale structural deployment of ECC. Further, constitutive models can be helpful in the deployment of integrated structural and materials design approach, where targeted structural performance can be downlinked to composite properties and material composition and microstructures. Such scale-linkage provides an efficient basis for ECC material design for optimal structural performance. While major advances have been made over the last decade on constitutive modeling of ECC, the goals identified above have yet to be realized. However, as this chapter demonstrates, a variety of constitutive models have successfully

© Springer-Verlag GmbH Germany, part of Springer Nature 2019 V. C. Li, Engineered Cementitious Composites (ECC), https://doi.org/10.1007/978-3-662-58438-5_5

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5 Constitutive Modeling of Engineered Cementitious Composites (ECC)

captured essential experimental trends. Specifically, this chapter presents two classes of constitutive models: phenomenological models and multiscale physics-based models. The phenomenological models account for 1D, 2D, and 3D stress states as well as monotonic, cyclic, and dynamic loading. These models have been verified with experimental data with various levels of successes. The multiscale model links microscale phenomena and material features to mesoscale and macroscale material and structural responses. The advantages of explicitly modeling the opening and sliding of multiple cracks of ECC are demonstrated. The models described lay the ground work for further much needed development in this field.

5.1

Introduction

Constitutive models of materials are needed to predict structural response. This is useful for optimizing structural design through deliberate choice of geometry, dimensions, and material details, including concrete property details and reinforcement details, while meeting design code requirements. Optimization can aim at minimizing weight, cost, and environmental impact, while maintaining safety for expected service loads. Constitutive models are also of great value in validating structural designs, without excessive experimentation, which can be expensive or impossible especially at full structural scale. These design considerations with appropriate constitutive models are even more critical when adopting a relatively new material like ECC in structural applications. For ECC, optimization for the performance of a structure can extend downscale to the ingredients that make up the composite material. This opportunity is offered by the fact that ECC has a design basis that relates composite properties to its composition and ingredient characteristics, as described in ▶ Chap. 2. In this context, Li [1] suggested the Integrated Structures and Materials Design (ISMD) approach, which in principle allows the specification of structural performance to link to ECC composite properties and ECC ingredient selection and tailoring (Fig. 5.1). A critical element for the ISMD approach to be effective is a constitutive model that, when combined with finite element method, connects composite material properties to structural performance. Apart from structural safety and resilience (▶ Chap. 6), the performance of structures in terms of durability (▶ Chap. 7) has gained significant attention. For ECC that may be used in the strain-hardening range due to its high tensile ductility, it is desirable to relate structural durability to microcrack development under loads, since the latter governs the transport of water and migration of aggressive agents that potentially leads to structural degradation. This consideration suggests preference to multiscale constitutive models capable of capturing microcrack pattern evolution under complex stress states. Apart from predicting structural response, constitutive models are also useful for gaining insights into the behavior of materials and structural elements that are not

5.1 Introduction

141 Structural Performance

Materials Properties

Structural Engineering Structural System and Shape

Materials Engineering Materials Microstructure

Processing

Fig. 5.1 ISMD linking structural performance to composite properties and material microstructure. Constitutive models support the quantitative linkage

easily visible during experimentation, especially those that occur in the specimen interior. Further, the evolution from initial damage to final failure captured numerically, which may not be easily observed experimentally, can aid in structural design enhancements. The constitutive modeling of ECC has a number of differences from that of normal concrete. In most circumstances, and because of the high tensile ductility of ECC material, it may be adequate to focus on the behavior of structures and material undergoing elastic and inelastic straining prior to fracture localization, without having to be concerned about the postpeak tension-softening behavior or fracture failure. In this sense, the material can be treated as a continuum, with no strain singularity to account for in the model. Microcracking during the inelastic straining of ECC can be treated as smeared strain, analogous to plastic yielding in metals. However, continuum models also have their limitation in not being able to capture the sequential formation of cracks in a representative volume element over which the crack strain is evaluated. An implication of this characteristic is that the direction of cracks may not be properly predicted when the ECC structural member undergoes nonproportional loading such as due to cracking-induced anisotropy, and may lead to over-estimation of structural load capacity [2, 3]. Modeling ECC can be quite complex. The complexity derives from the inelastic response associated with the development of multiple microcracks. The opening and sliding of multiple cracks under a rotating stress field induced by multiaxial loading further add to this complexity. The interactions between opening of multiple cracks under tension and closing under compression when a structure is subjected to fully reversed cyclic loading make simulation of ECC structural response challenging.

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5 Constitutive Modeling of Engineered Cementitious Composites (ECC)

Accounting rate sensitivity of ECC makes prediction of ECC structural behavior under dynamic loading nontrivial. In this chapter, two broad classes of constitutive models of ECC are discussed. Phenomenological models from simple one-dimensional stress state to more complex multiaxial stress states under monotonic, cyclic, and dynamic loads are presented in Sect. 5.2. Multiscale models linking material microstructural features to mesoscale single and multiple cracking of ECC are covered in Sect. 5.3. Examples of the use of these constitutive models together with finite element method in simulating structural response are included. A comprehensive summary of constitutive models for ECC can be found in [4].

5.2

Phenomenological Model

5.2.1

Modeling ECC Beam Behavior

Beams and slabs under bending load can be modeled assuming plane sections remain plane during deformation. In such a scenario, only the uniaxial tensile and compressive constitutive laws of ECC are needed for modeling beam response. Maalej and Li [5] studied the flexural/tensile strength ratio of ECC beams with no steel reinforcement. Szerszen et al. [6] developed close-form solutions for the flexural strength and ductility of steel-reinforced ECC beams.

5.2.1.1 Flexural/Tensile Strength Ratio of ECC Beams For a bilinear representation of the tensile and compressive uniaxial stress-strain relation of ECC (Figs. 5.2 and 5.3), 8 >
ðe  etc Þ : σ tc þ etu  etc

e < etc e  etc

(5:1)

in tension, and 8 > >
> σ 1 þ : cp 2 ecp

e < ecp =3 e  ecp =3

(5:2)

in compression. Assuming a linear strain-distribution profile in the cross-section of the beam (Fig. 5.4), the flexural moment and tensile strain at the base of the beam can be analytically expressed as a function of beam curvature by enforcing equilibrium in force and moment [5]. Failure of the beam occurs when this tensile strain reaches the

5.2 Phenomenological Model

143

Typical curve obtained from experiment

Stress

Assumed

Strain Fig. 5.2 Bi-linear representation of tensile stress-strain relation of ECC

Typical curve obtained from experiment

Stress

Assumed

2

/3

/3 Strain Fig. 5.3 Bi-linear representation of compressive stress-strain relation of ECC

ultimate strain capacity eut. The predicted flexural stress versus deflection curve based on parametric values from experimental data of uniaxial tension and compression testing of ECC reinforced with polyethylene fibers (PE-ECC) is shown in Fig. 5.5. It is seen that there is a reasonable match between the model prediction and the flexural beam behavior obtained experimentally. This model predicts that deflection hardening of ECC beams and slabs under flexural loading is guaranteed by

144

5 Constitutive Modeling of Engineered Cementitious Composites (ECC)

Beam Section M

M

d ( )

e c a

Inelastic microcracking zone

Strain distribution

Stress distribution

Fig. 5.4 Stress and strain distribution in beam cross-section, with neutral axis located at distance c from base of beam. Material microcracking extends to a distance a from base of beam 15

Flexural Stress (MPa)

Fig. 5.5 Model predicted and experimentally determined flexural behavior of an ECC beam, showing consistent deflection-hardening response

10

5 Experiment Model 0

0

2

4

6

8

10

12

Deflection (mm)

ECC’s tensile strain-hardening behavior in direct tension, as is consistent with a wide variety of experimental observations. The model offers insights into the ratio of the flexural strength (or modulus of rupture MOR) to first crack strength σ tc (Fig. 5.6) for ECC material, for a given tensile strength/first crack strength ratio. For the PE-ECC modeled with σ tu/ σ tc = 1.84, the predicted MOR/σ tc > 4. Similarly, for a PVA-ECC modeled with σ tu/σ tc = 1.5, the predicted MOR/σ tc = 3.5. In contrast, this ratio is equal to 3.0 for a perfectly elastic-plastic material for both tension and compression as in the case of metals; for tension-softening FRC, this ratio is between 1 and 3, depending on the rate of softening. The tensile strain-hardening is responsible for magnifying the MOR/σ tc of ECC seen in Fig. 5.6. The exact value of the MOR/σ tc ratio is also dependent on the compressive behavior of the specific ECC.

