Dynamic Behavior of Materials, Volume 1

River Rapids Conference Proceedings of the Society for Experimental Mechanics Series Dynamic Behavior of Materials, Volume 1 Dan Casem Leslie Lamberson Jamie Kimberley Proceedings of the 2016 Annual Conference on Experimental and Applied Mechanics River Publishers

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

River Publishers Dan Casem • Leslie Lamberson • Jamie Kimberley Editors Dynamic Behavior of Materials, Volume 1 Proceedings of the 2016 Annual Conference on Experimental and Applied Mechanics

Published, sold and distributed by: River Publishers Broagervej 10 9260 Gistrup Denmark www.riverpublishers.com ISBN 978-87-7004-935-1 (eBook) Conference Proceedings of the Society for Experimental Mechanics An imprint of River Publishers © The Society for Experimental Mechanics, Inc. 2017 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, or reproduction 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.

Preface Dynamic Behavior of Materials represents one of ten volumes of technical papers presented at the 2016 SEM Annual Conference & Exposition on Experimental and Applied Mechanics organized by the Society for Experimental Mechanics and held in Orlando, FL, on June 6–9, 2016. The complete proceedings also includes volumes on: Challenges in Mechanics of Time-Dependent Materials; Advancement of Optical Methods in Experimental Mechanics; Experimental and Applied Mechanics; Micro and Nanomechanics; Mechanics of Biological Systems and Materials; Mechanics of Composite & Multifunctional Materials; Fracture, Fatigue, Failure and Damage Evolution; Residual Stress, Thermomechanics & Infrared Imaging, Hybrid Techniques and Inverse Problems; and Joining Technologies for Composites and Dissimilar Materials. Each collection presents early findings from experimental and computational investigations on an important area within Experimental Mechanics. Dynamic Behavior of Materials is one of these areas. The Dynamic Behavior of Materials track was initiated in 2005 and reflects our efforts to bring together researchers interested in the dynamic behavior of materials and structures, and provide a forum to facilitate technical interaction and exchange. In the past years, this track has represented an ever growing area of broad interest to the SEM community, as evidenced by the increased number of papers and attendance. The contributed papers span numerous technical divisions within SEM, which may be of interest not only to the dynamic behavior of materials community but also to the traditional mechanics of materials community. The track organizers thank the authors, presenters, organizers, and session chairs for their participation, support, and contribution to this track. We are grateful to the SEM TD chairs for co-sponsoring and/or co-organizing the sessions in this track. They would also like to acknowledge the SEM support staff for their devoted efforts in accommodating the large number of paper submissions this year, making the 2016 Dynamic Behavior of Materials Track successful. Aberdeen, MD DanCasem Philadelphia, PA Leslie Lamberson Socorro, NM Jamie Kimberley v

Contents 1 Atomistic Simulation of a Two-Dimensional Polymer Tougher Than Graphene.................. 1 Emil Sandoz-Rosado, Todd D. Beaudet, Radhakrishnan Balu, and Eric D. Wetzel 2 Transverse Compression Response of Ultra-High Molecular Weight Polyethylene Single Fibers . . . . . 7 Subramani Sockalingam, John W. Gillespie Jr., Michael Keefe, Dan Casem, and Tusit Weerasooriya 3 Morphology and Mechanics of the Young Minipig Cranium................................. 15 Stephen Alexander, C. Allan Gunnarsson, Ann Mae DiLeonardi, and Tusit Weerasooriya 4 Dynamic Characterization of Nitronic 30, 40 and 50 Series Stainless Steels by Numerical Analysis . . . 21 C.G. Fountzoulas, E.M. Klier, and J.E. Catalano 5 Mechanical Response of T800/F3900 Composite at Various Strain Rates ....................... 31 Peiyu Yang, Jeremy D. Seidt, and Amos Gilat 6 Full-Field Temperature and Strain Measurement in Dynamic Tension Tests on SS 304............ 37 Jarrod L. Smith, Veli-Tapani Kuokkala, Jeremy D. Seidt, and Amos Gilat 7 Dynamic Fracture Response of a Synthetic Cortical Bone Simulant ........................... 45 Thomas Plaisted, Allan Gunnarsson, Brett Sanborn, and Tusit Weerasooriya 8 Fracture Response of Cross-Linked Epoxy Resins at High Loading Rate as a Function of Glass Transition Temperature...................................................... 51 John A. O’Neill, C. Allan Gunnarsson, Paul Moy, Kevin A. Masser, Joseph L. Lenhart, and Tusit Weerasooriya 9 Measurement of Dynamic Response Parameters of an Underdamped System.................... 59 Charandeep Singh, Satish Chaparala, and S.B. Park 10 Dynamic Penetration and Bifurcation of a Crack at an Interface in a Transparent Bi-Layer: Effect of Impact Velocity............................................................ 69 Balamurugan M. Sundaram and Hareesh V. Tippur 11 Influence of Loading Rate on Fracture Strength of Individual Sand Particles .................... 75 Andrew Druckrey, Dan Casem, Khalid Alshibli, and Emily Huskins 12 Arrested Compression Tests on Two Types of Sand....................................... 81 Eduardo Suescun-Florez, Stephan Bless, Magued Iskander, and Camilo Daza 13 Composite Plate Response to Shock Wave Loading........................................ 87 Douglas Jahnke, Vahid Azadeh Ranjbar, and Yiannis Andreopoulos 14 Initial Experimental Validation of an Eulerian Method for Modeling Composites ................ 103 Christopher S. Meyer, Christopher T. Key, Bazle Z. (Gama) Haque, and John W. Gillespie Jr. 15 Characterization of High Strain Rate Dependency of 3D CFRP Materials ...................... 111 N. Tran, J. Berthe, M. Brieu, G. Portemont, and J. Schneider vii

