Thermomechanics & Infrared Imaging, Inverse Problem Methodologies and Mechanics of Additive & Advanced Manufactured Materials, Volume 7: Proceedings of the 2020 Annual Conference on Experimental and Applied Mechanics [1 ed.] 3030598632, 9783030598631

Table of contents :
Preface
Contents
Chapter 1: Visualization and Simulation of Particle Rearrangement and Deformation During Powder Compaction
1.1 Introduction
1.2 Granular Materials
1.3 Compression Apparatus with Optical Access
1.4 Image Processing for Powder Bed Deformation
1.5 Simulation by DEM
1.6 Conclusion
References
Chapter 2: Full-Field Analysis of Strain-Induced Crystallization in Natural Rubber
2.1 Introduction
2.2 Crystallinity Measurement from Heat Source Reconstruction
2.3 Experimental Setup
2.4 Results
2.5 Conclusion
References
Chapter 3: Grain Size and Mechanical Property of Magnesium Experienced Rolling and Post Heat Treatment
3.1 Introduction
3.2 Experimental
3.3 Results and Discussions
3.4 Conclusion
References
Chapter 4: Evaluation and Comparison of the Mechanical Performance of Adhesively Bonded and Self-Piercing Riveted Aluminum Joints Under Tension Loading
4.1 Introduction and Background
4.2 Materials and Methods
4.2.1 Materials
4.3 Results and Discussion
4.4 Conclusion
References
Chapter 5: Dynamic Strain Aging in Additively Manufactured Steel at Elevated Temperatures
5.1 Introduction
5.2 Results
References
Chapter 6: Material Characterization of 3D Printed Components with Different Layup Orientation
6.1 Introduction
6.2 Experiemental Procedure
6.3 Experimental Results
6.4 Fatigue Analysis
6.5 Conclusion
References
Chapter 7: Strain Controlled Tensile Test Through High Rate Thermal Expansion
7.1 Introduction
7.2 Analysis
7.3 Conclusion
Chapter 8: High Temperature Welded Thermocouple Preparation and Calibration
8.1 Introduction
8.2 General Procedure
8.3 Experimental Design
8.4 Results
8.5 Conclusions
Reference
Chapter 9: Analytical Methods to Understand Deformation Mechanics in Additively Manufactured Metals
9.1 Introduction
9.2 Background
9.3 Analysis
9.4 Conclusion
References
Chapter 10: Infrared Thermography Applied to the Assessment of Fatigue Initiation
10.1 Introduction
10.2 Experimental Campaign
10.3 IR Uniaxial Quasi-Static Method
10.4 IR Biaxial Quasi-Static Method
10.5 Results: Uniaxial Tests
10.6 Results: Biaxial Tests
10.7 Conclusions
References
Chapter 11: DIC-IR Analysis of Transient Thermal Stresses
11.1 Introduction
11.2 Experimental Set-up and Procedure
11.3 Results
11.3.1 Thermal Expansion Coefficient Determination
11.3.2 Transient Problem: Temperature
11.3.3 Transient Problem: Strains
11.4 Conclusion
Appendices
References
Chapter 12: The Role of Extraneous Oxygen in the Formation of Oxide Inclusions in 316L Stainless Steel Manufactured by Laser Powder Bed Fusion
12.1 Introduction
12.2 Materials and Methods
12.3 Results and Discussion
12.4 Conclusion
References
Chapter 13: Evolution and Impact of Oxygen Inclusions in 316L Stainless Steel Manufactured by Laser Powder Bed Fusion
13.1 Introduction
13.2 Materials and Method
13.3 Results and Discussion
13.4 Conclusion
References
Chapter 14: Implementing a Commercially Available Self-Locking Screw System in Additively Manufactured Medical Implants
14.1 Introduction
14.2 Materials and Methods
14.3 Analysis
14.4 Conclusion
References
Chapter 15: Experimental Validation and Noise Assessment of the Thermal-VFM
15.1 Introduction
15.2 Identification Method
15.3 Experimental Set-up
15.4 Results and Discussions
15.5 Conclusion
References
Chapter 16: Role of Glass Transition Temperature on Energy Absorption Mechanisms in High Strain Rate Impact Performance of Fiber Reinforced Composites
16.1 Introduction
16.2 Experimental
16.2.1 Materials and Fabrication
16.2.2 Thermomechanical Characterization
16.2.3 Impact Measurements
16.3 Results
16.3.1 Composite Dynamic Mechanical Analysis
16.3.2 Impact Performance Results
16.4 Conclusion
References

Citation preview

Conference Proceedings of the Society for Experimental Mechanics Series

Sharlotte L.B. Kramer Rachel Tighe   Editors

Thermomechanics & Infrared Imaging, Inverse Problem Methodologies and Mechanics of Additive & Advanced Manufactured Materials, Volume 7 Proceedings of the 2020 Annual Conference on Experimental and Applied Mechanics

Conference Proceedings of the Society for Experimental Mechanics Series Series Editor Kristin B. Zimmerman Society for Experimental Mechanics, Inc., Bethel, CT, USA

The Conference Proceedings of the Society for Experimental Mechanics Series presents early findings and case studies from a wide range of fundamental and applied work across the broad range of fields that comprise Experimental Mechanics. Series volumes follow the principle tracks or focus topics featured in each of the Society's two annual conferences: IMAC, A Conference and Exposition on Structural Dynamics, and the Society's Annual Conference & Exposition and will address critical areas of interest to researchers and design engineers working in all areas of Structural Dynamics, Solid Mechanics and Materials Research. More information about this series at http://www.springer.com/series/8922

Sharlotte L.B. Kramer  •  Rachel Tighe Editors

Thermomechanics & Infrared Imaging, Inverse Problem Methodologies and Mechanics of Additive & Advanced Manufactured Materials, Volume 7 Proceedings of the 2020 Annual Conference on Experimental and Applied Mechanics

Editors Sharlotte L.B. Kramer Sandia National Laboratories Albuquerque, NM, USA

Rachel Tighe University of Waikato Hamilton, New Zealand

ISSN 2191-5644     ISSN 2191-5652 (electronic) Conference Proceedings of the Society for Experimental Mechanics Series ISBN 978-3-030-59863-1    ISBN 978-3-030-59864-8 (eBook) https://doi.org/10.1007/978-3-030-59864-8 © The Society for Experimental Mechanics, Inc. 2021 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, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Preface

Residual Stress, Thermomechanics & Infrared Imaging, Inverse Problem Methodologies and Mechanics of Additive & Advanced Manufactured Materials represents one of seven volumes of technical papers to be presented at the 2020 SEM Annual Conference and Exposition on Experimental and Applied Mechanics organized by the Society for Experimental Mechanics scheduled to be held in Orlando, FL, September 14–17, 2020. The complete proceedings also include volumes on: Dynamic Behavior of Materials; Challenges in Mechanics of Time-­ Dependent Materials, Fracture, Fatigue, Failure and Damage Evolution; Advancement of Optical Methods & Digital Image Correlation in Experimental Mechanics; Mechanics of Biological Systems and Materials, Micro- and Nanomechanics & Research Applications; and the Mechanics of Composite, Hybrid & Multifunctional Materials. Each collection presents early findings from experimental and computational investigations on an important area within experimental mechanics; residual stress, thermomechanics, and infrared imaging inverse problem methodologies; and the mechanics of additive and advanced manufactured materials being a few of these areas. In recent years, the applications of infrared imaging techniques to the mechanics of materials and structures has grown considerably. The expansion is marked by the increased spatial and temporal resolution of the infrared detectors, faster processing times, much greater temperature resolution, and specific image processing. The improved sensitivity and more reliable temperature calibrations of the devices have meant that more accurate data can be obtained than were previously available. Advances in inverse identification have been coupled with optical methods that provide surface deformation measurements and volumetric measurements of materials. In particular, inverse methodology was developed to more fully use the dense spatial data provided by optical methods to identify mechanical constitutive parameters of materials. Since its beginnings during the 1980s, creativity in inverse methods has led to applications in a wide range of materials, with many different constitutive relationships, across material heterogeneous interfaces. Complex test fixtures have been implemented to produce the necessary strain fields for identification. Force reconstruction has been developed for high strain rate testing. As developments in optical methods improve for both very large and very small length scales, applications of inverse identification have expanded to include geological and atomistic events. Researchers have used in situ 3D imaging to examine microscale expansion and contraction and used inverse methodologies to quantify constitutive property changes in biological materials. Mechanics of additive and advanced manufactured materials is an emerging area due to the unprecedented design and manufacturing possibilities offered by new and evolving advanced manufacturing processes and the rich mechanics issues that emerge. Technical interest within the society spans several other SEM technical divisions such as composites, hybrids and multifunctional materials, dynamic behavior of materials, fracture and fatigue, residual stress, time-dependent materials, and the research committee. The topic of mechanics of additive and advanced manufacturing included in this volume covers design, optimization, experiments, computations, and materials for advanced manufacturing processes (3D printing, micro- and nano-manufacturing, powder bed fusion, directed