5.2 Phenomenological Model

9 8 7 MOR/

Fig. 5.6 Model predicted flexural strength/tensile strength ratio (MOR/σ tc). Experimental data for PE-ECC and PVA-ECC shown are consistent with model prediction

145

6 5 PE-ECC

4

PVA-ECC

3 2

1

2

3

4

5.2.1.2 Flexural Behavior of Steel Reinforced ECC Beams The flexural behavior of ECC beams with conventional steel reinforcement was modeled by Szerszen et al. [6]. In that model, the ECC material response is further (and conservatively) simplified as elastic-perfectly plastic in both tension and compression, as is the case for the reinforcing steel. Again, assuming plane sections remain plane, and enforcing force and moment equilibrium, analytical closed-form solutions were derived for the moment-curvature relationship of the R/ECC beam. Perfect bonding between steel reinforcement and ECC was assumed, justified by observations (Sect. ▶ 6.2) from tension-stiffening experiments of R/ECC specimens. Five phases, corresponding to different levels (I-IV) of beam deformation (Fig. 5.7), can be identified. The predicted moment-curvature relationship normalized by the elastic limit in moment and curvature is shown in Fig. 5.8, for four levels of steel reinforcement ratio ρ = 0, ρT, ρB, ρC. When the reinforcement ratio is between 0 and ρT, beam failure is governed by exhausting the tensile strain capacity eut of ECC. Above ρ = ρT, ultimate beam failure is governed by exhausting the compressive strain capacity euc of ECC. When ρ = ρC, failure of ECC in compression and plastic yielding of steel is reached simultaneously. When ρ  ρC, steel reinforcement remains elastic throughout. Based on this model, the following insights on R/ECC beam behavior can be derived [6]: (a) No sudden load drop occurs in R/ECC beams as may occur in lightly reinforced R/C beams. Instead, deflection hardening is predicted. (b) The flexural stiffness in R/ECC beams in post-cracked Phase II is always higher than that of R/C beams despite ECC’s lower Young’s modulus compared to normal concrete, due to the ability of ECC to retain load carrying capacity after first crack. (c) The ductility of R/ECC beam is always higher than R/C beams.

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5 Constitutive Modeling of Engineered Cementitious Composites (ECC)

Fig. 5.7 (a) Phase I: All materials are elastic; (b) Phase II: ECC elastic-plastic in tension; (c) Phase III: ECC elastic-plastic in tension and steel yields; (d) Phase IV: ECC elastic-plastic in tension and compression and elastic steel; (e) Phase V: ECC and steel elastic-plastic

Fig. 5.8 Model predicted moment-curvature (m-k) relationship for R/ECC beam, for four characteristic reinforcement ratios ρ = 0, ρT, ρB, ρC. The five phases (I to V) correspond to those in Fig. 5.7

5.2 Phenomenological Model

147

The resulting moment-curvature relationship for R/ECC (Fig. 5.8) can serve as a design guide for beams or one-way slab.

5.2.2

Constitutive Model for 2D Stress State: Monotonic Loading

The uniaxial constitutive models used for beam analysis and described in the previous section are limited to structural elements with simple stress states, i.e., uniaxial tension and compression below and above the neutral axis in the critical beam section subjected to pure moment loading. For structural elements or applied loading that leads to more general stress states, a more complete constitutive model is needed. A plasticity-based phenomenological model that accounts for the strainhardening behavior of ECC has been proposed by Kabele [3, 7]. Multiple microcracking, initiated on planes normal to the maximum principal tensile stress direction when it reaches the first crack strength σ fc, is treated as smeared “plastic” or cracking strain ecij . Unloading of the material from the strain-hardening state leads to permanent deformation. The yield surface in 2D stress state is defined by the Rankine yield function:

F

σ xx þ σ yy 2

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi      ffi σ xx  σ yy 2 σ xy þ σ yx 2  σ fc ¼ 0 þ þ 2 2

(5:3)

where σ fc is the first crack strength, and σ xx , σ yy σ xy , and σ yx are defined by the kinematic hardening rule σ ij ¼ σ ij  αij

(5:4)

dαij ¼ hdecij

(5:5)

and

Equations 5.3, 5.4, and 5.5 are consistent with the earlier-mentioned assumptions for multiple microcrack initiation. The material constant h reflects the material hardening behavior and can be made a function of total cracking strain. For simplicity, h can be determined from the slope of a bi-linear approximation of a uniaxial tensile stress-strain curve between first crack stress and ultimate strength (Fig. 5.9). The associated flow rule enforces that the cracking strain increment is proportional to the vector normal to the yield surface, so that decij ¼ dλ where dλ is a nonnegative scalar quantity.

dF dσ ij

(5:6)

148

5 Constitutive Modeling of Engineered Cementitious Composites (ECC)

Fig. 5.9 Approximation of the uniaxial tensile stressstrain relation of ECC (with 2% PE fiber) and determination of first crack strength σ fc, the hardening index h, unloading slope θ and the tension-softening rate s. ecmb is the tensile strain capacity, and u is the uniaxial extension of the gage length l

a

b

Fig. 5.10 Sequential loading in two perpendicular direction and kinematic hardening response (a) loading in x-direction leads to a set of microcracks and expansion of the yield surface dαxx, while (b) subsequent unloading in the x-direction followed by loading in y-direction leads to an independent set of microcracks and expansion of the yield surface dαyy

Kabele and Horii [7] showed that the kinematic hardening rule adopted here reflects the behavior of ECC in that microcracking and strain-hardening in one direction does not affect the material behavior in a perpendicular direction. This is schematically illustrated in Fig. 5.10. Once the material is loaded to a stress state on the yield surface, standard incremental theory of plasticity is used to obtain the elasto-plastic incremental stress-strain relationship. The treatment of yield surface singularity is discussed in Kabele and Horii [7]. When the ultimate tensile strength σ mb is reached, localization onto a fracture plane is assumed, with crack opening governed by the tension-softening relation dt n ¼ sdδn

(5:7)

5.2 Phenomenological Model

149

where s is the softening rate (Fig. 5.9). In this model, the shear traction is assumed to be a constant once fracture localization takes place. The subscript n denotes the normal in the principle tensile direction. The constitutive model of ECC summarized above was implemented in an FEM program and applied to simulate the experimentally observed microcrack development around the notch of an ECC double cantilever beam (DCB) specimen [8, 9]. In this experiment, it was found that an expanded diffused microcracking zone (Fig. 5.11) involving a volume of material off the notch plane was responsible for the high inelastic energy absorption. The areal extent of microcracking was of the order of 1000 cm2, and the apparent fracture toughness exceeded 34 kJ/ m2. The diffused microcracking mode and zone size observed in ECC are distinctly different from the localized fracture extension on the notch plane for ordinary fiber reinforced concrete. The material parameters obtained from uniaxial tensile tests and used in the numerical simulation are shown in Table 5.1. Figure 5.12 shows the load versus load-line displacement curves from experimental data [8] and from the FEM simulation [7]. The predicted cracking strain fields in the DCB at two stages of loading (A and B in Fig. 5.12) are shown as contour lines of constant strain magnitudes in Fig. 5.13. At Stage A prior to peak load, the material at the notch tip experiences a tensile stress below σ mb with no extension of the notch which is surrounded by off-plane microcracks (Fig. 5.13a). At Stage B near the peak load, a rapid expansion of the microcracking zone is predicted (Fig. 5.13b) which spreads to the specimen boundary as experimentally observed (Fig. 5.11a). Onset of softening of the specimen is accompanied by fracture

Fig. 5.11 (a) DCB specimen of ECC with 2% fiber, showing diffused microcrack zone [8, 9], and (b) FEM model [7]