16 High-Strain Rate Compressive Behavior of a Clay Under Uniaxial Strain State.................. 117 Huiyang Luo, Zhenxing Hu, Tingge Xu, and Hongbing Lu 17 Mesoscopic Modelling of Ultra-High Performance Fiber Reinforced Concrete Under Dynamic Loading................................................................. 123 P. Forquin, J.L. Zinszner, and B. Lukic 18 Comparison of Failure Mechanisms Due to Shock Propagation in Forged, Layered, and Additive Manufactured Titanium Alloy............................................. 131 Melissa Matthes, Brendan O’Toole, Mohamed Trabia, Shawoon Roy, Richard Jennings, Eric Bodenchak, Matthew Boswell, Thomas Graves, Robert Hixson, Edward Daykin, Cameron Hawkins, Zach Fussell, Austin Daykin, and Michael Heika 19 Instrumented Penetration of Metal Alloys During High-Velocity Impacts ...................... 139 P. Jannotti, B. Schuster, R. Doney, T. Walter, and D. Andrews 20 Confined Underwater Implosions Using 3D Digital Image Correlation......................... 147 Helio Matos, Sachin Gupta, James M. LeBlanc, and Arun Shukla 21 Response of Composite Cylinders Subjected to Near Field Underwater Explosions ............... 153 E. Gauch, J. LeBlanc, C. Shillings, and A. Shukla 22 Microstructural Effects on the Spall Properties of 5083 Aluminum: Equal-Channel Angular Extrusion (ECAE) Plus Cold Rolling............................................ 159 C.L. Williams, T. Sano, T.R. Walter, and L.J. Kecskes 23 Experimental Study of the Dynamic Fragmentation in Transparent Ceramic Subjected to Projectile Impact ................................................................ 165 P. Forquin and J.L. Zinszner 24 Instrumented Projectiles for Dynamic Testing........................................... 171 Guojing Li, Dahsin Liu, and Dan Schleh 25 NIST Mini-Kolsky Bar: Historical Review.............................................. 177 R.L. Rhorer, J.H. Kim, and S.P. Mates 26 A General Approach to Evaluate the Dynamic Fracture Toughness of Materials ................. 185 Ali Fahad Fahem and Addis Kidane 27 Which One Has More Influence on Fracture Strength of Ceramics: Pressure or Strain Rate?. . . . . . . 195 M. Shafiq and G. Subhash 28 Dynamic Strength and Fragmentation Experiments on Brittle Materials Using Theta-Specimens ............................................................. 203 Jamie Kimberley and Antonio Garcia 29 DTEM In Situ Mechanical Testing: Defects Motion at High Strain Rates ....................... 209 Thomas Voisin, Michael D. Grapes, Yong Zhang, Nicholas J. Lorenzo, Jonathan P. Ligda, Brian E. Schuster, Melissa K. Santala, Tian Li, Geoffrey H. Campbell, and Timothy P. Weihs 30 High-Strain-Rate Deformation of Ti-6Al-4V Through Compression Kolsky Bar at High Temperatures .............................................................. 215 S. Gangireddy and S.P. Mates 31 Parametric Study of the Formation of Cone Cracks in Brittle Materials ....................... 221 Brady Aydelotte, Phillip Jannotti, Mark Andrews, and Brian Schuster 32 Shockless Characterization of Ceramics ................................................ 229 J.L. Zinszner, B. Erzar, and P. Forquin 33 Dynamic Hyper Elastic Behavior of Compression Shock Loaded Vibration Dampers ............. 237 V.B.S. Rajendra Prasad and G. Venkata Rao viii Contents

34 Specimen Size Effect on Stress-Strain Response of Foams Under Direct-Impact .................. 253 Behrad Koohbor, Addis Kidane, Wei-Yang Lu, and Ronak Patel 35 Texture Evolution of a Fine-Grained Mg Alloy at Dynamic Strain Rates ....................... 263 Christopher S. Meredith and Jeffrey T. Lloyd 36 Failure Processes Governing High Rate Impact Resistance of Epoxy Resins Filled with Core Shell Rubber Nanoparticles ................................................. 271 Erich D. Bain, Daniel B. Knorr Jr., Adam D. Richardson, Kevin A. Masser, Jian Yu, and Joseph L. Lenhart 37 Ballistic Response of Polydicyclopentadiene vs. Epoxy Resins and Effects of Crosslinking.......... 285 Tyler R. Long, Daniel B. Knorr Jr., Kevin A. Masser, Robert M. Elder, Timothy W. Sirk, Mark D. Hindenlang, Jian H. Yu, Adam D. Richardson, Steven E. Boyd, William A. Spurgeon, and Joseph L. Lenhart Contents ix