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energy deposition, etc.) with particular focus on mechanics aspects (e.g., mechanical properties, residual stress, deformation, failure, rate-dependent mechanical behavior). Albuquerque, NM, USA Hamilton, New Zealand 

Sharlotte L.B. Kramer Rachael Tighe

Contents

1 Visualization and Simulation of Particle Rearrangement and Deformation During Powder Compaction ���������������������������������������������������������  1 Marcia A. Cooper, Joel T. Clemmer, Michael S. Oliver, Dan S. Bolintineanu, and Jeremy B. Lechman 2 Full-Field Analysis of Strain-Induced Crystallization in Natural Rubber �������������  9 S. Charlès and J. -B. Le Cam 3 Grain Size and Mechanical Property of Magnesium Experienced Rolling and Post Heat Treatment ������������������������������������������������������������������������������� 13 Jiaying Wang and Qizhen Li 4 Evaluation and Comparison of the Mechanical Performance of Adhesively Bonded and Self-Piercing Riveted Aluminum Joints Under Tension Loading ����������������������������������������������������������������������������������������������� 21 Ahmed H. Ibrahim and Duane S. Cronin 5 Dynamic Strain Aging in Additively Manufactured Steel at Elevated Temperatures��������������������������������������������������������������������������������������������� 27 Bonnie R. Antoun, Coleman Alleman, and Joshua Sugar 6 Material Characterization of 3D Printed Components with Different Layup Orientation������������������������������������������������������������������������������� 33 H. Bae, M. Michaelis, V. Black, N. Navarra, and A. Hossain 7 Strain Controlled Tensile Test Through High Rate Thermal Expansion����������������� 43 W. Carter Ralph, James R. Hawbaker, and Benjamin D. Carmichael 8 High Temperature Welded Thermocouple Preparation and Calibration��������������� 47 Shelby Massey 9 Analytical Methods to Understand Deformation Mechanics in Additively Manufactured Metals����������������������������������������������������������������������������� 53 Thomas A. Ivanoff, Nathan M. Heckman, Sharlotte L.B. Kramer, Jonathan D. Madison, Bradley H. Jared, and Brad L. Boyce 10 Infrared Thermography Applied to the Assessment of Fatigue Initiation��������������� 57 V. E. L. Paiva, G. L. G. Gonzáles, J. L. C. Diniz, R. D. Vieira, J. L. F. Freire, and A. L. F. S. d’Almeida 11 DIC-IR Analysis of Transient Thermal Stresses ������������������������������������������������������� 67 J. A. O. González, V. E. L. Paiva, G. L. G. Gonzáles, J. L. F. Freire, and I. Miskioglu

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12 The Role of Extraneous Oxygen in the Formation of Oxide Inclusions in 316L Stainless Steel Manufactured by Laser Powder Bed Fusion����������������������� 75 Pu Deng, Mallikarjun Karadge, Raul B. Rebak, Vipul K. Gupta, Bart C. Prorok, and Xiaoyuan Lou 13 Evolution and Impact of Oxygen Inclusions in 316L Stainless Steel Manufactured by Laser Powder Bed Fusion���������������������������������������������������� 81 Pu Deng, Mallikarjun Karadge, Raul B. Rebak, Vipul K. Gupta, Bart C. Prorok, and Xiaoyuan Lou 14 Implementing a Commercially Available Self-Locking Screw System in Additively Manufactured Medical Implants ��������������������������������������������������������� 87 Ralf D. Fischer, Jan Klasen, and Bart C. Prorok 15 Experimental Validation and Noise Assessment of the Thermal-VFM������������������� 93 Marco Rossi, Marco Sasso, Attilio Lattanzi, and Gianluca Chiappini 16 Role of Glass Transition Temperature on Energy Absorption Mechanisms in High Strain Rate Impact Performance of Fiber Reinforced Composites ��������������������������������������������������������������������������������� 99 Brendan A. Patterson, Casey Busch, Kevin A. Masser, and Daniel B. Knorr

Contents

Chapter 1 Visualization and Simulation of Particle Rearrangement and Deformation During Powder Compaction Marcia A. Cooper, Joel T. Clemmer, Michael S. Oliver, Dan S. Bolintineanu, and Jeremy B. Lechman

Abstract  Two key mechanical processes exist in the formation of powder compacts. These include the complex kinematics of particle rearrangement as the powder is densified and particle deformation leading to mechanical failure and fragmentation. Experiments measuring the time varying forces across a densifying powder bed have been performed in powders of microcrystalline cellulose with mean particle sizes between 0.4 and 1.2 mm. In these experiments, diagnostics measured the applied and transmitted loads and the bulk powder density. Any insight into the particle behavior must be inferred from deviations in the smoothly increasing stress-density compaction relationship. By incorporating a window in the compaction die body, simultaneous images of particle rearrangement and fracture at the confining window are captured. The images are post-processed in MATLAB® to track individual particle motion during compression. Complimentary discrete element method (DEM) simulations are presented and compared to experiment. The comparison provides insight into applying DEM methods for simulating large or permanent particle deformation and suggests areas for future study. Keywords  Granular material · Compression · Fracture · Discrete element method · Imaging

1.1  Introduction Granular materials are commonly processed for applications ranging from pharmaceuticals, to structural materials, to energy storage. Much of the literature data reports experimental compaction curves obtained at slow compression rates on materials where the particles have specific size, morphology, and surface characteristics. However, the compaction behavior of a granular material is strongly dependent on individual particle strength and characterization of the particle mechanics. Few models have incorporated representations of particle strength [1–3], while other particle characteristics of morphology and surface roughness are largely ignored. Computational methods including discrete element method (DEM) [4] and peridynamics [5] offer new capabilities in improved modeling treatments of granular materials in compression. Our efforts are aimed at developing a multi-scale, computational-experimental approach to create novel capabilities enabling process-structureproperty-­performance design and optimization of powder compacts. Uniaxial and triaxial confined compression data of powders are common in the experimental literature. In compression, the processes of particle rearrangement, local elastic and plastic deformation, and fragmentation are all present to varying levels as determined by particle characteristics of strength, size, and shape. These levels often must be inferred from bulk measurements of boundary forces and bed volume. Previous experiments have visualized stress networks in optically accessible experiments [6]. The advancement of X-ray methods is affording new opportunities for particle visualizations in 3D [7–9]. However, current micro-­computed tomography (micro-CT) technology has relatively large voxel sizes and long scan time durations that limit its usefulness to many particle systems of industrial interest. Our research began with uniaxial confined compressions in a traditional cylindrical apparatus with microcrystalline cellulose (MCC) particles of different mean size [10]. We seek to avoid some of the immediate challenges of micro-CT imaging

M. A. Cooper (*) · M. S. Oliver Explosive Technologies, Sandia National Laboratories, Albuquerque, NM, USA e-mail: [email protected] J. T. Clemmer · D. S. Bolintineanu · J. B. Lechman Engineering Sciences, Sandia National Laboratories, Albuquerque, NM, USA © The Society for Experimental Mechanics, Inc 2021 S. L.B. Kramer, R. Tighe (eds.), Thermomechanics & Infrared Imaging, Inverse Problem Methodologies and Mechanics of Additive & Advanced Manufactured Materials, Volume 7, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-030-59864-8_1

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during compression and instead simply apply optical access to our benchtop compression apparatus. This enables high-definition (HD) imaging of the particles during all compression regimes with adequate temporal resolution. Post-processing of the particle motion as viewed along the optically-accessible boundary is useful for correlating to particle simulations across the regimes of particle compression including fracture and crushing. Granular systems are often simulated using the discrete element method. These models represent the system as a discrete collection of interacting particles. There are many varieties of DEMs and the fundamental particles can take on a wide range of shapes and sizes that interact via many different forces. Here, we present some initial DEM results using a model that represents the experimental compression apparatus dimensions and MCC particles. The DEM simulations were run using LAMMPS, a collection of parallel algorithms for the numerical integration of particle dynamics [4]. Model treatments for representing particle deformation and fracture are explored. Ultimately, our goal is to relate macroscale behavior (constitutive model) to particle characteristics as well as process to properties to structure.

1.2  Granular Materials MCC particles consisted of Vivapur® MCC Spheres of type 350 and 1000 from JRS PHARMA (Weissenborn, Germany). The Vivapur® 350 (Batch No. 5135073146 X), and Vivapur® 1000 (Batch No. 5100070317 X) are referred to as V350 and V1000, respectively. Particle size distributions were measured with a Beckman Coulter LS 13320 laser diffraction particle size analyzer with 50% of the particle size distribution equal to 0.473 ± 0.006 mm (V350) and 1.163 ± 0.128 mm (V1000). The particle shapes are roughly spherical and have internal porosity typically in form of a single void as shown in the images of Fig. 1.1. Water content in the particles was measured by drying under vacuum at 105 °C for 24 h and was nominally constant at 4.5%. Literature values for MCC report a value of the elastic modulus of 7.5 GPa [11].