150

5 Constitutive Modeling of Engineered Cementitious Composites (ECC)

Table 5.1 Material parametric values used in constitutive model for FEM simulation h 0.2

Fig. 5.12 Predicted and experimentally determined load-displacement relation of the ECC DCB specimen (a = 11.7 cm; W = 31 cm; H = 30 cm). After [7]. While the general load-displacement relationship is captured, the model does predict higher peak load

ecmb (%)

σ fc (MPa) 2.2

δo (mm) 6.62

σ mb (MPa) 4.32

5.78

1.8 Load per Unit Thickness [kN/cm]

E (GPa) 22

experiment

B

analysis

A 1.2 a 0.6

H

W 0.0

0

1

2

3

4

5

Load-Line Displacement [cm]

localization ahead of the notch tip (Fig. 5.13c). The authors also calculated inelastic energy absorbed by cracking of the specimen. They found that the diffused microcracking accounted for more than half of the total dissipated energy, while the rest was released through the extension of the localized softening crack. The plasticity-based phenomenological constitutive model appears to qualitatively capture the structural response of the DCB specimen. However, while the overall experimental load-displacement behavior and microcrack zone development is reasonably reproduced, the model tends to overestimate the peak load. Kabele and Horii suggested that the experimentally observed lower peak load might have resulted from reduced fiber bridging efficiency due to the bi-axial stress state with the minimum principal stress reaching the first crack strength, in addition to potential experimental errors. An alternative interpretation of the discrepancy between model prediction and experiment is that the present model does not capture potential sliding on the planes of multiple cracks, which may be responsible for the predicted higher structural strength and stiffness shown in Fig. 5.12. This is further discussed in Sect. 5.3.

5.2.3

Constitutive Model for 2D Stress State: Cyclic Loading

For simulation of seismic response of structures, a constitutive model that accounts for cyclic loading is needed. Billington and co-workers [10, 11] studied experimentally the behavior of ECC under reversed cyclic loading based on which a cyclic constitutive model was formulated. See also, Vorel and Boshoff [12]. In

5.2 Phenomenological Model Fig. 5.13 Predicted cracking strain contours at (a) Stages A and (b) B in Fig. 5.12. The principal cracking strain distribution near the notch tip is shown in (c). After [7]

151

a 0.3 0.6 1.2

b

0.3 0.6 1.2 2.4 4.8

c

Localized crack with bridging

Billington and co-workers’ study, data were obtained for ECC with PE fibers and ECC with PVA fibers. In some specimens, coarser aggregates were used. Both dog-bone and cylindrical specimens were tested. The specimens with coarser aggregates and especially those in cylindrical form show very limited strain-hardening. Under predominantly compression-compression cyclic testing using PVA-ECC cylindrical specimens, it was observed that the envelope of the cyclic compression behavior is similar to the stress-strain curve obtained under monotonic compression loading (Fig. 5.14). Prior to reaching compression peak load, the load cycles involve elastic loading and unloading. Beyond compression peak load, however, softening of the specimen in each load cycle was observed, and elastic unloading was followed by a parabolic curve to a small residual strain. Tensile loading was needed to return the specimen to zero deformation due to damage induced in the compression cycle.

152

5 Constitutive Modeling of Engineered Cementitious Composites (ECC) 10 -4.0

-5.0

-3.0

-2.0

-1.0 0

Stress (MPa)

-10 -20 -30 -40 PVA-ECC–Compression monotonic PVA-ECC–Compression-compression cyclic

-50 -60

Strain (%)

Fig. 5.14 Predominantly cyclic compression-compression behavior of PVA-ECC. A monotonic compressive stress-strain curve is also shown. After [10]. (Authorized reprint from ACI Mater. J. 100(5), 381–390 (2003)) 5

Stress (MPa)

-0.5

1.0

2.0

3.0

4.0

-20 -30 -40 -50

PE-ECC–Cyclic tension-tension PE-ECC–Monotonic Tension

% Strain

Fig. 5.15 Predominantly cyclic tension-tension behavior of PE-ECC. Compression loading was used to close the tensile cracks. A monotonic tensile stress-strain curve is also shown. The tensile strain capacity is not influenced by the cyclic loads. After [10]. (Authorized reprint from ACI Mater. J. 100(5), 381–390 (2003))

Under predominantly tensile-tensile cyclic testing, it was found that the tensile strain capacity of the material was not affected (Fig. 5.15). Compression loading was necessary to close the tensile microcracks. Under balanced tensile-compressive cyclic testing, the tensile strain capacity of the material was found to diminish if softening is reached in the previous compression cycle (Fig. 5.16). This behavior was attributed to the interference of the multiple cracking development under tensile loading by splitting cracks resulted from previous compression loading cycles.

5.2 Phenomenological Model

-4.0

5

-2.0

Stress (MPa)

a

153

2.0

4.0

-15

-30

Strain (%)

-45

Stress (MPa)

b 3.0 Cycle following the onset of softening in compression

2.0 PE-A Monotonic tensile loading

1.0

0.0 0.0

1.0

2.0

3.0

Fig. 5.16 Balanced tension-compression cyclic behavior of PE-ECC with coarser aggregates. (a) Full tension-compression response and (b) enlarged tensile response showing comparison with a monotonic tensile stress-strain curve. After [10]. (Authorized reprint from ACI Mater. J. 100(5), 381–390 (2003))

The observations derived from the cyclic tests were used to formulate a cyclic constitutive model for ECC [11]. It was noted that data from monotonic tension and compression tests can serve as input to the constitutive model as long as compression softening is not experienced in the modeled structure. A coaxial rotating crack model [11, 13] with two orthogonal sets of cracks and based on total strain is implemented for ECC (Fig. 5.17). The local principal stress components σ nn and σ ss are assumed uncoupled, so that σ nn ¼ F ðenn , αnn Þ σ ss ¼ F ðess , αss Þ

(5:8)

where αnn and αss are internal state variables used to track the material loadingunloading history. The failure envelopes in tension and compression were idealized [11] as shown in Fig. 5.18, so that the F-function in Eq. 5.8 is defined as

154

5 Constitutive Modeling of Engineered Cementitious Composites (ECC)

Fig. 5.17 Local (n-s)–global (x-y) coordinate for the coaxial rotating crack model. After [11]

: Rotation angle

Cracks

b a

Tension

Compression

Fig. 5.18 Failure envelopes assumed for ECC in (a) tension and (b) compression. After [11]. (Authorized reprint from ACI Struct. J. 100(6), 749–757 (2003))

F tensile

8 Ee >   > >   e  et0 > > > < σ t0 þ σ tp  σ t0  etp  et0 ¼ e  e > tp > > σ tp 1  > > etu  etp > : 0

and F compressive

8 Ee > >  <  e  ecp ¼ σ cp 1  > ecu  ecp > : 0

0  e < et0 et0  e < etp (5:9) etp  e < etu etu  e

ecp  e < 0 ecu  e < ecp e  ecu

(5:10)

5.2 Phenomenological Model

155

with the delimiting stress and strain variables defined in Fig. 5.18. The failure envelope in tension (5.9) is similar to that used by Kabele [7] with the exception that softening beyond peak load is represented as smeared strain rather than localized crack-opening. The material unloading and reloading behavior in tension and in compression is approximated by Eqs. 5.11 and 5.12 and as illustrated in Fig. 5.19.