Contributors Stephen Alexander TKC Global Solutions LLC, Herndon, VA, USA Khalid Alshibli Department of Civil and Environmental Engineering, University of Tennessee, Knoxville, TN, USA Yiannis Andreopoulos Department of Mechanical Engineering, The City College of New York, New York, NY, USA D. Andrews U.S. Army Research Laboratory, Aberdeen, MD, USA Mark Andrews U.S. Army Research Laboratory, Aberdeen Proving Ground, Aberdeen, MD, USA Brady Aydelotte U.S. Army Research Laboratory, Aberdeen Proving Ground, Aberdeen, MD, USA Erich D. Bain U.S. Army Research Laboratory, Aberdeen Proving Ground, Aberdeen, MD, USA Radhakrishnan Balu U.S. Army Research Laboratory, Materials and Manufacturing Sciences Division, Aberdeen Proving Ground, Aberdeen, MD, USA Todd D. Beaudet U.S. Army Research Laboratory, Materials and Manufacturing Sciences Division, Aberdeen Proving Ground, Aberdeen, MD, USA J. Berthe Onera—The French Aerospace Lab, Lille, France Stephan Bless Tandon School of Engineering, New York University, Brooklyn, NY, USA Eric Bodenchak University of Nevada, Las Vegas, Las Vegas, NV, USA Matthew Boswell University of Nevada, Las Vegas, Las Vegas, NV, USA Steven E. Boyd U.S. Army Research Laboratory, Aberdeen Proving Ground, Aberdeen, MD, USA M. Brieu Centrale Lille/LML, Villeneuve d’Ascq, France Geoffrey H. Campbell Materials Science Division, Lawrence Livermore National Laboratory, Livermore, CA, USA DanCasem Army Research Laboratory, Aberdeen, MD, USA J.E. Catalano RDRL-WMM-F, Aberdeen Proving Ground, Aberdeen, MD, USA Satish Chaparala Corning Incorporated, Corning, NY, USA Austin Daykin National Security Technologies, LLC, North Las Vegas, NV, USA Edward Daykin National Security Technologies, LLC, North Las Vegas, NV, USA Camilo Daza Tandon School of Engineering, New York University, Brooklyn, NY, USA Ann Mae DiLeonardi US Army Research Laboratory, Aberdeen Proving Ground, Aberdeen, MD, USA R. Doney U.S. Army Research Laboratory, Aberdeen Proving Ground, Aberdeen, MD, USA Andrew Druckrey Department of Civil and Environmental Engineering, University of Tennessee, Knoxville, TN, USA Robert M. Elder U.S. Army Research Laboratory, Aberdeen Proving Ground, Aberdeen, MD, USA xi

B. Erzar CEA/DAM/GRAMAT, Gramat, France Ali Fahad Fahem Department of Mechanical Engineering, University of South Carolina, Columbia, SC, USA Department of Mechanical Engineering, University of Al-Qadisiyah, Al-Diwaniyah, Qadisiyah Province, Iraq P. Forquin Soils Solids Structures Risks (3SR) Laboratory, Grenoble-Alps University, Grenoble Cedex 9, France C.G. Fountzoulas U.S. Army Research Laboratory, WMRD, RDRL-WMM-B, Aberdeen, MD, USA Zach Fussell National Security Technologies, LLC, North Las Vegas, NV, USA S. Gangireddy MML, NIST, Materials Science and Engineering Division, Gaithersburg, MD, USA Antonio Garcia Department of Mechanical Engineering, New Mexico Institute of Mining and Technology, Socorro, NM, USA E. Gauch Naval Undersea Warfare Center, Division Newport, Newport, RI, USA Amos Gilat Scott Laboratory, Department of Mechanical and Aerospace Engineering, The Ohio State University, Columbus, OH, USA John W. Gillespie Jr. Center for Composite Materials, University of Delaware, Newark, DE, USA Department of Mechanical Engineering, University of Delaware, Newark, DE, USA Department of Materials Science and Engineering, University of Delaware, Newark, DE, USA Department of Civil and Environmental Engineering, University of Delaware, Newark, DE, USA Michael D. Grapes Department of Materials Science and Engineering, Johns Hopkins University, Baltimore, MD, USA Thomas Graves National Security Technologies, LLC, New Mexico Operations, Los Alamos, NM, USA C. Allan Gunnarsson US Army Research Laboratory, Aberdeen Proving Ground, Aberdeen, MD, USA Sachin Gupta Dynamic Photo Mechanics Laboratory, Department of Mechanical, Industrial and Systems Engineering, University of Rhode Island, Kingston, RI, USA Bazle Z. (Gama) Haque Center for Composite Materials, University of Delaware, Newark, DE, USA Cameron Hawkins National Security Technologies, LLC, North Las Vegas, NV, USA Michael Heika National Security Technologies, LLC, North Las Vegas, NV, USA Mark D. Hindenlang U.S. Army Research Laboratory, Aberdeen Proving Ground, Aberdeen, MD, USA Robert Hixson National Security Technologies, LLC, New Mexico Operations, Los Alamos, NM, USA Zhenxing Hu Department of Mechanical Engineering, The University of Texas at Dallas, Richardson, TX, USA Emily Huskins Department of Mechanical Engineering, United States Naval Academy, Annapolis, MD, USA Magued Iskander Tandon School of Engineering, New York University, Brooklyn, NY, USA Douglas Jahnke Department of Mechanical Engineering, The City College of New York, New York, NY, USA P. Jannotti U.S. Army Research Laboratory, Aberdeen Proving Ground, Aberdeen, MD, USA Richard Jennings University of Nevada, Las Vegas, Las Vegas, NV, USA L.J. Kecskes U. S. Army Research Laboratory, Aberdeen Proving Ground, Aberdeen, MD, USA Michael Keefe Center for Composite Materials, University of Delaware, Newark, DE, USA Department of Mechanical Engineering, University of Delaware, Newark, DE, USA Christopher T. Key Applied Physical Sciences, Groton, CT, USA Addis Kidane Department of Mechanical Engineering, University of South Carolina, Columbia, SC, USA xii Contributors