1.3  Compression Apparatus with Optical Access The MCC particles are compressed uniaxially in a load-­controlled manner by the apparatus of Fig. 1.2. The apparatus consists of a pneumatic cylinder (Bimba Flat-I, Model FOS-1251.5-4GLV) to apply force to the top of a confined powder sample. A support structure vertically aligns the axis of the pneumatic cylinder to the axis of the confined sample. The sample is confined by the rectangular walls of the compression die body and confined axially by an upper and lower ram. Three walls of the compression die body are formed by a 304 stainless steel channel with height of 3.81 ± 0.02 cm, wall thickness of 1.91 ± 0.02 cm, and an inner channel that is 0.660 ± 0.02 cm square and machined for a loose slip fit to the square portion of the upper and lower rams. The fourth side of the confiner was 1.588 ± 0.02 cm thick borosilicate glass secured in place with

Fig. 1.1  Scanning electron microscope (a) and micro-CT image (b) of V1000 particles showing nearly spherical particle shape and the existence of a single, large internal void

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Fig. 1.2  Illustration of the compression apparatus with optical access. (a) Isometric view. (b) Side view in cross section

a 0.953 ± 0.02 cm thick stainless-­steel clamp which had a machined window that provided optical access to the test sample located in the inner channel. To cushion the interface between the confiner window and metal surfaces, one layer of 68.6-μm-thick Kapton tape was used and included in the inner channel dimensions. The upper and lower rams are 304 stainless steel square bars machined to 0.645 ± 0.02 cm square to fit the inner channel of the confiner. The load cell end of each ram was turned to 0.643 ± 0.02 cm to mate to the load cell adapters. The lower ram is stationary while the position and force of upper ram is controlled by pressure within the pneumatic cylinder. Each test began with a partially assembled compression apparatus by positioning the confiner/window body and lower ram onto the lower load cell (Transducer Techniques, Model THD-5 K-T-OPT-HT). The sample material is weighed and poured into the confiner channel. For most tests, a carbide tipped hand held engraving tool (like McMaster Carr Part No. 1613 T2) was used to vibrate the setup in order to settle the particles. The carbide tip was held against the plate the confiner rested on for a period of at least 30 s. Then, the upper ram is installed at the upper load cell (Transducer Techniques, Model THD-5 K-T-OPT-HT) and plunger of the pneumatic piston such that it was elevated above the top surface of the particulate sample. The downward motion of the upper ram was initiated and the distance between the ram-mounted flags (Fig. 1.2b) decreased as measured by the laser micrometer (Micro-Epsilon, Model 2500). Pressurization of the pneumatic piston is controlled with a LabView program and a voltage-controlled pressure regulator (Proportion-Air Model QB1SSFEE500) resulting in a constant rate of load applied by the upper ram. Force on the particulate sample increased at the preprogramed loading rate until the maximum load was achieved. The force was applied at a rate of 0.22 kN/min resulting in a varying displacement rate during compression nominally between 0.01 mm/s and 0.0001 mm/s. The maximum applied load was determined by the pneumatic cylinder’s maximum pressure rating of 1.4 MPa and was connected to bottled air. The LabView program controlled the maximum applied force to 6.7 kN. During a test, the LabView program controlled the pneumatic cylinder pressurization and recorded the laser micrometer sensor and load cell data at a rate of 1 Hz. The maximum force was held for 5 min and then released. Figure 1.3 plots the compression curve data from the compression apparatus with optical access (Fig. 1.2) with the data from a cylindrical compression apparatus [10]. The data from the different compression experiments show good agreement in terms of applied stress and strain (Fig. 1.3a). When plotted in terms of relative density and applied stress in a linear-log plot (Fig. 1.3b), the new data from the optical compression apparatus begins at a lower tapped density. This is consistent with prior testing and is a trend with the aspect ratio (initial bed height/length scale of confiner cross section) of the powder bed [10]. The average aspect ratio for the data of Fig. 1.3 is 2.1 (cylindrical) and 1.2 (optical). Video of each experiment was captured using a 2.1-­megapixel HD CVI cube camera adapted to a K-Series long distance video microscope lens and recorded in HD format. Fiber-light illumination was directed into the side of the confiner window. Image size was 1920 × 1080 pixels and image magnification of nominally 152.5 px/mm. Frames extracted from a movie compressing V1000 particles appears in Fig. 1.4. MCC particle fracture and crushing was observed earlier in the compres-

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Fig. 1.3  Data from compression apparatus with optical access (dashed lines) compared to prior data [10] from a cylindrical die body (solid lines) for V1000 and V350 particles. (a) Applied stress versus strain. (b) Relative density versus applied stress

Fig. 1.4  Frames extracted from high-definition movie collected during axial compression. The top ram moves downward in each image frame to compress the particles. The images are annotated with red dots representing the particle centers found through the image processing scheme. The rotated text appearing at the bottom left of each image is a timestamp added by the video recorder. This timestamp is not used in the analysis of particle location and may be ignored in this presentation

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sion process at the boundary with the moving ram (at frame 101) and then throughout the particle bed in the later images (frame 151 and later) of the compression process. The fracture and crushing characteristics were consistent with observations in literature [12]. For the remainder of this work, only the optical compression data from the V1000 particles are presented and compared to simulations.

1.4  Image Processing for Powder Bed Deformation The HD images were processed in Matlab® following the typical initial process for marker-controlled segmentation. This process often precedes a watershed transformation to identify object boundaries. In these images, the slight transparency of the particles and relatively low contrast at the particle boundaries along with the increase in particle boundaries due to fracture and crushing prevented a direct application of watershed segmentation methods. Rather, the centroid of each particle was identified by finding the best marker location that was in the middle of each particle boundary in the gradient magnitude image. This was completed with a polar coordinate transformation and then a minimization of the radial distance from the found particle center and nearest boundaries in a region of interest about each marker. Several frames are extracted from the compression data with the found particle centers annotated by red dots (Fig. 1.4). In general, the image processing found nearly all visible particle centers in successive frames such that quantitative evaluation of particle motion was possible. The individual particle centers throughout the image sequence are annotated in Fig. 1.5a illustrating how a particle moves along the optical window in time. The image colormap changes from cyan to magenta with increasing frame number. The particle centers are plotted in Fig. 1.5b in terms of applied stress and axial strain. The applied stress (Fig. 1.3) measured at the top ram at the time of the extracted frame is plotted on the y-axis. The x-axis strain corresponds to the strain experienced by each particle. Thus, for one compression experiment many stress-strain curves are extracted for the visible particles. Particle displacement is reported relative to the moving ram position and strain is calculated relative to the initial image frame at the start of the applied load.

Fig. 1.5 (a) Frame from image sequence at the start of compression annotated with particle position during compression. The colormap changes from cyan to magenta with increasing frame number. (b) Applied stress versus axial strain of particles

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Fig. 1.6  Rendered images of DEM simulations at 40% strain. In the non-bonded DEM (a) each grain consists of a single particle while in the bonded DEM (b) each grain consists of a few thousand particles. For the bonded DEM, λc is set to 1.5. Particles within each grain are colored uniformly. Note that the final configuration of grains differs