F tensile

8 Ee > > >  at

> > e  etul >  > > max 0, σ > tmax > etmax  etul > > >  

<   e  etul ¼ max 0, σ tul þ σ tmax  σ tul > etmax  etul > >  

> > > e  etul > > max 0, σ tmax > > e > tmax  etul > > : 0

0  etmax < et0 et0  etmax < etp ,e_ < 0 et0  etmax < etp ,e_  0 : etp  etmax < etu etu  etmax (5:11)

where etmax

¼

etmax for initial unloading etmax  etmax etprl for unloading followed by partial reloading

and etprl is defined as the maximum tensile strain during partial unloading and σ tmax is the stress associated with etmax . In Eq. 5.11, etul is determined by etul ¼



etul for initial unloading etpul for unloading followed by partial reloading

etul = bt  etmax and etpul = minimum strain during partial unloading in tension. at and bt are material constants experimentally calibrated. The parameters etmax, etprl, and etpul are internal variables (αns) in tension that need to be traced during the loading and unloading processes. F compressive 8 Ee > > >  ac

> > e  ecul >  > > < min 0, σ cmin e  e cul cmin  

¼   e  ecul > >   > min 0, σ cu þ σ cmin  σ cmin > > ecmin  ecul > > > : 0

ecp  ecmin < 0 ecu  ecmin < ecp ,e_ > 0 : ecu  ecmin < ecp ,e_  0 ecmin < ecu (5:12)

where

156

5 Constitutive Modeling of Engineered Cementitious Composites (ECC)

Fig. 5.19 Schematic of unloading and reloading behavior in tension and compression. (a) Up to tensile strain-hardening: O➔A➔B: loading; B➔C: partial unloading; C➔D: partial reloading; D➔E: full unloading; E➔O: assumed behavior for further unloading to origin; O➔E➔B: full reloading; B➔F: further loading; (b) During tensile softening: G➔H➔O unloading; O➔H➔G➔I: reloading and further loading; (c) Up to compression softening: O➔J➔K➔L➔M➔N➔O: unloading; O➔N➔K➔P: reloading; (d) Two cycles of reverse loading; O➔A➔B➔C➔D➔O: first loading cycle in tension to strain-hardening regime; O➔J➔K➔L➔M➔O: first loading cycle in compression to softening regime; O➔D➔B➔F➔I➔O: second loading cycle in tension up to complete failure; O➔M➔K➔P➔O: second loading cycle in compression up to complete failure. After [11]. (Authorized reprint from ACI Struct. J. 100(6), 749–757 (2003))

ecmin

¼

ecmin for initial unloading ecmin  ecmin ecprl for unloading followed by partial reloading

and ecprl is defined as the minimum strain during partial reloading in compression and σ cmin is the stress associated with ecmin . In Eq. 5.12, ecul is determined by ecul for initial unloading  ecul ¼ ecpul for unloading followed by partial reloading

5.2 Phenomenological Model

a

157

b

18

9 Load [kN]

9 Load [kN]

18

0

0 -9

-9

Case 1 Case 3

Experiment

-18 -6

-4

-2

0 2 Drift [%]

4

6

-18 -6

-4

-2

0

2

4

6

Drift [%]

Fig. 5.20 (a) Experimental and (b) model predicted load-drift relationship of R/ECC beam. Case 1: No bond-slip, and Case 3: Bond-slip assumed for steel reinforcements. After [11]. (Authorized reprint from ACI Struct. J. 100(6), 749–757 (2003))

ecul = bc  ecmin and ecpul = minimum strain during partial unloading in compression. ac and bc are material constants experimentally calibrated. The parameters ecmin, ecprl, and ecpul are internal variables (αns) in compression that need to be traced during the loading and unloading processes. The constitutive model summarized above was used with a 2D finite element model to simulate the reversed cyclic behavior of a cantilever R/ECC beam (see also Sect. ▶ 6.3.1.1). Figure 5.20 shows the comparison between experimental and predicted load-drift response. When bond-slippage was accounted for (Case 3 in Fig. 5.20b), the modeled loaddrift relation showed increased pinching as expected. Han et al. [11] also studied the influence of reducing the initial stiffness of ECC to account for shrinkage cracking in the beam, as well as variations in unloading/reloading scheme. Figure 5.21 shows a comparison of the microcracking pattern in the experimental R/ECC beam and the principal strain contour predicted by the FEM model. It is noted that the tensile cracking damage is distributed over a volume of material above the base of the beam as observed in the test. The experimentally observed hysteresis behavior and the general damage pattern appear to be well captured by the model.

5.2.4

Constitutive Model for 3D Stress State: Dynamic Loading

As a concrete-like material, ECC shares similar challenges in constitutive modeling as for regular concrete. These challenges that make concrete different from steel in constitutive behavior include (1) failure in tension differs significantly from failure in compression and (2) failure is sensitive to hydrostatic pressure. As is already known, ECC is also different from concrete in that the material undergoes tensile “yielding” and strain-hardening when loaded beyond the elastic state until an ultimate strength is reached. Like concrete and steel, ECC mechanical properties are loading rate sensitive. A 3D rate-dependent dynamic constitutive model was

158

5 Constitutive Modeling of Engineered Cementitious Composites (ECC)

Fig. 5.21 (a) Cracking pattern from experiment and (b) the maximum principal strain contour from model, at 5% drift. After [11]. Distributed damage near the base of the R/ECC beam is experimentally observed and model predicted. (Authorized reprint from ACI Struct. J. 100(6), 749–757 (2003))

proposed by Ranade and Li [14–16] for ECC structures subjected to impact loading. This model is based on a plasticity model [17] originally developed for concrete but modified for the unique characteristics of ECC. It is convenient to represent the stress state by three stress-invariants (ξ, r, θ) in the principal stress-space (σ 1, σ 2, σ 3) (Fig. 5.22), where ξ is a measure of the hydrostatic pressure, r denotes the effective deviatoric stress, and θ represents the closeness of σ2 to σ1 relative to closeness of σ 2 to σ 3. This representation is chosen as stressinvariants are independent of the spatial coordinate system chosen. The three-dimensional failure surface at a given damage state can be defined by an envelope of critical combination of 3D stresses. The stress-states on the envelope represent inelastic behavior, while that inside represent elastic behavior. Stress-states outside the envelope cannot be attained, although the envelope itself can move and enlarge in accordance to the damage state (plastic strain) of the material. The 3D failure surface is completely defined if (1) the p failure curve p-Δσ ffiffiffi (in a meridian plane) between the hydrostatic pressure (p ¼ ξ= 3) and deviatoric stress capacity (Δσ) in the compressive meridian plane at a specific damage state is known, and (2) a scaling rule for Δσ dependent on the damage state is specified.

5.2 Phenomenological Model

159

Fig. 5.22 P represents a 3D stress state expressed in terms of the stress-invariants ξ, r, θ. Also shown is a 3D failure surface used in LS-Dyna material model MAT_072R3. The meridian plane (θ = constant) and the deviatoric plane (ξ = constant) are perpendicular to each other. After [14]

The dynamic constitutive model for ECC is based on a concrete damage model (MAT_072R3 of LS-Dyna material library, [17]) that implements three separate fixed loading surfaces (yield, ultimate, and residual) and allows independent control of damage parameters in tension and in compression. The concept of three specific damage states corresponding to yield capacity, maximum capacity, and residual capacity of a given material is illustrated in Fig. 5.23 for the simple case of uniaxial loading. Generalizing from uniaxial to multiaxial loading, three fixed “loading surfaces” can be defined corresponding to these three damage states for ECC. The failure surface moves between these three fixed loading surfaces, depending on the damage state of the material. Equations 5.13a, 5.13b, and 5.13c define the three fixed loading surfaces in the compressive meridian in the MAT_072R3 model. In this equation, the subscripts “y,” “m,” and “r” refer to the loading surface at “yield,” “maximum,” and “residual” damage states, respectively. The “a”-parameters in the model are based on experimental data. Δσ y ¼ a0y þ

p a1y þ a2y p

(5:13a)

p a1 þ a2 p

(5:13b)

Δσ m ¼ a0 þ Δσ r ¼

p a1f þ a2f p

(5:13c)

160

5 Constitutive Modeling of Engineered Cementitious Composites (ECC)

Maximum Capacity

Yield Capacity

Residual Capacity

Elastic Inelastic Fig. 5.23 Illustration of damage states for defining fixed loading surface locations, for the case of uniaxial loading. After [14]