J.H. Kim Materials Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, MD, USA Jamie Kimberley New Mexico Institute of Mining and Technology, Socorro, NM, USA Energetic Materials Testing and Research Center, New Mexico Institute of Mining and Technology, Socorro, NM, USA E.M. Klier RDRL-WMM-F, Aberdeen Proving Ground, Aberdeen, MD, USA Daniel B. Knorr Jr. U.S. Army Research Laboratory, Aberdeen Proving Ground, Aberdeen, MD, USA Behrad Koohbor Department of Mechanical Engineering, University of South Carolina, Columbia, SC, USA Veli-Tapani Kuokkala Department of Materials Science, Tampere University of Technology, Tampere, Finland James M. LeBlanc Naval Undersea Warfare Center, Division Newport, Newport, RI, USA Joseph L. Lenhart U.S. Army Research Laboratory, Aberdeen Proving Ground, Aberdeen, MD, USA GuojingLi Department of Mechanical Engineering, Michigan State University, East Lansing, MI, USA TianLi Materials Science Division, Lawrence Livermore National Laboratory, Livermore, CA, USA Jonathan P. Ligda Weapons and Materials Research Directorate, Army Research Laboratory, Aberdeen Proving Ground, Aberdeen, MD, USA DahsinLiu Department of Mechanical Engineering, Michigan State University, East Lansing, MI, USA Jeffrey T. Lloyd Weapons and Materials Research Directorate, Army Research Lab, Aberdeen Proving Ground, Aberdeen, MD, USA Tyler R. Long U.S. Army Research Laboratory, Aberdeen Proving Ground, Aberdeen, MD, USA Nicholas J. Lorenzo Weapons and Materials Research Directorate, Army Research Laboratory, Aberdeen Proving Ground, Aberdeen, MD, USA Hongbing Lu Department of Mechanical Engineering, The University of Texas at Dallas, Richardson, TX, USA Wei-Yang Lu Sandia National Laboratories, Livermore, CA, USA Huiyang Luo Department of Mechanical Engineering, The University of Texas at Dallas, Richardson, TX, USA Kevin A. Masser U.S. Army Research Laboratory, Aberdeen Proving Ground, Aberdeen, MD, USA S.P.Mates Materials Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, MD, USA Helio Matos Dynamic Photo Mechanics Laboratory, Department of Mechanical, Industrial and Systems Engineering, University of Rhode Island, Kingston, RI, USA Melissa Matthes University of Nevada, Las Vegas, Las Vegas, NV, USA Christopher S. Meredith Weapons and Materials Research Directorate, Army Research Lab, Aberdeen Proving Ground, Aberdeen, MD, USA Christopher S. Meyer U.S. Army Research Laboratory, ATTN: RDRL-WML-H, Proving Ground, Aberdeen, MD, USA PaulMoy Army Research Laboratory, Aberdeen Proving Ground, Aberdeen, MD, USA John A. O’Neill Army Research Laboratory, Aberdeen Proving Ground, Aberdeen, MD, USA Brendan O’Toole University of Nevada, Las Vegas, Las Vegas, NV, USA S.B. Park Department of Mechanical Engineering, State University of New York at Binghamton, Binghamton, NY, USA Ronak Patel Department of Mechanical Engineering, University of South Carolina, Columbia, SC, USA Thomas Plaisted Weapons and Materials Research Directorate, U.S. Army Research Laboratory, Aberdeen Proving Ground, Aberdeen, MD, USA G. Portemont Onera—The French Aerospace Lab, Lille, France Contributors xiii

V.B.S. Rajendra Prasad Vasavi College of Engineering, Ibrahimbagh, Hyderabad, Telangana, India Vahid Azadeh Ranjbar Department of Mechanical Engineering, The City College of New York, New York, NY, USA G. Venkata Rao Vasavi College of Engineering, Ibrahimbagh, Hyderabad, Telangana, India R.L. Rhorer Engineering Laboratory, National Institute of Standards and Technology, Gaithersburg, MD, USA Adam D. Richardson U.S. Army Research Laboratory, Aberdeen Proving Ground, Aberdeen, MD, USA Shawoon Roy University of Nevada, Las Vegas, Las Vegas, NV, USA Brett Sanborn Oak Ridge Institute for Science and Education, Oak Ridge, TN, USA Sandia National Laboratory, Albuquerque, NM, USA Emil Sandoz-Rosado U.S. Army Research Laboratory, Materials and Manufacturing Sciences Division, Aberdeen Proving Ground, Aberdeen, MD, USA T. Sano U. S. Army Research Laboratory, Aberdeen Proving Ground, Aberdeen, MD, USA Melissa K. Santala Materials Science Division, Lawrence Livermore National Laboratory, Livermore, CA, USA Dan Schleh Liuman Technologies, Lansing, MI, USA J. Schneider SAFRAN Snecma, Moissy-Crammayel, France Brian E. Schuster Weapons and Materials Research Directorate, Army Research Laboratory, Aberdeen Proving Ground, Aberdeen, MD, USA Jeremy D. Seidt Scott Laboratory, Department of Mechanical and Aerospace Engineering, The Ohio State University, Columbus, OH, USA M. Shafiq Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL, USA C. Shillings Naval Undersea Warfare Center, Division Newport, Newport, RI, USA Arun Shukla Dynamic Photo Mechanics Laboratory, Department of Mechanical, Industrial and Systems Engineering, University of Rhode Island, Kingston, RI, USA Charandeep Singh Department of Mechanical Engineering, State University of New York at Binghamton, Binghamton, NY, USA Timothy W. Sirk U.S. Army Research Laboratory, Aberdeen Proving Ground, Aberdeen, MD, USA Jarrod L. Smith Scott Laboratory, Department of Mechanical Engineering, The Ohio State University, Columbus, OH, USA Subramani Sockalingam Center for Composite Materials, University of Delaware, Newark, DE, USA William A. Spurgeon U.S. Army Research Laboratory, Aberdeen Proving Ground, Aberdeen, MD, USA G. Subhash Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL, USA Eduardo Suescun-Florez Tandon School of Engineering, New York University, Brooklyn, NY, USA Balamurugan M. Sundaram Department of Mechanical Engineering, Auburn University, Auburn, AL, USA Hareesh V. Tippur Department of Mechanical Engineering, Auburn University, Auburn, AL, USA Mohamed Trabia University of Nevada, Las Vegas, Las Vegas, NV, USA N. Tran SAFRAN Snecma, Moissy-Crammayel, France Thomas Voisin Department of Materials Science and Engineering, Johns Hopkins University, Baltimore, MD, USA T.R. Walter U. S. Army Research Laboratory, Aberdeen Proving Ground, Aberdeen, MD, USA Tusit Weerasooriya US Army Research Laboratory, Aberdeen Proving Ground, Aberdeen, MD, USA xiv Contributors