1.5  Simulation by DEM One can subdivide DEMs into two classes, non-bonded and bonded models. In non-bonded models, each particle represents a single grain. This representation allows simulations to reach large scales representing millions of grains. Alternatively, each particle can represent a subdomain of an individual grain. A single grain is therefore made up of many particles which are bonded together with a network of attractive forces that maintains cohesion. This representation allows the shape of grains to deform and allows for the possibility of fracture under a large enough applied force. We are developing both classes of DEMs and are exploring how initial simulation results compare to experimental m ­ easurements. These early results highlight qualitative changes in behavior and identify directions of future research. Two DEMs are used to study the uniaxial loading of granular packings. The first DEM, referred to as the nonbonded model, represents each grain as a single particle. Each particle has translational as well as rotational degrees of freedom. Particles interact with Hertzian contact forces as well as tangential, rolling, and twisting forces. 125 particles were poured into a square box with frictional walls under gravity. Micro-CT images of the VP1000 samples found particles were nearly spherical suggesting this is a reasonable representation of the actual geometry. After particles settled, they were uniaxially compressed at a constant displacement rate. In Fig. 1.6a, a system is rendered at a strain of 40%. Grains have significant overlap and one might expect to be beyond the limit of Hertzian contact. The second DEM, the bonded model, represents each grain as a disordered collection of bonded point particles. While bonded, two particles interact with a piecewise potential. The potential has an equilibrium distance set to the initial distance r0 between the particles to create a stress-free reference state. In compression, particles interact with a repulsive LennardJones (LJ) interaction. In extension, an attractive interaction includes a harmonic term that is continuously smoothed to zero force at a distance of λcr0 where λc represents a critical stretch. If a bond is stretched beyond this threshold, it is permanently broken. Non-bonded particles interact with a repulsive LJ interaction. Specifics of the model are discussed in Ref. [13]. Initially, particles within an individual grain are connected by bonds to provide cohesion. The same granular packing was used to initialize both the bonded and non-bonded DEM simulations. Systems were enclosed by frictionless, repulsive LJ walls and were uniaxially compressed. In Fig. 1.6b, a sample system is rendered for λc = 1.5 at a strain of 40%. At this high value of the critical stretch, effectively no bonds break but the initially spherical grains undergo significant distortion. At smaller values of λc, one finds bonds breaking near the contacts. In Fig. 1.4, one can see significant distortion of MCC grains as well as fracture at high strains suggesting that a bonded DEM is necessary to capture the experimental behavior at large pressures. In Fig. 1.7, normalized stress-strain curves are plotted for both the experimental system (Fig. 1.3) and the two DEMs. The compressive stress is normalized by the elastic modulus of a grain. In the simulations, the strain is calculated using a reference geometry identified when the normalized compressive stress first exceeds 3 × 10−5 to avoid fluctuations at small strains due to system preparation. In the nonbonded DEM, decreasing λc reduces the stiffness of the system and allows one to model

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Fig. 1.7  The compressive stress normalized by the elastic modulus is plotted as a function of strain from experimental and simulated systems

a wide range of responses. It is suggestive that that the experimental results for the compression of MCC (Fig.  1.3) lie between the limits of high and low λc. However, one cannot make any conclusions due to differences between the systems. For instance, the bonded DEM does not contain frictional walls nor do its grains contain internal porosity. We plan to explore these features in greater depth in the future. Several of the bonded models show a discontinuity in the compression curves at low values of strain near 0.1 which corresponds to a large particle rearrangement event. We expect such discontinuities would be less observable for simulations with more particles producing a smoother compression curve.

1.6  Conclusion We present a new experimental apparatus for compression of particles with the ability to watch the particle motion, deformation and ultimately fracture or crush. Through post-­p rocessing of the collected image sequence, the strain and stress for the particles is extracted and used for comparison to DEM simulations. For an initial effort, the comparison between the bonded DEM model with the bulk compression data appears promising. Future work on the advancement of DEM for the prediction of granular material compression will address friction and internal particle porosity. Acknowledgements  This work is funded by Sandia’s Laboratory Directed Research and Development program. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525. This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government.

References 1. Adams, M.J., McKeown, R.: Micromechanical analyses of the pressure-volume relationship for powders under confined uniaxial compression. Powder Technol. 88(2), 155–163 (1996) 2. Krairi, A., Matouš, K., Salvadori, A.: A poro-viscoplastic constitutive model for cold compacted powders at finite strains. Int. J. Solids Struct. 135, 289–300 (2018) 3. Kenkre, V.M., Endicott, M.R., Glass, S.J., Hurd, A.J.: A theoretical model for compaction of granular materials. J. Am. Ceram. Soc. 79(12), 3045–3054 (1996) 4. Plimpton, S.: Fast parallel algorithms for short-range molecular dynamics. J. Comput. Phys. 117, 1–19 (1995) 5. Silling, S.A., Ebrahim, A.: A meshfree method based on the peridynamic model of solid mechanics. Comput. Struct. 83(17–18), 1526–1535 (2005) 6. Hurley, R., Marteau, E., Ravichandran, G., Andrade, J.E.: Extracting inter-particle forces in opaque granular materials: beyond photoelasticity. J. Mech. Phys. Solids. 63, 154–166 (2014)

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7. Jin, H., et  al.: Multiscale XCT scans to study damage mechanism in syntactic foam. In: Lin, M.T., et  al. (eds.) Advancements in Optical Methods & Digital Image Correlation in Experimental Mechanics, Vol. 3. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Berlin (2020) 8. Hurley, R.C., Lind, J., Pagan, D.C., Akin, M.C., Herbold, E.B.: In situ grain fracture mechanics during uniaxial compaction of granular solids. J. Mech. Phys. Solids. 112, 273–290 (2018) 9. Erikson, W.W., Cooper, M.A., Guo, S., Roberts, S.A., Bolintineanu, D.S.: CT scan characterization of thermally damaged energetic materials. In: Proceedings of the 15th International Detonation Symposium, Cambridge, MD (2018) 10. Cooper, M.A., Oliver, M.S., Bufford, D.C., White, B.C., Lechman, J.: Compression behavior of microcrystalline cellulose spheres: Single particle compression and confined bulk compression across regimes. Powder Technol. 374, 10–21 (2020) 11. Jonsson, H., Frenning, G.: Investigations of single microcrystalline cellulose-based granules subjected to confined triaxial compression. Powder Technol. 289, 79–87 (2016) 12. Jonsson, H., Öhman-Mägi, C., Alderborn, G., Isaksson, P., Frenning, G.: Crack nucleation and propagation in microcrystalline-­cellulose based granules subject to uniaxial and triaxial load. Int. J. Pharm. 559, 130–137 (2019) 13. Clemmer, J.T.: Scale invariant dynamics of interfaces and sheared solids, PhD Thesis, Johns Hopkins University (2019)

Chapter 2 Full-Field Analysis of Strain-Induced Crystallization in Natural Rubber S. Charlès and J. -B. Le Cam

Abstract  Since its discovery, X-ray diffraction is the main experimental method used to investigate the strain-induced crystallization of natural rubber. However, this method only provides a single value of the crystallinity at a specific spot. Moreover, the measurement represents a mean value over the beam area. Recently, an alternative method has been proposed based on the fact that the strain-­induced crystallization is an exothermal phenomenon. In this study, the latter method is used to map the crystallinity using a single mechanical loading. Keywords  Strain-induced crystallization · Heat source reconstruction · Infrared thermography

2.1  Introduction Strain-induced crystallization is generally considered to be responsible for the excellent properties of natural rubber, especially its remarkable crack growth resistance. The strain-induced crystallization of rubber is classically studied by using X-ray diffraction (XRD). The XRD technique gives access to the crystallinity but also information of paramount importance on the crystalline phase structure [1–4], chain orientation [5], kinetics of crystallization [6, 7], non-exhaustively. However, this method only provides this information at one point, the point being in fact an area defined according to the X-ray beam. Furthermore, a new method based on infrared thermography has recently been proposed in [8] to determine the crystallinity from the heat source variations due to the material deformation and crystallization. First results using such a method are in good agreement with results obtained from the XRD technique [9]. In the present study, infrared thermography is used during a mechanical test on a natural rubber sample in order to measure heat source field. The method does not only provide the crystallinity in the sample during the test, but also information on the local variation of the phenomenon. First, the methodology used to measure the field of crystallinity is described, especially the theoretical framework to reconstruct heat source field. Then, the experimental setup will be presented. The last section gives the results obtained.

2.2  Crystallinity Measurement from Heat Source Reconstruction Recently, Le Cam [8] proposed a new method to determine experimentally the crystallinity of a rubber specimen during a mechanical loading. This method is based on the measurement of heat produce during the SIC phenomenon. Actually, the total heat source produce by a material during its deformation is given by [10]:

S. Charlès (*) · J. -B.Le Cam University of Rennes 1, IPR (Institut de Physique de Rennes)—UMR 6251, Rennes, France e-mail: [email protected] © The Society for Experimental Mechanics, Inc 2021 S. L.B. Kramer, R. Tighe (eds.), Thermomechanics & Infrared Imaging, Inverse Problem Methodologies and Mechanics of Additive & Advanced Manufactured Materials, Volume 7, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-030-59864-8_2

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S  Dint  T

m A  P   : F T :  T  1 T

with Dint the intrinsic dissipation, also called mechanical dissipation, T the absolute temperature, P the first Piola-­Kirchhoff ∂P  stress tensor, F the deformation gradient tensor. In fact, the term T : F represents the heat source due to thermo-elastic ∂T A  couplings, and the term T :   corresponds to the other thermo-mechanical couplings, such as the SIC. It should be noted T that the term thermo-elastic coupling is used here to mean the coupling between temperature and strain. It is mainly entropic but isentropic couplings can also occur. The method is separated in three steps. 1. First, the total heat source produces by the material is determined from the temperature field measurement obtained using infrared thermography. 2. Then, the heat source part due to SIC is determined, by removing the part due to thermo-elastic couplings. 3. Last, the crystallinity is deduced from the heat source. The total heat source produced by the specimen can be obtained from infrared thermography, using the heat diffusion equation and some assumptions to simplify it [11]. The heat source can be formulated by:



  S  0C      k0  2 D  

with ρ0 the mass density of the material, C the heat capacity, θ the temperature variation, τ a time constant that represents heat exchange with the ambient air, k0 the thermal conductivity and Δ2D the Laplacian operator in the specimen plane. In the case where there is neither intrinsic dissipation nor other thermo-mechanical couplings excepted the SIC phenomenon, the heat diffusion equation leads to:



  0C     

   k0  2 D  Sel  SSIC 

with Sel the heat source from thermo-elastic couplings and SSIC due to SIC phenomenon. The heat source due to thermo-elastic couplings have to be estimated. In this study, it is estimated using the Neo-­Hookean thermo-mechanical model. By assuming that the material is incompressible, and that the biaxiality coefficient is constant over the time, the heat source produce by a Neo-­Hookean material is formulated as:





SNH  NkT   B 2 B 1   B  1  2 B 3

 ddt

with λ the maximal principal stretch, B the biaxiality coefficient, N the number of network chains per unit volume and k the Boltzmann’s constant. While the absolute temperature is approximately constant over the time (a few degrees during the mechanical loading), the reference temperature will be used (T = Tref) in the following. It leads to the final heat source due to Neo-Hookean thermo-elastic couplings:





SNH  2C NH   B 2 B 1   B  1  2 B 3

 ddt

1 with C NH = 2 NkTref the Neo-Hookean constant. Since the heat source due to thermo-elastic couplings can be obtained, the heat source from SIC is deduced with:

 d  SSIC  0 C      k0  2 D  2C NH   B 2 B 1   B  1  2 B 3  dt 





It should be noted that other polynomials can be used to predict the heat source due to thermo-elastic couplings once the crystallization starts, for instance a Yeoh-like polynomial such as used in [9]. Results obtained are very close. Once the heat source due to SIC is known, an equivalent temperature variation due to SIC can be deduced, using the formulation:

2  Full-Field Analysis of Strain-Induced Crystallization in Natural Rubber

Tcryst  t  

11

t

1 SSIC  u  du 0C u 0

Then, the crystallinity χ in percent can be deduced from the temperature variation due to SIC, by considering that the crystallization energy can be approximated by the enthalpy of fusion ΔH:

 t  

0C Tcryst  t  H

2.3  Experimental Setup The present methodology is applied on an unfilled natural rubber (NR). Since this material does not produce any detectable intrinsic dissipation, the only contribution of heat source is due to either thermo-elastic couplings or SIC. Temperature measurements were performed by using a FLIR IR camera with a resolution of 640 × 512 pixels, at the rate of 50 Hz. The calibration of camera detectors was performed using a one-point Non-Uniformity Correction procedure at this frequency. For a range between 5 and 40 °C, the noise equivalent temperature difference is equal to 20 mK. The material emissivity is measured and equal to 0.94, which is in good agreement with the literature.

2.4  Results Results obtained shows that this method allows to not only measure the crystallinity with a spatial resolution of one pixel, but also to map the crystallinity in a given region of interest. Results will be presented and discussed more deeply during the talk.

2.5  Conclusion While XRD gives different information of interest on crystallites, especially their structure and orientation, the technique only allows measuring at a given time, the crystallinity at a point of a given size, depending of the X-ray beam used. To bypass this drawback, a new methodology has been proposed for evaluating the crystallinity, based on the determination of the heat produced by the crystallization phenomenon during the material stretching. This technique enables us to evaluate the crystallinity at several points simultaneously and therefore to map the crystallinity field. Acknowledgements  The authors thank the National Center for Scientific Research (MRCT-CNRS and MI-CNRS), Rennes Metropole and Region Bretagne for financially supporting this work.

References 1. Bunn, C.W.: Molecular structure and rubber-like elasticity I.  The crystal structures of β gutta-percha, rubber and polychloroprene. Proc. R. Soc. Lond. Ser. A Math. Phys. Sci. 180(980), 40–66 (1942) 2. Takahashi, Y., Kumano, T.: Crystal structure of natural rubber. Macromolecules. 37(13), 4860–4864 (2004) 3. Immirzi, A., Tedesco, C., Monaco, G., Tonelli, A.E.: Crystal structure and melting entropy of natural rubber. Macromolecules. 38(4), 1223– 1231 (2005) 4. Rajkumar, G., Squire, J.M., Arnott, S.: A new structure for crystalline natural rubber. Macromolecules. 39(20), 7004–7014 (2006) 5. Toki, S., et al.: Strain-induced molecular orientation and crystallization in natural and synthetic rubbers under uniaxial deformation by in-situ synchrotron X-ray study. Rubber Chem. Technol. 77(2), 317–335 (2004) 6. Toki, S., Fujimaki, T., Okuyama, M.: Strain-induced crystallization of natural rubber as detected real-time by wide-angle X-ray diffraction technique. Polymer. 41(14), 5423–5429 (2000) 7. Trabelsi, S., Albouy, P.A., Rault, J.: Effective local deformation in stretched filled rubber. Macromolecules. 36(24), 9093–9099 (2003)

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8. Le Cam, J.B.: Strain-induced crystallization in rubber: A new measurement technique. Strain. 54(1), e12256 (2018) 9. Le Cam, J.B., Albouy, P.A., Charlès, S.: Comparison between X-ray diffraction and quantitative surface calorimetry based on IR thermography to evaluate strain-induced crystallinity in natural rubber. Rev. Sci. Instrum. 91, 044902 (2020) 10. Balandraud, X., Le Cam, J.B.: Some specific features and consequences of the thermal response of rubber under cyclic mechanical loading. Arch. Appl. Mech. 84(6), 773–788 (2014) 11. Samaca Martinez, J.R., Balandraud, X., Toussaint, E., Le Cam, J.B., Berghezan, D.: Thermomechanical analysis of the crack tip zone in stretched crystallizable natural rubber by using infrared thermography and digital image correlation. Polymer. 55(24), 6345–6353 (2014)

Chapter 3 Grain Size and Mechanical Property of Magnesium Experienced Rolling and Post Heat Treatment Jiaying Wang and Qizhen Li

Abstract  The pure magnesium (Mg) sheet with remarkably refined grains was achieved through the route of 200 °C rolling and 400 °C post heat treatment. To explore the relations of grain size and mechanical properties of pure Mg at room temperature, the rolled Mg sheets were kept at 400 °C for 10 min, 30 min, 2 h, 4 h, 8 h, and 24 h to get different grain sizes. The microstructures were characterized through optical microscopy (OM) after metallographic preparation. Although the grain size was not very sensitive to the heat time, the longer the heat time was, the larger the average grain size was, and the wider size distribution was. Stress-strain curves were obtained through testing. The yield strength and tensile strength of the rolled Mg were the highest, but the fracture strain was only 6%. For heat treated samples, 24 h treatment sample had the highest strength and 8 h treatment sample had 13% strain at fracture. Keywords  Magnesium · Rolling · Heat treatment · Grain size · Mechanical properties

3.1  Introduction Recently, Mg and its alloys are increasingly applied in aerospace [1, 2], medical science [3], and the automotive industry [4]. This is due to their special merits, such as low density, good electrical and thermal conductivity, nontoxicity, and biocompatibility [5, 6]. Applying the Mg widely is very economical and sustainable [7] because the amount of element Mg is abundant on the earth [8], especially in the ocean [9]. Most Mg and its alloys on the market are produced by casting. Owing to the poor mechanical properties and low corrosion resistance [10, 11], casting Mg and its alloys are difficult to have excellent performance and extensive application. Previous research has shown that plastic deformation can effectively refine grains and change the mechanical behaviors of Mg and its alloys [12]. For mechanical behaviors, some of them are better, others are worse. The relations between grain size and strength can be explained and analyzed qualitatively by the Hall-Petch relation [13, 14]. There are some common severe plastic deformation processes such as hot-rolling [15–17], friction stir processing [18, 19], high strain rate rolling [20, 21], and equal channel angular pressing [22–27]. Rolling is a traditional and outstanding plastic deformation processing method that has been widely used. It can effectively break coarse grains, reduce or eliminate casting defects, transform as-cast structures into deformed structures, and enhance the processing performance of metals and alloys. Moreover, rolling operation is simple, and the cost is low [28, 29]. In this paper, the effects of rolling and post treatment on microstructure and correlated mechanical behaviors of pure Mg were investigated.