The loading surfaces in the tensile meridian can also be defined using Eqs. (5.13a, 5.13b, and 5.13c) but reduced by a numerical factor > > > >
> πd f τ0 ðLe  uÞ 1 þ β > > df > : 0

during debonding (5:15) during sliding after fiber ruptured or pulled out

where τo, Gd are fiber/matrix interface frictional and chemical bond, β is a sliphardening or slip-weakening parameter that describes the changing shear resistance caused by fiber fibrillation and jamming or fiber tunnel smoothing during sliding, and df and Le are fiber diameter and embedment length. The demarcation between fiber debonding and fiber sliding is governed by a critical u = uo defined by Eq. ▶ 2.13. Equation 5.15 is derived for a fiber bridging across a continuously opening crack. For the case of a crack which first opens to a value ω and then undergoes shear by an amount Δ (Fig. 5.33), the fiber end displacement is modified [18, 26] so that u¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Δ2 þ ω2

(5:16)

and the fiber bridging force P is aligned with the fiber axis inclined at an angle γ to the direction normal of the crack plane. This force can be resolved into two components normal (Pn) and tangential (Pt) to the crack plane: Pn ¼ P cos γ Pt ¼ P sin γ

(5:17)

5.3 Multiscale Model

169

a

b Matrix P

Pn u

Fiber

Pt

Fig. 5.33 A fiber bridging across a crack that undergoes (a) opening and then (b) shear sliding. After [27]

with the angle γ defined by the shear and opening displacement ratio: γ ¼ tan 1 ðΔ=ωÞ

(5:18)

The assumption behind (5.17) is that the fiber acts as a flexible rope which is appropriate for low modulus fibers with small diameter, especially at crack opening that is large relative to the fiber diameter. Otherwise, the shear resistance of the fiber becomes nonnegligible [28].

5.3.3

Micro-Meso I Linkage

For a pure opening mode, scale linking to the meso-level stress–crack opening (σ-δ) relationship (Fig. 5.31c) is performed by integrating the effects of different groups of fibers that undergo debonding, sliding, or already pulled-out, for a given crack opening δ, as shown in ▶ Chap. 2 for the case of a crack in the pure opening mode (Eq. ▶ 2.5). For the case of a crack that opens and then shears (Fig. 5.31h), Eq. ▶ 2.5 can be generalized to a bridging tensile traction normal to the crack plane [18]. Vf σ ðω,ΔÞ ¼ Af

ð π=2 ð Lf cos ϕ ð 2π 2

ϕ¼0

z¼0

θ¼0

Pn ðu,zÞg ðαÞpðzÞpðϕÞpðθÞdθdzdϕ

(5:19)

and a bridging shear traction tangential to the crack plane Vf τðω,ΔÞ ¼ Af

ð π=2 ð Lf cos ϕ ð 2π 2

ϕ¼0

z¼0

θ¼0

Pt ðu,zÞgðαÞpðzÞpðϕÞpðθÞdθdzdϕ

where the angles α and θ are defined in Fig. 5.34, and

(5:20)

170

5 Constitutive Modeling of Engineered Cementitious Composites (ECC)

Fig. 5.34 3-D spatial definition of angles α, γ, and θ

α ¼ cos 1 ð cos ϕ cos γ þ sin ϕ sin γ cos θÞ

(5:21)

For 3D uniform fiber distribution, the probability density functions of random variables z, ϕ, and θ in Eqs. 5.19 and 5.20 are given by 2 , 0  z  Lf =2 Lf pðϕÞ ¼ sin ϕ, 0  ϕ  π=2 1 pðθÞ ¼ , 0  θ  2π 2π

pð z Þ ¼

(5:22)

The normal and shear stresses expressed in Eqs. 5.19 and 5.20 are coupled since Pn, Pt and the snubbing function g depends on the ratio (Δ/ω) through the angle γ. They allow the computation of normal and shear stresses for a given opening ω and shear sliding Δ on a single crack.

5.3.4

Meso I-Meso II Linkage

Equations 5.19 and 5.20 can be used to formulate constitutive relations for the representative volume element RVE at the Meso II level (Fig. 5.31g). This RVE embodies two orthogonal sets of multiple cracks with normals in the ξ- and η-directions (Fig. 5.31g) and is subjected to uniform boundary conditions σξξ, σηη, and σξη. The overall strain for this element can be expressed as [19]. mc,ξ

eij ¼ eeij þ eij

mc,η

þ eij

(5:23)

5.3 Multiscale Model

171

The first term in Eq. 5.23 is the elastic strain between cracks, while the second and third terms refer to inelastic strains due to the opening and sliding of each of the two sets of multiple microcracks (superscript “mc”) with crack-plane normals in the ξ- and η-directions. Specifically, the inelastic strains due to the set of cracks with normal in the ξ-direction is given by mc,ξ

eξξ

¼

mc,ξ

eξη

ð 1 Xpξ ωk dS þ , k¼1 V S ξþ k mc,ξ

¼ eηξ

¼

mc,ξ eηη ¼0

ð 1 Xpξ 1 Δk dS þ k¼1 V 2 S ξþ k

(5:24)

(5:25)

Similarly, the inelastic strains due to the set of cracks with normal in the η-direction is mc,η eηη ¼

mc,η

eξη

ð 1 Xpη ωk dS þ , k¼1 V S ηþ k mc,η

¼ eηξ

¼

mc,η

eξξ

¼0

ð 1 Xpη 1 Δk dS þ k¼1 ηþ V Sk 2

(5:26)

(5:27)

where pξ and pη are the numbers of cracks in each set, and V is the volume of the RVE. The functions ωk and Δk define the tensile opening and shear sliding displacements on the kth crack (Eqs. 5.18 and 5.19). In this manner, the constitutive model σ ij = σ ij(eij) for the RVE with two orthogonal sets of cracks is established.

5.3.5

Meso II-Macro Linkage

Once the constitutive model for the RVE is established, it can be embodied in a general-purpose FEM to predict the response of a structure under load. As a result, the structural response reflects the material response at each material point, accounting for elastic as well as inelastic behavior associated with multiple cracking. The formulation highlighted above allows for the potential formation of two orthogonal sets of cracks and makes provision for multiple crack opening and sliding for each set of cracks. In turn, the resistance to opening and sliding takes into account information on fiber bridging that ultimately links to the debonding, sliding, and pull-out of fibers across crack planes.

5.3.6

Application of Multiscale Model

The above multiscale model implemented in a 2-D FEM has been applied in a numerical simulation [27, 28] of a steel reinforced ECC beam subjected to shear

172

5 Constitutive Modeling of Engineered Cementitious Composites (ECC)

loading [29]. Once the strain capacity of the ECC has been exhausted, fracture localization was handled with a crack-band model. A phenomenological model was employed for modeling the compressive response. The geometry as well as the loading and reinforcement configurations of the Ohno shear beam are shown in Fig. 5.35. The model-predicted shear load versus shear deformation is shown in Fig. 5.36, together with experimental data. The general trend and shear capacity are seen to be well captured. The predicted diagonal multiple cracking evolution during loading beyond the elastic limit stage A is consistent with experimental observations. Beam failure at stage B was associated with fracture localization in a Z-shaped pattern. The

Fig. 5.35 Reinforcement and loading configurations of the Ohno shear beam modeled. After [27, 28]

100 B

Vs (kN)

80 A

60

40 FE analysis 20

0

Experiment

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

-2 av (10 )

Fig. 5.36 Experimental and model predicted shear load-deformation curve for Ohno shear beam. Loading stages A and B demarcate the on-set of diagonal multiple cracking and fracture localization. After [27, 28]

5.4 Summary and Conclusions

173

Fig. 5.37 (a) Model-predicted strain distribution at beam failure and (b) observed damage pattern in beam specimen (Courtesy of Dr. Kanda (KaTRI)). After [27, 28]

predicted strain damage distribution at failure is shown in Fig. 5.37a. It can be seen that the damage pattern matches well that observed experimentally (Fig. 5.37b). Kabele [3, 19] emphasized the importance of capturing the shear sliding of the multiple cracks that had formed, when rotation of the stress field occurred during loading.

5.4

Summary and Conclusions

The development of constitutive models for ECC has made great strides since the invention of ECC as a new concrete material. The desire to take advantage of the unique properties of ECC in structural applications has prompted their development. These models differ from typical constitutive models of normal concrete in that they have been constructed specifically to accommodate the tensile strain-hardening properties of ECC when loaded beyond the elastic domain.