Timothy P. Weihs Department of Materials Science and Engineering, Johns Hopkins University, Baltimore, MD, USA Eric D. Wetzel U.S. Army Research Laboratory, Materials and Manufacturing Sciences Division, Aberdeen Proving Ground, Aberdeen, MD, USA C.L. Williams U. S. Army Research Laboratory, Aberdeen Proving Ground, Aberdeen, MD, USA TinggeXu Department of Mechanical Engineering, The University of Texas at Dallas, Richardson, TX, USA Peiyu Yang Scott Laboratory, Department of Mechanical and Aerospace Engineering, The Ohio State University, Columbus, OH, USA JianH. Yu U.S. Army Research Laboratory, Aberdeen Proving Ground, Aberdeen, MD, USA YongZhang Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD, USA J.L. Zinszner Soils Solids Structures Risks (3SR) Laboratory, Grenoble-Alps University, Grenoble Cedex 9, France CEA/DAM/GRAMAT, Gramat, France Contributors xv

Chapter 1 Atomistic Simulation of a Two-Dimensional Polymer Tougher Than Graphene Emil Sandoz-Rosado, Todd D. Beaudet, Radhakrishnan Balu, and Eric D. Wetzel Abstract A graphene/polyethylene hybrid 2D polymer, “graphylene”, exhibits a higher theoretical fracture toughness than graphene, while remaining 2 stiffer and 9 stronger than Kevlar ® , per mass. Within the base structure of graphylene, the sp3-bonded polyethylene linkages provide compliance for ductile fracture, while the benzene rings contribute to high stiffness and strength. Combining stiff and compliant units to achieve enhanced mechanical performance demonstrates the potential of designing 2D materials at the molecular level. 1.1 Introduction The extraordinary in-plane stiffness and intrinsic strength of graphene [1] in its pristine state have made it a desirable candidate as a structural material. Chemical vapor deposition of large-area graphene has been refined [2] to the point that grain boundaries of graphene approach the breaking strength of perfect crystalline graphene [3], a phenomenon that has been supported by atomistic simulations [4]. Graphene has the theoretical potential to enable ballistic barriers that have 10–100 less weight than barriers composed of Kevlar with the same ballistic limit [5], and has also demonstrated a specific kinetic energy of penetration an order of magnitude greater than steel and 2–3 greater than Kevlar, as measured by microscale ballistic experiments [6]. However, because graphene is a network of very stiff sp2 bonds, it is highly resistant to fracture initiation but, once formed, a crack will propagate in a brittle manner [7, 8]. This brittle behavior may limit graphene’s potential as a structural engineering material, as local failure due to a flaw or stress concentration is likely to trigger a sudden and catastrophic global failure. To demonstrate a two-dimensional (2D) material with a more ductile fracture response compared to graphene, we propose a new family of 2D polymer which we refer to as “graphylene.” This 2D covalent polymer network can be conceptually described as a graphene/polyethylene hybrid comprising benzene rings linked by short polyethylene chains. These short polyethylene links give graphylene in-plane stiffness and strength values that are somewhat lower than graphene. However, we demonstrate that the flexibility of the sp3 bonded carbon atoms in the polyethylene chains leads to ductile fracture propagation behavior, with significantly higher energy required to propagate cracks relative to graphene. 2D polymers in the form of hexagonal carbon rings connected by linear carbon links have been recently described. Graphyne [9] and related allotropes [10] are composed strictly of extremely stiff carbon–carbon double and triple bonds, likely leading to brittle behavior. Graphane [11] adds single hydrogen bonds to each carbon atom in graphene, resulting in a hexagonal network of sp3 bonds. Studies have also examined carbon allotropes that are randomly hydrogen functionalized [12]. Stiffness and strength in these graphene-like polymers have been incompletely reported, while fracture has not been directly studied in any of these systems. The polyethylene links in the graphylene 2D polymer structure should add compliance mechanisms that are not present in graphene, graphyne, graphane, or other 2D carbon allotropes, allowing for local ductility and greater flaw tolerance. E. Sandoz-Rosado • T.D. Beaudet • R. Balu • E.D. Wetzel (*) U.S. Army Research Laboratory, Materials and Manufacturing Sciences Division, Bldg. 4600, Aberdeen Proving Ground, Aberdeen, MD 21005, USA e-mail: eric.d.wetzel2.civ@mail.mil #The Society for Experimental Mechanics, Inc. 2017 D. Casem et al. (eds.), Dynamic Behavior of Materials, Volume 1, Conference Proceedings of the Society for Experimental Mechanics Series, DOI 10.1007/978-3-319-41132-3_1 1