J. Wang · Q. Li (*) School of Mechanical and Materials Engineering, Washington State University, Pullman, WA, USA e-mail: [email protected] © The Society for Experimental Mechanics, Inc 2021 S. L.B. Kramer, R. Tighe (eds.), Thermomechanics & Infrared Imaging, Inverse Problem Methodologies and Mechanics of Additive & Advanced Manufactured Materials, Volume 7, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-030-59864-8_3

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3.2  Experimental In this research, the first step was to process pure Mg by rolling and thermal treating, and the second step was to obtain microstructures and test mechanical properties. Pure Mg block with 33 mm diameter and 8 mm height was placed in a 400 °C furnace for 3 h. Then the rolling process was carried out. The Mg ingot was put into a 200 °C furnace for 5 min after each rolling. The decreased height of each rolling was about 0.04 mm. Finally, a 1 mm thick Mg sheet was obtained. Then, the rolled Mg sheets were heated in a 400 °C furnace for 10 min, 30 min, 2 h, 4 h, 8 h and 24 h to obtain different samples. The sample microstructure was characterized by optical microscopy (OM) after metallographic preparation. The sample was first roughly and finely grounded by 600 grit and 1500 grit sandpapers, then polished with sandpaper up to 2500 grit on a polishing machine and washed continuously with a small flow of alcohol. Alcohol reduced the temperature, removed the surface impurities, and prevented metal surface oxidation. The polished Mg surface was bright without scratch. Then the specimen was rinsed with alcohol and dried with cold air for subsequent etching. The etching solution was composed of 1 mL alcohol, 3 mL distilled water, 1 mL 1 M acetic acid, and 1 mL 4.67wt.% picric acid. Next, the etched sample was washed with alcohol and dried with cold air. Then the metallography could be observed under an optical microscope. Photographs with different magnifications were taken for subsequent microstructural analysis. The tensile specimen was extracted from the Mg sheet. The tensile tests was undertaken by using a testing machine at a ~10−3/s strain rate under ambient conditions. Then, yield strength, tensile strength, and strain at fracture were obtained.

3.3  Results and Discussions The microscopic image showed the sample microstructure. After measuring about 1500 grains, the grain size distribution of each sample was obtained. The grain average diameter of each sample was also obtained by calculation. The homogeneity of grain size was reflected by the shape of the distribution curve in Figs. 3.1–3.4 and the variance in Table 3.1. The grain size of the original Mg was about 104.19 ± 60.91 μm. The original grains were large and uneven, as illustrated in Fig. 3.1. It was found from Table 3.1 that the grains were obviously refined after rolling. The heat treatment made the grains grow slightly. The grain sizes of 10 min and 30 min heat treatment in Fig. 3.2 were almost the same. And in Fig. 3.3, the grain sizes of 2 h, 4 h, and 8 h heat treatment were also similar. Therefore, the grain growth trend was not obvious during 2–8 h heat treating. By extending the heat treatment time to 24 h, the grain size had a significant increment, as shown in Fig. 3.4. At the same time, the size difference between grains became more serious with increasing treated time. Figure 3.5 illustrated the tensile stress-strain curves of different samples. The data were summarized in Table 3.1. In the early stage of deformation, the stress-strain curves rose rapidly. With further tension, the stress-strain curves tended to be flat. Also, rolled Mg with heat treatment for 10 min, 30 min, 2 h, 4 h, and 8 h had very similar results in the mechanical property tests. The curves of these samples were almost overlapped. Besides, after 8 h post treatment, strain at fracture of Mg was improved to 13%. Compared with post treatment Mg, the rolled Mg had the highest yield strength value and tensile strength value because of grain refinement strengthening. The fine grain strengthening of metallic materials at room temperature had become a recognized fact. And the classical Hall-Petch relationship, shown as Eq. (3.1), had been well proved in many materials. σ was yield strength, d was average diameter, σ0 and K were constants related to the crystal type. In the Hall-Petch relation, the grain size could be explained from the viewpoint of grain boundary and dislocation.



  0  k

1 d

(3.1)

In the rolling process, many dislocations were produced and became into boundaries in the original large grains, and the grains were refined into small grains by these boundaries. In the same volume of metal, the finer the grain was, the more the grain boundaries and obstacles. The yield strength of pure Mg was determined by the resistance that must be overcome by dislocation movement in the crystal under stress. In the process of dislocation movement, when

3  Grain Size and Mechanical Property of Magnesium Experienced Rolling and Post Heat Treatment

15

Fig. 3.1 (a) Original Mg microstructure and (b) grain size distribution graph

the dislocation moved to the grain boundary, the dislocation must overcome the barriers of the grain boundary so that the deformation could be transferred to another grain. Besides, the interaction between dislocations and other crystal defects hindered the movement of dislocations. So, the smaller the grain, the greater the yield strength of the Mg. For the rolled Mg, the work hardening phenomenon made the Mg in an unstable high-energy state. Therefore, the rolled sample had the highest strength and the weakest plasticity. At the same time, the strain at fracture was also influenced by grain size. This was shown in heat treatment Mg samples. The finer the grain was, the smaller the stress concentration was, and the crack was not easy to initiate. Moreover, there were more grain boundaries, which could absorb more energy in the process of fracture and show ­better plasticity. This was why rolled Mg after 24 h heat treatment had a lower strain at fracture. Although grain grew up markedly after the heat treatment, the yield strength and tensile strength were excellent. The stress-strain curve of rolled Mg alloy after 24 h heat treatment was a unique S shape because of the different microstructure. The grain size of 24  h post heat treatment sample was large, but the grain uniformity was very poor. As dislocations moved in these grains, and the resistance was also great. So, even if rolled Mg with 24 h heat treatment had larger grains, its yield strength value and tensile strength value were higher than those of other post treated samples.

3.4  Conclusion The microstructure and mechanical properties of rolled Mg and rolled Mg with different heat treatment conditions were studied and the following conclusions were drawn. First, Mg sheets with fine-grained and high-strength were prepared by the rolling process. The grain size of rolled Mg was the smallest, about 15.62 μm, and the grains were most uniform. The yield and tensile strength were also excellent. In terms of plasticity, the rolled Mg was not very good, which was reflected from the low strain at fracture because of the work hardening. Second, the heat treatment after rolling made the grains grow. The longer the heating time was, the larger and more uneven the grains were. However, the time of heat treatment and the grain size was not a linear correlation. At a certain time, the increase in heating time had some effect on the grain size. Third, grain refinement was an efficient way to enhance the mechanical properties of pure Mg. This followed the classical Hall-Petch relationship. Compared with the heat-treated samples, the strength of the rolled Mg was higher due to the finer grains. Among the heat-treated samples, the finer grains provided higher strain at fracture.

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Fig. 3.2 (a) Rolled Mg microstructure and (b) grain size distribution graph; (c) rolled Mg with 10 min heat treatment microstructure and (d) grain size distribution graph; (e) Rolled Mg with 30 min heat treatment microstructure and (f) grain size distribution graph

3  Grain Size and Mechanical Property of Magnesium Experienced Rolling and Post Heat Treatment

17

Fig. 3.3 (a) Rolled Mg with 2 h heat treatment microstructure and (b) grain size distribution graph; (c) rolled Mg with 4 h heat treatment microstructure and (d) grain size distribution graph; (e) rolled Mg with 8 h heat treatment microstructure and (f) grain size distribution graph

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Fig. 3.4 (a) Rolled Mg with 24 h heat treatment microstructure and (b) grain size distribution graph Table 3.1  Grain sizes and mechanical properties of different Mg samples Material Rolled 400 °C, 10 min 400 °C, 30 min 400 °C, 2 h 400 °C, 4 h 400 °C, 8 h 400 °C, 24 h

Grain size (μm) 15.62 ± 5.53 23.16 ± 9.28 24.63 ± 9.70 32.42 ± 11.20 31.22 ± 11.88 30.32 ± 11.60 86.25 ± 31.85

Yield strength (MPa) 123 83 76 87 81 83 124

Tensile strength (MPa) 206 177 171 177 180 181 190

Strain at fracture (%) 6 10.3 10 10.5 8.5 13 7

Fig. 3.5  Tensile stress-strain curves of different pure Mg samples Acknowledgements  The authors appreciate the support from US Department of Energy, Office of Basic Energy Sciences (No. DESC0016333).