174

5 Constitutive Modeling of Engineered Cementitious Composites (ECC)

The phenomenological models discussed in Sect. 5.2 accommodate monotonic, cyclic, and dynamic type loading. While their applications to specific structures have demonstrated their versatilities, shortcomings have also been discovered. Among these is the tendency to predict stiffer and stronger structural response compared to experimental observations. This has been attributed to the assumption that the multiple cracks can only deform in the opening mode, but not in the sliding mode. The latter may be activated when principle stress rotation occurs during structural loading, especially in structures that may experience shear-critical failure. The multiscale model discussed in Sect. 5.3 has the ability to handle both crack opening and sliding. Because of scale linking down to the microlevel, this model has the potential to support the integrated structures and materials design (ISMD) concept by tailoring material composition and ingredients for infrastructural resilience, durability, and sustainability. These aspirations, however, have yet to be fully realized. Further, research on extending the current multiscale approach to more complex loading such as impact or cyclic loading is needed. Despite their current limitations, it is clear that constitutive models represent an important tool in the quantitative connection between ECC material design and structural design and in supporting deeper understanding of structural behavior both in the mechanical sense and in the durability sense. It can be expected that the maturation of constitutive models for ECC will enable more effective and wider use of this material in critical infrastructures in future.

References 1. Li, V.C.: Integrated structures and materials design. Mater. Struct. 40(4), 387–396 (2007) 2. Kabele, P.: Some issues in modeling and characterization of SHCC materials and structures. In: FRC Workshop, Stanford University, 17–18 Nov 2014 (2014) 3. Kabele, P.: Finite element fracture analysis of reinforced SHCC members. In: Advances in Cement-Based Materials, Proc. of the International Conference on Advanced Conrete Materials, Stellenbosch, South Africa, pp. 237–244 (2009) 4. Rokugo, K., Kanda, T.: Strain Hardening Cement Composites: Structural Design and Performance, vol. 6. RILEM, Springer (2013) 5. Maalej, M., Li, V.C.: Flexural/tensile strength ratio in engineered cementitious composites. J. Mater. Civ. Eng. 6(4), 513–528 (1994) 6. Szerszen, M.M., Szwed, A., Li, V.C.: Flexural response of reinforced beam with high ductility concrete material. In: BMC-8, Woodland Publishing, Warsaw, Poland, pp. 263–274 (2006) 7. Kabele, P., Horii, H.: Analytical model for fracture behavior of pseudo strain- hardening cementitious composites. Concr. Libr. JSCE. 29, 105–120 (1997) 8. Maalej, M., Hashida, T., Li, V.C.: Effect of fiber volume fraction on the off-crack-plane fracture energy in strain-hardening engineered cementitious composites. Am. Ceram. Soc. 78(12), 3369–3375 (1995) 9. Li, V.C., Hashida, T.: Engineering ductile fracture in brittle-matrix composites. J. Mater. Sci. Lett. 12(12), 898–901 (1993) 10. Kesner, K.E., Douglas, K.S., Billington, S.L.: Cyclic response of highly ductile fiber-reinforced cement-based composites. ACI Mater. J. 100(5), 381–390 (2003) 11. Han, T.S., Feenstra, P.H., Billington, S.L.: Simulation of highly ductile fiber-reinforced cementbased composite components under cyclic loading. ACI Struct. J. 100(6), 749–757 (2003)

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12. Vorel, J., Boshoff, W.P.: Numerical simulation of ductile fiber-reinforced cement-based composite. J. Comput. Appl. Math. 270, 433–442 (2014) 13. Feenstra, P.H., Rots, J.G., Arnesen, A., Teigen, J.G., Hoiseth, K.V.: A 3D constitutive model for concrete based on a co-rotational concept. In: Computational Modelling of Concrete Structures, Proceedings of EURO-C 1998, Brookfield, Rotterdam, pp. 13–22 (1998) 14. Ranade, R.: Advanced Cementitious Composite Development for Resilient and Sustainable Infrastructure. PhD Thesis, University of Michigan, Ann Arbor, MI (2014) 15. Ranade, R., Li, V.C.: Material model for simulating strain-hardening cementitious composites in LS-DYNA. In: SHCC3, Dordrecht, The Netherlands, pp. 235–242 (2014) 16. Lee, S.C.: Finite Element Modeling of Hybrid-Fiber ECC Targets Subjected to Impact and Blast. National University of Singapore, Singapore (2006) 17. Malvar, L.J., Crawford, J.E., Wesevich, J.W., Simons, D.: A plasticity concrete material model for DYNA3D. Int. J. Impact Eng. 19(9–10), 847–873 (1997) 18. Kabele, P.: New developments in analytical modeling of mechanical behavior of ECC. J. Adv. Concr. Technol. 1(3), 253–264 (2003) 19. Kabele, P.: Multiscale framework for modeling of fracture in high performance fiber reinforced cementitious composites. Eng. Fract. Mech. 74(1–2), 194–209 (2007) 20. Suryanto, B., Nagai, K., Maekawa, K.: Modeling and analysis of shear-critical ECC members with anisotropic stress and strain fields. J. Adv. Concr. Technol. 8(2), 239–258 (2010) 21. Kang, J., Bolander, J.E.: Multiscale modeling of strain-hardening cementitious composites. Mech. Res. Commun. 78, 47–54 (2016) 22. Luković, M., Dong, H., Šavija, B., Schlangen, E., Ye, G., Van Breugel, K.: Tailoring strainhardening cementitious composite repair systems through numerical experimentation. Cem. Concr. Compos. 53, 200–213 (2014) 23. Li, V.C., Wu, H.: Conditions for pseudo strain-hardening in fiber reinforced brittle matrix composites. Appl. Mech. Rev. 45(8), V. C. Li, Ed. ASME, 390–398 (1992) 24. YANG, E., Li, V.C.: Numerical study on steady-state cracking of composites. Compos. Sci. Technol. 67(2), 151–156 (2007) 25. Kabele, P., Stemberk, M.: Stochastic model of multiple cracking process in FRCC. In: Proceedings of ICF11, Paper 4825 on CD-ROM, Torino, Italy, pp. 3–8 (2005) 26. Wu, C., Leung, C.K.Y., Li, V.C.: Derivation of crack bridging stresses in engineered cementitious composites under combined opening and shear displacements. Cem. Concr. Res. 107, 253–263 (2018) 27. Kabele, P.: Equivalent continuum model of multiple cracking. Eng. Mech. 9(1/2), 75–90 (2002) 28. Kabele, P.: Fracture behavior of shear-critical reinforced HPFRCC members. In: International RILEM Workshop on High Performance Fiber Reinforced Cementitious Composites in Structural Applications. In: Fischer, G., Li, V.C.,(eds.), RILEM Publisher, Bagneux, pp. 383–392 (2006) 29. Kanda, T.: Design of Engineered Cementitious Composites for Ductile Seismic Resistant. University of Michigan, Ann Arbor (1998)

6

Resilience of Engineered Cementitious Composites (ECC) Structural Members

Contents 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Damage Tolerance and Tension Stiffening of Steel Reinforced ECC . . . . . . . . . . . . . . . . . . . 6.3 Performance of R/ECC Elements Under Fully Reversed Cyclic Loads . . . . . . . . . . . . . . . . . 6.4 Resilience of ECC Members Under Impact Loads . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

178 179 183 210 221 222

Abstract

An original driving force behind the development of Engineered Cementitious Composites (ECC) was the potential enhancement of structural safety given the collapse of some reinforced concrete structures under earthquake loads. Since then, extensive amounts of testing at the structural element level have demonstrated significant improvements in structural resilience characterized by delayed failure, limited degradation in structural function during the load event, and rapid recovery of structural functions postevents. These experiments have been conducted for beams, columns, beam-column connections, frames, and wall systems. Apart from improving structural resilience, ECC has the potential to enhancing constructability by eliminating steel congestion when a large amount of steel is used to overcome severe member forces. This is accomplished by the intrinsic shear capacity of ECC so that the transverse reinforcing steel often adopted in seismic detailing is rendered unnecessary. The compatible deformation between ECC and axial steel, even when both are loaded to beyond the elastic stage, allows large energy absorption in R/ECC members. The ability to strain-hardening to several percent tensile strain in ECC

© Springer-Verlag GmbH Germany, part of Springer Nature 2019 V. C. Li, Engineered Cementitious Composites (ECC), https://doi.org/10.1007/978-3-662-58438-5_6

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assures this compatible deformation and eliminates the commonly observed bond failure and bond splitting in concrete cover. Instead, distributed microcracking represents a commonly observed damage pattern of overloaded structural members. This chapter describes the unique behavior of R/ECC structural members under fully reversed cyclic load and under impact load. The fundamental mechanisms behind the enhanced structural resilience are emphasized. The knowledge gained should be helpful in further structural designs by optimal utilization of the tensile ductility of ECC.