1.2 Establishing the Structure of Graphylene We have broadly considered the graphylene-n(GrE-n) family of 2D polymers, where nindicates the characteristic length of the polyethylene (PE) chains in terms of the number of methylene bridge units (–CH2–) between each nearest neighbor C6 ring. A complete description of the various GrE-n configurations considered is provided in the Supplemental Information, with the results summarized as follows. Since the system is composed of more rigid graphene units (C6 rings) and softer polyethylene (CH2)n units, we hypothesize that global stiffness and strength will reduce, while fracture toughness will increase, with increasingn. Simulations of various GrE-npolymers revealed that oddnconfigurations were more difficult to solve for converged stable states compared to even n configurations, primarily due to symmetry challenges that required larger unit cells and computational domain sizes. Therefore, although odd n graphylene systems are likely to be physically realizable, only even n systems were considered for further study. Of the possible n ¼2, 4, 6, etc. configurations, GrE-2 polymers were selected as our system of interest as the closest comparison to graphene. 1.3 Elastic Modulii of Graphylene First-principles DFT uniaxial stress calculations for both the first and second C6 nearest-neighbor (1NN and 2NN, respectively) directions of GrE-2 were performed to determine its strength and stiffness, and to benchmark subsequent molecular dynamics (MD) predictions. The elastic modulii were extracted from this stress–strain response during uniaxial tensile testing according to the following relationship: σ2D ¼E2DE þD2DE 2 ð1:1Þ where σ2D is stress, E is strain, and E2D and D2D are the first and second order elastic modulii respectively [5]. Because graphylene is being studied as an atomically-thin sheet, the stress and moduli values are expressed in units of [N/m]. In-plane elastic modulii are calculated by curve fitting the DFT data with Eq. (1.1) to find E2Dand D2Dfor the 1NN and 2NN lattice directions. Analogous uniaxial tensile calculations were performed using classical MD modeling via the LAMMPS software package, which will also be used for subsequent fracture studies. A single sheet of GrE-2 with dimensions 21.5 nm 25.5 nm (Fig. 1.1a) held at 0 K was stretched by fixing one edge and displacing the opposing edge at a constant rate of 0.1 nm/ps for a strain rate of 0.5 ns 1 which is of the same order as strain rates for other graphene fracture simulation studies [13, 14]. To achieve uniaxial stress, the boundaries normal to the direction of stretching are periodic, but permitted to relax (Fig. 1.1a). In-plane elastic modulii, and stress and strain to failure determined by DFT are reported in Table 1.1 for both directions of crystalline symmetry. Figure 1.1b shows the comparison between DFT and MD for tensile simulations. The results show that graphylene-2 is somewhat anisotropic, with the 1NN and 2NN directions having linear elastic modulii values of E2D ¼78.9 N/mand E2D ¼97.6 N/m respectively. The linear elastic modulus values are over three times smaller than that of pristine graphene, which is reported to be 340 N/m by numerous theoretical and experimental studies [5], but is still over 2 and5 higher, per mass, than high performance engineering materials such as Kevlar and titanium, respectively [5] (based on an initial GrE-2 areal density of 6.53 10 7 kg/m2). The non-linear stress–strain response in GrE-2 manifests at smaller strains than graphene, making it a nonlinear elastic material. The elastic response of GrE-2 predicted by the DFT and MD simulations are in good agreement (Fig. 1.1a), indicating that the REBO potential is suitable for modeling graphylene polymers. However, the ultimate stress to failure of GrE-2 predicted by MD is significantly lower than that predicted by DFT. This We attribute the discrepancy in failure points to the interaction cutoff imposed on the REBO potential [4, 7, 11] to prevent aphysical carbon-carbon scissioning that is a result of computational artifacts in the potential’s switching function [15]. While the MD simulations of GrE-2 may fail prematurely they will not contain any of the strain-hardening and high breaking strengths typical to REBO simulations without cutoffs. Therefore, the following MD simulations characterizing fracture toughness can be considered conservative, and that true intrinsic toughness values of graphylene may be even higher than our predictions. 2 E. Sandoz-Rosado et al.

1.4 Initiation of Mode-I Crack Growth in GrE-2 Graphylene The intrinsic ability of a material to resist the initiation of crack growth from a pre-existing crack is quantified in terms of fracture toughness. There are three metrics we use to quantify the fracture behavior of graphylene: (i) critical fracture energy (quasi-static), (ii) flaw-tolerance (quasi-static) and (iii) fracture energy release rate (dynamic). To characterize the critical fracture energy of graphylene, we performed MD simulations of fracture of a domain of GrE-2 with a pre-existing crack and benchmarked it with graphene under the same conditions. The crack domain, depicted in Fig. 1.2a, is 60 nm by 30 nm which corresponds to an aspect ratio acceptable for modeling crack growth [16] and matches the dimensions of previous MD simulations of graphene fracture [7]. The domain was permitted to relax in the direction perpendicular to strain. A pre-crack of length a0 was created in the GrE-2 and graphene domains and strain was applied at a constant rate in the direction perpendicular to the pre-crack. This configuration is consistent with a mode-I crack, the results of which can be seen in Fig. 1.2b. The crack width was 0.3 nm and the crack tip radii were 0.15 nm for consistency. To quantify fracture toughness we adopt a 2D formulation of the quasi-static critical fracture energy of a Griffith crack which is formulated assuming linear elasticity appropriate for the small (less than 5 %) strain in our crack models: GIc,2D ¼ K2 Ic,2D E2D ¼ σ2 c,2D 2E2D πa0 ð1:2Þ Table 1.1 In-mechanical properties of GrE-2 determined fromDFT E2D [N/m] D2D [N/m] σf [N/m] Ef [ ] First NN 78.9 94.7 11.4 0.19 SecondNN 97.6 107.1 16.4 0.23 First and second nearest neighbor directions are denoted as 1NN and 2NN respectively 0 4 8 12 16 20 0.00 0.05 0.10 0.15 0.20 0.25 Stress, σ2D [N/m] Strain, Œ [-] DFT 1NN DFT 2NN MD 1NN MD 2NN 20 b a y x Fig. 1.1 (a) MD domain and boundary conditions for modeling GrE-2 under uniaxial tension. Hydrogen atoms are not depicted for ease of viewing. (b) Predicted nominal stress vs. nominal strain for uniaxial tension simulations of GrE-2 to failure using both DFT and MD in 1NN and 2NN directions. Inlays depict deformed lattices (from MD simulations) in both directions at 12.5 % strain. Solid lines depict curve fits of Eq. (1.1) to the DFT data 1 Atomistic Simulation of a Two-Dimensional Polymer Tougher Than Graphene 3