References 1. Eliezer, D., Aghion, E., Froes, F.S.: Magnesium science, technology and applications. Adv. Perform. Mater. 5, 201–212 (1998) 2. Gwynne, B., Lyon, P.: Magnesium alloys in aerospace applications, past concerns, current solutions. In: Triennial International Aircraft Fire and Cabin Safety Research Conference, 29 October–1 November, 2007

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3. Li, N., Zheng, Y.: Novel magnesium alloys developed for biomedical application: A review. J. Mater. Sci. Technol. 29, 489–502 (2013) 4. Kulekci, M.K.: Magnesium and its alloys applications in automotive industry. Int. J. Adv. Manuf. Technol. 39, 851–865 (2008) 5. Mordike, B., Ebert, T.: Magnesium: Properties—applications—potential. Mater. Sci. Eng. A. 302, 37–45 (2001) 6. Lupescu, S., Istrate, B., Munteanu, C., Minciuna, M.G., Focsaneanu, S., Earar, K.: Characterization of some master mg-X system (Ca, Mn, Zr, Y) alloys used in medical applications. Rev. Chim. 68, 1408–1413 (2017) 7. Aghion, E., Bronfin, B.: Magnesium alloys development towards the 21st century. Mater. Sci. Forum. 350, 19–30 (2000) 8. Handler, M.R., Baker, J.A., Schiller, M., Bennett, V.C., Yaxley, G.M.: Magnesium stable isotope composition of Earth's upper mantle. Earth Planet. Sci. Lett. 282, 306–313 (2009) 9. Culkin, F., Cox, R.: Sodium, potassium, magnesium, calcium and strontium in sea water. Deep Sea Res. Oceanogr. Abstr. 13(5), 789–804 (1966) 10. Harris, I., Varley, P.: Factors influencing brittleness in aluminium-­magnesium-­silicon alloys. J. Inst. Metals. 82, 379 (1954) 11. Zeng, R.-c., Zhang, J., Huang, W.-j., Dietzel, W., Kainer, K., Blawert, C., Wei, K.: Review of studies on corrosion of magnesium alloys. Trans. Nonferrous Metals Soc. China. 16, s763–s771 (2006) 12. Kubota, K., Mabuchi, M., Higashi, K.: Review processing and mechanical properties of fine-grained magnesium alloys. J. Mater. Sci. 34, 2255–2262 (1999) 13. Armstrong, R.W., Li, Q.: Dislocation mechanics of high-rate deformations. Metall. Mater. Trans. A. 46, 4438–4453 (2015) 14. Somekawa, H., Mukai, T.: Hall–Petch breakdown in fine-grained pure magnesium at low strain rates. Metall. Mater. Trans. A. 46, 894–902 (2015) 15. Cao, F., Shi, Z., Song, G.-L., Liu, M., Dargusch, M.S., Atrens, A.: Influence of hot rolling on the corrosion behavior of several mg–X alloys. Corros. Sci. 90, 176–191 (2015) 16. Jiang, B., Xiang, Q., Atrens, A., Song, J., Pan, F.: Influence of crystallographic texture and grain size on the corrosion behaviour of as-­extruded mg alloy AZ31 sheets. Corros. Sci. 126, 374–380 (2017) 17. Li, Q., Tian, B.: Mechanical properties and microstructure of pure polycrystalline magnesium rolled by different routes. Mater. Lett. 67, 81–83 (2012) 18. Ma, Z.: Friction stir processing technology: A review. Metall. Mater. Trans. A. 39, 642–658 (2008) 19. Besharati-Givi, M.-K., Asadi, P.: Advances in Friction-Stir Welding and Processing. Elsevier, Amsterdam (2014) 20. Chen, C., Chen, J., Yan, H., Su, B., Song, M., Zhu, S.: Dynamic precipitation, microstructure and mechanical properties of mg-5Zn-­1Mn alloy sheets prepared by high strain-rate rolling. Mater. Des. 100, 58–66 (2016) 21. Zhu, S., Yan, H., Chen, J., Wu, Y., Su, B., Du, Y., Lian, X.: Feasibility of high strain-rate rolling of a magnesium alloy across a wide temperature range. Scr. Mater. 67, 404–407 (2012) 22. Iwahashi, Y., Horita, Z., Nemoto, M., Wang, J., Langdon, T.G.: Principle of equal-channel angular pressing for the processing of ultra-fine grained materials. Scr. Mater. 35, 143–146 (1996) 23. Valiev, R.Z., Langdon, T.G.: Principles of equal-channel angular pressing as a processing tool for grain refinement. Prog. Mater. Sci. 51, 881–981 (2006) 24. Li, Q.: Evolution of heterogeneous microstructure of equal-channel angular pressed magnesium. In: Magnesium Technology 2019, pp. 59–63. Springer, Cham (2019) 25. Li, Q., Jiao, X.: Exploration of equal channel angular pressing routes for efficiently achieving ultrafine microstructure in magnesium. Mater. Sci. Eng. A. 733, 179–189 (2018) 26. Jiao, X., Li, Q.: An observation about global microstructure of ECAPed magnesium. Emerg. Mater. Res. 3, 261–264 (2014) 27. Li, Q., Jiao, X.: Recrystallization mechanism and activation energies of severely-deformed magnesium during annealing process. Materialia. 5, 100188 (2019) 28. Liu, X.-h.: Prospects for variable gauge rolling: Technology, theory and application. J. Iron Steel Res. Int. 18, 1–7 (2011) 29. Ataka, M.: Rolling technology and theory for the last 100 years: The contribution of theory to innovation in strip rolling technology. ISIJ Int. 55, 89–102 (2015)

Chapter 4 Evaluation and Comparison of the Mechanical Performance of Adhesively Bonded and Self-Piercing Riveted Aluminum Joints Under Tension Loading Ahmed H. Ibrahim and Duane S. Cronin

Abstract  Vehicle weight reduction and fuel efficiency can be improved using multi-material structures incorporating high-performance materials such as aluminum, ultra-­high-­strength steel, and carbon fibre reinforced polymer composites. Critical to enabling the adoption of aluminum alloys in lightweight multi-material structures are robust joining methods that play a key role in structural performance; crashworthiness; durability; and noise, vibration and harshness. Recent studies have investigated the mechanical performance parameters (i.e. strength, stiffness and energy absorption) of joints created using adhesive bonding and self-piercing riveting (SPR). However, a number of questions regarding the implications of sheet thickness selection on the mechanical performance parameters of adhesively bonded and SPR aluminum joints subjected to tension loading remain to be addressed in order to improve the mechanical performance of joined structures and maximize weight reduction opportunities. In the present study, experimental testing of adhesively bonded and SPR aluminum joints under tension loading was investigated to evaluate the mechanical performance parameters of individual joining methods across a range of typical aluminum alloy sheet thicknesses used in transportation structures (1, 2 and 3 mm). The experimental results showed that increasing sheet metal thickness significantly improved joint strength and stiffness response in both adhesively bonded and SPR joints owing to reduced compliance of the joint. While adhesively bonded joints provided up to 20.5% higher joint strength and up to 421% higher stiffness response, SPR joints achieved up to 353% higher energy absorption. In adhesively bonded joints, energy absorption increased almost linearly with sheet thickness; however, SPR joints demonstrated an optimum energy absorption for a particular sheet thickness. Keywords  Self-piercing riveting · Adhesive bonding · Aluminum joints · Hybrid joining · Vehicle weight reduction

4.1  Introduction and Background Passenger vehicle and light truck emission standards and regulations established worldwide have motivated transportation manufacturers to achieve a significant reduction in vehicle weight and improve fuel economy [1]. While advances have been achieved in drivetrain efficiency and vehicle aerodynamics, recent studies have demonstrated that significant weight reduction can be realized by adopting multi-material structures incorporating light-weight high-­performance materials, such as aluminum, ultra-high-­strength steel and carbon fibre reinforced polymer composites [2–4]. Robust joining methods with capabilities to join aluminum in multi-material structures offer weight reduction opportunities without sacrificing structural performance; crashworthiness; durability; and noise, vibration and harshness. Although structural adhesives have enabled efficient and reliable joining of similar and dissimilar light-weight materials, fixturing of adhesively bonded parts and curing time required for joint strength development are two major challenges that need to be addressed [5, 6]. Thus, researchers have investigated augmenting adhesive bonding with mechanical joining (i.e. hybrid joining). In particular, recent work has focused on combining structural adhesives with self-piercing riveting (SPR) to overcome the challenges associated with adhesive bonding and improve the strength and stiffness of SPR joints [7–9]. According to Di Franco et al. [8], there is a need for additional research in the hybrid joining space to improve the strength, stiffness, energy absorption of hybrid joints. In order to address this gap and advance the research in hybrid joining while achieving weight reduction requirements, it is critical to address the following literature limitations: (1) evaluating and comparing the joint strength, A. H. Ibrahim (*) · D. S. Cronin Department of Mechanical and Mechatronics Engineering, University of Waterloo, Waterloo, ON, Canada e-mail: [email protected] © The Society for Experimental Mechanics, Inc 2021 S. L.B. Kramer, R. Tighe (eds.), Thermomechanics & Infrared Imaging, Inverse Problem Methodologies and Mechanics of Additive & Advanced Manufactured Materials, Volume 7, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-030-59864-8_4