6.1

Introduction

Resilience of structures requires more than structural safety. Structures that are resilient possess at least three characteristics [1]. These characteristics are schematically illustrated in Fig. 6.1 that shows the contrast in changes in quality of infrastructure between one that is more resilient (dashed line) and one that is less so (solid line). Specifically, a resilient infrastructure reveals (a) a delay in failure (e.g., from t0 to t0’), (b) limited functional degradation at failure (e.g., loss of 25% instead of 50% in terms of quality of infrastructure), and (c) quick recovery of functions in terms of time (e.g., (t1’– t0’) vs. (t1 – t0)) and cost. The design of concrete materials for structural resilience has been a long-standing challenge. Increasing the compressive strength of concrete is not always consistent with the desire for structural resilience. Instead, a ductile concrete reduces the probability of failure by virtue of elimination of the catastrophic brittle fracture failure mode of normal concrete that could lead to a sudden collapse of a structure [2]. A concrete that is damage tolerant can limit the magnitude of degradation, such as maintaining load-bearing capacity despite suffering damage and potential loss of

Quality of structure (%) 100 Q’ Q

0

t0

t0’

t1’

t1

Time

Fig. 6.1 A resilient structure shows delayed failure, less degradation in function, and recovers functionality faster (dashed line) compared to that of a less resilient one. (Adapted from [1])

6.2 Damage Tolerance and Tension Stiffening of Steel Reinforced ECC

179

structural stiffness. A controlled distributed form of damage that minimizes required repair could lead to rapid recovery and limit economic loss subsequent to a major hazard event. ECC, which is ductile, damage tolerant, with damage in the form of distributed microcracking that allows self-healing (▶ Chap. 10), could support infrastructure designed for high resilience [3]. Fukuyama [4] has been among the first to propose the use of ECC to enhance resilience of building infrastructure subjected to seismic loads. An increasing body of knowledge on the ability of ECC to enhance structural resilience has been accumulated based on a variety of structural scale tests under various loading conditions. This chapter examines experimental findings on the resilient response of structural elements using ECC under seismic and impact load hazards.

6.2

Damage Tolerance and Tension Stiffening of Steel Reinforced ECC

Concrete is generally not recognized as a damage tolerant material. This means that the introduction of a crack or an artificial notch will dramatically reduce the effective tensile strength of the material, more than that due to the loss of crosssectional area due to the presence of the notch. In contrast, ECC is a notch insensitive material [5]. This is best demonstrated by the double edge notched tensile test illustrated in Fig. 6.2a. Despite the notches, microcracks in the notch plane diffuse away as load increases. Experiments with different notch depth reveal

a

b

Failure load/width, P (N/mm)

400 Averaged P for un-notched specimens

300

a 200

a W

100

0

0

0.4 0.8 1.0 0.2 0.6 Normalized crack length, 2a/W

1.2

Fig. 6.2 Damage tolerant behavior of ECC, showing (a) the diffusion of microcrack damage away from the notch plane as tensile load increases and (b) notch insensitivity in load-carrying capacity. A notch-sensitive material would have load capacity decaying faster than the linear line

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6 Resilience of Engineered Cementitious Composites (ECC) Structural Members

that the specimen maintained a load carrying capacity proportional to the remaining ligament area (Fig. 6.2b). Indeed, the fact that the data points lie slightly above the linear decay line of load P suggests that the artificial forcing of failure in the notch plane (caused by the reduction in cross-sectional area on the notch plane) decreases the probability of the specimen naturally failing in the plane with the lowest fiber bridging capacity. The latter is governed by the nonuniform distribution of fibers in the specimen. The damage-tolerant behavior of ECC overcomes one of the major deficiencies of concrete materials, as it is able to carry higher tensile loads beyond cracking. The damage tolerance of ECC translates into enhancement in the tensionstiffening response of R/ECC members. In general, tension-stiffening is defined as the increase in stiffness over the bare steel reinforcement due to the tensile load carried by the concrete material after cracking. Fischer and Li [6] analyzed the load sharing behavior between reinforcing steel (420 MPa yield strength with 25 mm rebar diameter) and ECC when the assembly is loaded beyond the elastic stage. Tensile loading was applied directly on the protruding steel ends (Fig. 6.3a). A notch was introduced to initiate a matrix crack at a specified location. Strain gages embedded inside the steel bar monitored the steel deformation at different positions from the top exposed end of the re-bar. Linear voltage differential transducers

a

b 300 40

R/ECC specimen

250

40 LVDT

120 120 220 235 250 265

Axial Load P (kN)

R/C specimen

120

500

Embedded strain gages

Control

P

200

150

Yielding of reinforcement

100

Bare steel reinforcement 50

0

0

1000

Crack formation starts 2000 3000

P 4000

5000

-6

Axial deformation (mm/mm x 10 )

Fig. 6.3 (a) Specimen configuration (dimensions in mm) and (b) Measured tension-stiffening responses of the R/ECC and R/C specimens. ECC retains load carrying capacity well after steel yields, translating ECC’s tensile ductility into compatible deformation and load sharing with the reinforcing steel

6.2 Damage Tolerance and Tension Stiffening of Steel Reinforced ECC

181

(LVDTs) mounted on the steel reinforcing bar close to the embedded portion were used to measure the overall elongation of the specimen. A control R/C specimen was also tested to observe the change in composite tensile behavior brought about by the damage-tolerant nature of ECC. The tension-stiffening in the R/ECC specimen is definitively different from that of the R/C specimen. The measured axial load is shown in Fig. 6.3b as a function of elongation normalized by the LVDT gage length. As expected, the stiffness of the assembly is significantly higher than the bare steel reinforcement prior to crack formation. Once the concrete crack forms at about 110 kN, a jump in deformation is observed in the R/C specimen, reducing the overall specimen stiffness to essentially the same as that of bare steel. The load bearing capacity of the R/C assembly, especially after steel yielding (at about 2000
106 mm/mm), is only marginally above that of the bare steel. In the case of the R/ECC specimen, multiple microcracks in the ECC diminish the stiffness of the R/ECC assembly compared to the elastic state. However, this postcracking composite stiffness remains substantially higher than that of the bare steel since the ECC continues to carry load in its strainhardening state. After steel yielding, and even when the normalized elongation reaches 5000
106 mm/mm, the assembly continues to carry a load about 50% above that of the bare steel. This implies that the ECC shares tensile load bearing capacity with steel much after plastic yielding of the reinforcing steel in an R/ECC structural element. The load-deformation response of the R/ECC specimen can be further understood in the following manner. For a low applied load, e.g., at 50 kN, both ECC and steel are elastic. At higher applied load P (e.g., at 150 kN), the deformation of the R/ECC assembly is substantially lower than that of the R/C assembly (500
106 mm/mm vs. 1200
106 mm/mm) at the corresponding load due to the fact that the ECC continues to contribute to composite stiffness. At this load, the steel has not yet yielded. At still higher applied load P (e.g., at 280 kN), both ECC and steel undergo inelastic straining. At very large deformation (e.g., at 5% strain much beyond the 0.5% max value in the plot of Fig. 6.3b) of the assembly, the three curves are expected to converge with only the steel contributing to the load bearing capacity (assuming a strain capacity of less than 5% for ECC). The yield plateau in the bare steel is followed by a strain-hardening response that allows the steel to carry substantially higher stress than the yield strength (about 50% more for this grade of steel). The observed tension-stiffening behavior of R/ECC is significantly more effective than R/C and is attributed to the damage tolerant nature of ECC. Load sharing between ECC and steel is further revealed by investigating the internal stress in the matrix and the steel/matrix bond. Figure 6.4 shows a crosssectional cut of the R/C and R/ECC specimens after the tension-stiffening tests. Interface bond cracking and transverse fracture are clearly visible in the R/C specimen, in contrast to the integrity maintained by the R/ECC specimen. It may be interpreted that prior to matrix cracking, load is shared between steel and matrix according to their relative stiffness (Fig. 6.5a). Once concrete fractures, however, the tensile load bearing capacity across the concrete crack drops to zero, transferring all tensile load to the steel reinforcement crossing that crack. While the surrounding