where GIc,2D is the 2D mode-I critical fracture energy, KIc,2D is the critical 2D mode-I stress concentration factor and σc,2D is the 2D critical fracture stress. The critical fracture energy was first determined for graphene with a pre-crack length of a0 of 10 nm, resulting in a value of GIc,2D ¼2.28 nJ/m, in agreement with the critical fracture energy of graphene reported by a previous study, GIc,2D ¼2.33 nJ/m [7]. This value was found to be constant across all pre-crack lengths for the same domain dimensions, a signature of brittle material response. A parametric study of pre-crack length was then performed for GrE-2, and the critical fracture energy can be seen in Fig. 1.2c compared to that of graphene. Immediately it is clear that GrE-2, unlike graphene, has a critical fracture energy that is dependent on pre-crack length, a signature of ductile fracture response. Furthermore, the critical fracture energy of GrE-2, (GIc,2D ¼2.51 nJ/m at a0 ¼20 nm) rapidly exceeds that of graphene (GIc,2D ¼2.28 nJ/m across all pre-crack lengths) as pre-crack length increases. While GrE-2 shows initial crack growth at a lower critical stress than graphene, this initiation event occurs at a significantly higher strain than graphene. Another metric for flaw tolerance is the ratio of the strain energy of the flawed material relative to the strain energy of the pristine material [17]. The simulation results show that GrE-2 exhibits three times the value of this metric compared to graphene (Fig. 1.2d). In other words, pre-existing defects in graphene will deteriorate the toughness of the material twice as much as identical pre-existing defects in graphylene. 0 0.5 1 1.5 2 2.5 3 0 5 10 15 20 25 Cri cal Fracture Energy GIc, 2D[nJ/m] Ini al Crack Length, a0 [nm] Graphene GrE-2 0 10 20 30 40 0.00 0.05 0.10 0.15 0.20 0.25 Stress, σ2D [N/m] Strain, å [-] Graphene (Pristine) Graphene (Crack) GrE-2 (Pristine) GrE-2 (Crack) = 0.078 = 0.023 0 2 4 6 8 10 0 0.02 0.04 0.06 0.08 Stress, σ2D [N/m] Strain, å [-] Graphene, ∈ = 2.0 1/ns, T=300K GrE-2, ∈ = 2.0 1/ns, T=300K GrE-2, ∈ = 0.167 1/ns, T=0K GrE-2, ∈ = 2.0 1/ns, T=0K Duc le (Stable) Bri le (Catastrophic) a0 nm 60nm a d b c Fig. 1.2 (a) Crack domain of GrE-2 to examine fracture toughness, (b) nominal stress vs. nominal strain of graphene and a GrE-2 Griffith crack propagating perpendicular to the 1NN direction at various conditions (a0 ¼10 nm), (c) the critical fracture energy of graphene and GrE-2 at varying initial crack lengths initialized at 0 K, and (d) comparison in stress–strain response between pristine and cracked graphene and GrE-2 at 0 K demonstrating superior flaw tolerance of GrE-2 4 E. Sandoz-Rosado et al.

1.5 Conclusions The simulations in this study suggest that GrE-2 graphylene exhibits features consistent with ductile fracture propagation, in contrast to the brittle fracture that has been predicted and observed for graphene. Combined with its very high stiffness and strength relative to current engineering materials, graphylene possesses a unique set of mechanical properties that could enable engineering structures with unprecedented performance. Although not presented here, simulations of the transport and electronic properties of graphylene are also underway. The present GrE-2 graphylene polymer is a useful model system, in particular considering the maturity of DFT and MD bond potential functions for the comprising benzene and polyethylene subcomponents of the structure. However, a nearly limitless range of 2D polymers can be imagined, providing ample opportunity for further study and improvement in properties. The practical realization of these materials will require parallel mechanical modeling and synthesis efforts to identify systems with useful properties that can also be readily fabricated. References 1. Lee, C., et al.: Measurements of the elastic properties and intrinsic strength of monolayer graphene. Science 321(5887), 385–388 (2008) 2. Petrone, N., et al.: Chemical vapor deposition-derived graphene with electrical performance of exfoliated graphene. Nano Lett. 12(6), 2751–2756 (2012) 3. Lee, G.-H., et al.: High-strength chemical-vapor–deposited graphene and grain boundaries. Science 340(6136), 1073–1076 (2013) 4. Grantab, R., Shenoy, V.B., Ruoff, R.S.: Anomalous strength characteristics of tilt grain boundaries in graphene. Science 330(6006), 946–948 (2010) (Copyright 2010, The Institution of Engineering and Technology) 5. Wetzel, E.D., Balu, R., Beaudet, T.D.: A theoretical consideration of the ballistic response of continuous graphene membranes. J. Mech. Phys. Solids 82, 23–31 (2015) 6. Lee, J.-H., et al.: Dynamic mechanical behavior of multilayer graphene via supersonic projectile penetration. Science 346(6213), 1092–1096 (2014) 7. Zhang, P., et al.: Fracture toughness of graphene. Nat. Commun. 5, 3782 (2014) 8. Hwangbo, Y., et al.: Fracture characteristics of monolayer CVD-graphene. Sci. Rep. 4, 4439 (2014) 9. Cranford, S.W., Buehler, M.J.: Mechanical properties of graphyne. Carbon 49(13), 4111–4121 (2011) 10. Enyashin, A.N., Ivanovskii, A.L.: Graphene allotropes. Phys. Status Solidi B248(8), 1879–1883 (2011) 11. Pei, Q., Zhang, Y., Shenoy, V.: A molecular dynamics study of the mechanical properties of hydrogen functionalized graphene. Carbon48(3), 898–904 (2010) 12. Li, Y., et al.: Mechanical properties of hydrogen functionalized graphene allotropes. Comput. Mater. Sci. 83, 212–216 (2014) 13. Zhang, Z., Wang, X., Lee, J.D.: An atomistic methodology of energy release rate for graphene at nanoscale. J. Appl. Phys. 115(11), 114314 (2014) 14. Le, M.-Q., Batra, R.C.: Single-edge crack growth in graphene sheets under tension. Comput. Mater. Sci. 69, 381–388 (2013) 15. Pastewka, L., et al.: Describing bond-breaking processes by reactive potentials: importance of an environment-dependent interaction range. Phys. Rev. B78(16), 161402 (2008) 16. Buehler, M.J., Gao, H.: Modeling dynamic fracture using large-scale atomistic simulations. In: Shukla, A. (ed.) Dynamic Fracture Mechanics, p. 1. World Scientific, Singapore, (2006) 17. Markus, J.B., et al.: Cracking and adhesion at small scales: atomistic and continuum studies of flaw tolerant nanostructures. Model. Simul. Mater. Sci. Eng. 14(5), 799 (2006) 1 Atomistic Simulation of a Two-Dimensional Polymer Tougher Than Graphene 5