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stiffness and energy absorption of individual joining methods to achieve the maximum performance improvement from adopting hybrid joining, and (2) investigating the implications of sheet thickness selection on the mechanical performance parameters of individual joining methods to determine the optimum sheet metal thickness required for maximizing structure weight reduction. The H-specimen test, comprising two U-sections, has been successfully adopted for the testing of SPR aluminum joints [10], SPR multi-material joints [11], adhesively bonded steel joints [12] and hybrid (bonding/resistance spot welding) steel joints [13] under tension loading. A study on adhesively bonded, SPR and hybrid joints has been carried out by Meschut et al. [11] comparing the effect of joining methods on the maximum shear and tension strengths using single-lap shear and LWF-KS2 (i.e. two U-sections) test specimens made of aluminum (AA6016-T6) and press hardened steel. The study reported that adhesive-only bonding outperformed SPR joining and hybrid joining in terms of shear strength. In addition, SPR-only joints exhibited 43% lower strength under tension loading compared to shear loading. However, this study did not consider evaluating adhesively bonded joints under tension loading. Lee et al. [14] compared the crashworthiness of SPR joined, adhesively bonded, and spot-welded double hat channels, composed of steel and aluminum. The authors identified adhesive bonding and SPR joining as strong alternatives to spot welding in lightweight applications due to their high specific energy absorption capabilities in axial crush tests. Failure analysis of the double-hat channels demonstrated that the failure modes of SPR and adhesive joints were tail pull-out (i.e. loss of mechanical interlock between rivet tail and bottom sheet) and cohesive failure (i.e. failure within the adhesive layer) due to peeling, respectively. This work has highlighted potential failure modes of individual joining methods when subjected to mixed modes of loading during axial crush tests; however, evaluating individual joining methods under tension loading, which is commonly associated with the highlighted potential modes of failure, was not investigated. Several studies have shown that sheet thickness, which directly correlates to structural weight, influences strength, stiffness and energy absorption of joined structures. da Silva et al. [15] have investigated the effect of sheet thickness on adhesively bonded single-lap shear joint strength, illustrating that the increase in joint strength is almost linear with the increase in sheet thickness. However, the effect of sheet thickness on adhesively bonded and SPR joints under tension loading was not considered in this study. Furthermore, Han et  al. [16] have adopted cross-tension test specimens made from aluminum (AA5754) to investigate the mechanical performance of SPR and resistance spot welding joints with symmetrical stacks of (1 + 1) mm, (2 + 2) mm, and (3 + 3) mm. The SPR joints subjected to tension loading showed an increase in joint strength and energy absorption with the increase in stack thickness. Similar to the previous study [15], adhesively bonded joints under tension loading were not considered, thus additional work to investigate the implications of sheet thickness on the mechanical performance parameters of adhesively bonded joints is required. In the current study, an H-specimen test was used to evaluate the mechanical performance parameters (strength, stiffness, energy absorption) of adhesively bonded and SPR aluminum AA6061-T6 joints under tension loading. The mechanical performance parameters were compared between the two joining methods across a range of aluminum sheet thicknesses, and two-way repeated-measures ANOVA with Tukey posthoc analysis was used to interpret the implications of sheet thickness and joining method selections on the mechanical performance of the joints.

4.2  Materials and Methods 4.2.1  Materials An artificially aged precipitation-hardened aluminum alloy, AA6061-T6, was used in this study because it is a commonly adopted alloy in different industries for a wide range of structural applications, is readily available at a range of sheet thicknesses, and has relatively comparable yield strength, tensile strength, and elongation to the aluminum alloys used in the transportation industry. Three sheet thicknesses (1, 2 and 3 mm), commonly used in the transportation industry, were used to fabricate the U-sections which was designed to facilitate the fabrication from tempered rolled aluminum blanks. A two-part structural toughened epoxy adhesive (07333, 3M Canada) designed for automotive applications was applied to the adhesively bonded specimens. Due to the difference in sheet thickness, three rivet models with a diameter of 5 mm and two die models were utilized in three rivet/die combinations (C50541A/DP09–200, C50642A/DP09–200, K50844A/DP10–200; Henrob, Atlas Copco USA) according to the manufacturer recommendation for each stack thickness. Specimen Preparation  In order to fabricate the U-sections required for joining the H-specimens, sheet metal blanks were cut using a water jet cutter to the required dimensions (Fig. 4.1a, b), then, bent into the final geometry (Fig. 4.1c) using a press brake. Adhesively bonded specimens were grit-­blasted in a cross-pattern using 80 grit aluminum oxide media at 65 psi

4  Evaluation and Comparison of the Mechanical Performance of Adhesively Bonded and Self-Piercing Riveted Aluminum Joints…

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followed by acetone degreasing and a­ ir-­drying. A preliminary surface preparation study was carried out to compare different mechanical and chemical surface treatment techniques, and grit-blasting was found to consistently improve joint strength by achieving cohesive failure mode. Surface roughness values measured using a stylus profilometer (Surtronic 25, Taylor Hobson, England) were as follows: Ra = 1.58 μm ± 0.08 (SE), Rz = 10.53 μm ± 0.58 (SE), Rt = 15.8 μm ± 1.68 (SE). Teflon spacers were applied to obtain a bond line thickness of 0.3 mm and to facilitate the removal of adhesive spew and minimize the edge effects. The adhesive was applied to an area of 18 × 50 mm2 to match the standard width of flanges seen in transportation structures; after that, the U-sections were mated and fixtured, then cured at 80° C for 90 min. SPR specimens did not require surface preparation, but a high-resolution 3D printed template was required in order to achieve a rivet location within ± 0.2 mm from the center of the joining area (Fig. 4.1d). Joint Assessment  Prior to the mechanical testing, the quality of the SPR joints for each stack was assessed based on the physical attributes of the joint cross-section. Each stack was assessed in terms of mechanical interlocking (i.e. rivet flaring and undercut, head height, bottom thickness, top and bottom seals, and leg buckling, bending and fracturing). Adhesively bonded joints were assessed in terms of bond line thickness and surface area. An Optodigital microscope (VHX-5000, Keyence Canada) was used to capture high-­resolution images under 20× magnification, and to perform the required measurements for assessment (Fig. 4.2). Mechanical Testing  Adhesively bonded and SPR joined H-specimens were tested using a custom-made hydraulic load frame having a 4″ bore × 6″ stroke cylinder (Cylinders and Actuators; Parker Canada) controlled using a hydraulic controller (MTS 407; MTS USA) at a constant crosshead velocity of 6 mm/min. The load data was measured using a 90 kN load cell and the displacement was measured using a linear variable differential transformer (LVDT). A high-­resolution digital singlelens reflex (DSLR) camera (D3200, Nikon Japan) fitted with a 105 mm f2.8 macro lens was used to record each test and optically track the localized separation of the H-specimens.

4.3  Results and Discussion The H-specimen test results for the adhesively bonded and SPR joints were evaluated for symmetrical stack thicknesses of (1 + 1) mm, (2 + 2) mm, and (3 + 3) mm. The mechanical performance parameters of adhesively bonded joints were compared with those of SPR joints, made using the manufacturer recommended process variables for each stack. Force-­ displacement response of the adhesively bonded joints (Fig. 4.3) showed higher strength and stiffness compared to SPR joints (Fig. 4.4); however, the latter joint failed at significantly higher displacement values achieving higher energy absorption. In addition, adhesively bonded joints showed a sharp change in stiffness prior to reaching the peak force, while SPR joints demonstrated a smooth gradual drop in the stiffness. In adhesively bonded joints, the larger load bearing area (18 W × 50 L mm2), compared to SPR joining, distributed the maximum load along the two 50 mm long edges of the bonding area, and when a crack initiated the stiffness exhibited a sharp drop due to the overall joint stiffness degradation caused by

Fig. 4.1 (a) Dimensions of the U-sections in millimetres, (b) Sheet metal after water-jet cutting, (c) U-sections bent into the final geometry, and (d) 3D printed template used for achieving the required SPR rivet location

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Fig. 4.2  Optodigital microscope images to assess the bond line thickness of adhesive joints (a), and measure the physical attributes of SPR joints (b)

Fig. 4.3  Force-displacement response of the adhesively bonded H-specimens under tension loading

Fig. 4.4  Force-displacement response of the SPR joined H-specimens under tension loading

adhesive damage. Also, the adherend exhibited progressive bending deformation around the edges, progressing as the crack propagated through the width of the bonding area. The crack progressed from the edges toward the centerline of the bonded area until the joint failed due to cohesive failure. In contrast, tension loading of SPR joints induced localized plastic deformation in the H-specimen around the rivet causing the rivet tail to lose the mechanical interlock with the bottom sheet and fail in a tail pull-out mode. Figure 4.5 shows a strong positive correlation between the sheet metal thickness and joint strength and stiffness response. The results of the two-way repeated-measures ANOVA with Tukey posthoc analysis revealed that there was a significant main effect of sheet thickness on joint strength (p