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Fig. 6.4 Cross-sectional view of (a) concrete fracture and steel/concrete interface bond failure in R/C and (b) distributed microcracking in ECC with steel/matrix bond retaining integrity in R/ECC. Compatible deformation between steel and ECC well after the elastic stage of both materials is responsible for the low shear stress at the steel/matrix interface

concrete elastically relaxes, the steel must locally elongate (Fig. 6.5b), resulting in an incompatible deformation and a high shear stress at their interface. This high shear stress is largely responsible for the steel/concrete interface delamination and slippage, radial cracking, bond splitting, and spalling, which are commonly observed damage in R/C structural members under seismic loading. In contrast, the inelastic strain-hardening behavior of ECC (up to several % strain) allows both materials to undergo compatible deformation (Fig. 6.5c) well beyond the plastic yield strain of steel at about 0.2%. This compatible deformation between ECC and steel leads to a relatively low interfacial shear between the two materials and suppresses the loss of structural capacity and the failure modes of R/C members. Beyond maintaining integrity, the ability of ECC to deform compatibly with steel well into the plastic state has important implications in terms of energy absorption of R/ECC members especially during seismic loading. This is because a longer segment of the reinforcing steel can undergo plastic yielding in R/ECC members, whereas plastic yielding of steel may be localized at where concrete cracks in an R/C member. Local necking of the steel segment adjacent to a concrete fracture could lead to collapse of the structural member. In this manner, ECC has the unique ability to delay failure of an R/ECC member through loadsharing with steel loaded well past the elastic deformation stage, thus enhancing structural resilience.

6.3 Performance of R/ECC Elements Under Fully Reversed Cyclic Loads

183

Fig. 6.5 Stress profile in steel and matrix (a) during elastic stage, (b) after concrete cracking; concrete elastically relaxes while local steel section takes over the load shed by concrete, and (c) after ECC microcrack damage with no localized fracture and compatible deformation between steel and ECC. Note that unlike concrete cracks, microcracks in ECC continue to carry tensile load until its strain capacity is exhausted

6.3

Performance of R/ECC Elements Under Fully Reversed Cyclic Loads

6.3.1

Performance of R/ECC Beams Under Flexure

6.3.1.1 ECC Beams Reinforced with Steel To reveal the flexural behavior of R/ECC elements under reversed cyclic loading, 1/5-scale specimens (Fig. 6.6) were investigated by Fischer and Li [7]. The total longitudinal reinforcement ratio was 3.14%, provided by four reinforcement bars (∅10 mm). The control R/C specimen (Fig. 6.6a) has seismic detailing. Transverse reinforcement was provided by stirrups (∅ 3 mm) at 25 mm spacing (ρtransverse = 0.57%) in the joint region and at the base of the cantilever (below 150 mm from the top of the base block) and at 75 mm spacing (ρtransverse = 0.19%) above the 150 mm level. Given the ability of ECC to carry tensile and shear loads, the R/ECC specimen (Fig. 6.6b) was designed to have no shear reinforcement. Lateral loading was applied at the top of the element, with the base block fixed. The displacement-controlled loading sequence is depicted in Fig. 6.7. In some specimens, axial load was applied through an external steel tendon tensioned by hydraulic actuators. The test setup is shown in Fig. 6.8.

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6 Resilience of Engineered Cementitious Composites (ECC) Structural Members

a

b

Fig. 6.6 (a) R/C flexural specimen with transverse reinforcement at 0.57% below and 0.19% above the 150 mm level from the top of the base block, and (b) R/ECC specimen with no shear reinforcement. (After [7])

Drift (%)

Lateral displacement (mm)

Fig. 6.7 Loading sequence of actuator imposed lateral displacement. (After [7])

Loading cycle

The contrasting hysteresis behavior of R/C and R/ECC members shown in Fig. 6.9 confirms the expected failure delay associated with the tensile ductility of ECC. Despite the elimination of transverse reinforcement, failure of the R/ECC was delayed and occurred at a higher ultimate load (16.5 kN vs. 13.8 kN)

6.3 Performance of R/ECC Elements Under Fully Reversed Cyclic Loads

185

Actuator

Tendon

Pin

Specimen Loading frame

Hydraulic actuator Fig. 6.8 Test set-up showing specimen and loading configuration

a 6

4

2

0

2

4

6

8 [Δ/Δ ]

10 0 -20 -20 -16

b 20 Horizontal Load [kN]

Horizontal Load [kN]

20

8

-8

0 8 Drift Ratio [%]

16

6

4

2

0

2

4

6 [Δ/Δ ]

10 0 -20 -20 -16

-8

0 8 Drift Ratio [%]

16

Fig. 6.9 Hysteresis behavior of (a) R/C and (b) R/ECC flexural members. Failure is delayed to a higher load and deformation. The rate of load drop after peak is substantially lower in the R/ECC member due to continued confinement effectiveness of ECC

and at a larger ultimate drift ratio (11% vs. 7%) when compared with that of the R/C element. The mode of failure and functional degradation was also distinctively different (Fig. 6.10). For the R/ECC member, the peak load was governed by localization of a crack at the base of the cantilever beam, at about 11% drift, and rupture of the

186

6 Resilience of Engineered Cementitious Composites (ECC) Structural Members

Fig. 6.10 Deflected shape and damage pattern at 10% drift for (a) R/C and (b) R/ECC flexural members. Bond splitting was followed by spalling of cover in the R/C member. In the R/ECC member, spreading of damage away from the base is evident. The contrast in damage pattern suggests that R/ECC members can recover faster after a seismic event, in some cases with minimal repair

longitudinal steel reinforcement at a drift of 15%. For the R/C member, load capacity and structural stiffness was limited by bond splitting and spalling of the concrete cover at drift of 7%, followed by combined shear and compression failure of the concrete core and buckling of the flexural reinforcement in the plastic hinge region at 9% drift. The hysteresis loops for R/ECC showed a more stable load envelope and substantially larger amount of energy absorption due to elimination of the pinching phenomenon in the R/C member. ECC was effective in serving as confinement for the axial steel that did not buckle even when axial load was added. The limited functional degradation of the flexural element is attributed to the synergistic interaction between ECC and steel, as both materials are able to deform compatibly well into their inelastic regimes. The damage patterns are also significantly different between the R/C and R/ECC members. For the R/C member, shear fractures of the concrete become prevalent beyond steel yielding, ultimately leading to the disintegration of the concrete cover. For the R/ECC member, shear fracture was fully suppressed, replaced by closely spaced flexural microcracks that are distributed over a larger height above the base of the element. This expands the plastic hinge zone and engages a longer segment of steel to undergo plastic yielding and is responsible for the larger amount of energy absorption for the R/ECC member. The expanded plastic hinge zone is reflected in

6.3 Performance of R/ECC Elements Under Fully Reversed Cyclic Loads

187

Fig. 6.11 Contrast in behavior of R/ECC and R/C flexural elements subjected to reversed cyclic loading. The spreading of microcrack damage of R/ECC prevents premature localized failure, allows a larger segment of reinforcing steel in plastic yielding and energy absorption, and avoids the sharp curvature at the beam base that could lead to compression crushing failure

the lowered measured maximum curvature at a given drift and reduces the sectional demand at the base of the flexural element. In addition, the crack widths are tightly controlled (