Chapter 2 Transverse Compression Response of Ultra-High Molecular Weight Polyethylene Single Fibers Subramani Sockalingam, John W. Gillespie Jr., Michael Keefe, Dan Casem, and Tusit Weerasooriya Abstract This work reports on the experimental quasi static transverse compression response of ultra-high molecular weight polyethylene (UHMWPE) Dyneema SK76 single fibers. The experimental nominal stress-strain response of single fibers exhibits nonlinear inelastic behavior under transverse compression with negligible strain recovery during unloading. Scanning electron microscopy (SEM) reveals the presence of significant voids along the length of the virgin and compressed fibers. The inelastic behavior is attributed to the microstructural damage within the fiber. The compressed fiber cross sectional area is found to increase to a maximum of 1.83 times the original area at 46 % applied nominal strains. The true stress strain behavior is determined by removing the geometric nonlinearity due to the growing contact area. The transverse compression experiments serve as validation experiments for fibril-length scale models. Keywords UHMWPE • Ballistic impact • Transverse compression • Finite element analysis (FEA) • Constitutive model 2.1 Introduction Ultra-high molecular weight polyethylene (UHMWPE) fibers are used in personnel protection ballistic impact applications [1] in the form flexible textile fabrics and laminated composites. UHMWPE fiber is made up of extremely long chains of polyethylene (monomer unit >250,000 per molecule) with a hierarchy of sizes and exhibits a fibrillar structure. Macro-fibrils [2] consist of bundles of micro-fibrils which in turn are composed of bundles of nano-fibrils. These fibers lend themselves to such applications due to their superior specific axial tensile strength and specific modulus. The fibers experience multi-axial loading [3] including axial tension, axial compression, transverse compression and transverse shear during impact. While axial specific toughness and longitudinal wave speed are important fiber properties contributing to the ballistic performance [4], the role of transverse properties and multi-axial loading during impact is not well understood. In this work we investigate the quasi static (QS) transverse deformation behavior of UHMWPE Dyneema SK76 single fibers. S. Sockalingam (*) Center for Composite Materials, University of Delaware, Newark, DE, USA e-mail: sockalsi@udel.edu J.W. Gillespie Jr. Center for Composite Materials, University of Delaware, Newark, DE, USA Department of Mechanical Engineering, University of Delaware, Newark, DE, USA Department of Materials Science and Engineering, University of Delaware, Newark, DE, USA Department of Civil and Environmental Engineering, University of Delaware, Newark, DE, USA M. Keefe Center for Composite Materials, University of Delaware, Newark, DE, USA Department of Mechanical Engineering, University of Delaware, Newark, DE, USA D. Casem • T. Weerasooriya Army Research Laboratory, Aberdeen, MD, USA #The Society for Experimental Mechanics, Inc. 2017 D. Casem et al. (eds.), Dynamic Behavior of Materials, Volume 1, Conference Proceedings of the Society for Experimental Mechanics Series, DOI 10.1007/978-3-319-41132-3_2 7

2.2 Experimental Set up The QS experimental set up involves compressing a single fiber between rigid parallel platens (Sapphire substrates) in plane strain conditions as shown in the schematic in Fig. 2.1. The compressive load per unit length (F), platen displacement (u) and compressed width (2w) of the fiber are measured in real time. Contact width (2b) is measured post-test at different applied load levels. The fibers are compressed at 0.1μm/s (average strain rate of 0.0059 s 1). A more detailed explanation of the experimental set up is reported in [5]. 2.3 Results and Discussion The QS experimental nominal stress σ ¼F d nominal strain ε ¼u d (d is undeformed fiber diameter) response due to monotonic and cyclic loading is shown in Fig. 2.2. The fibers exhibit a nonlinear inelastic response. The nonlinearity is attributed to both geometric stiffening due to growing contact area and material softening. After each load-unload cycle residual strains are measured. Figure 2.3 shows scanning electron microscopy (SEM) images of fibers subjected to different levels of maximum nominal strains. The undeformed fiber shown in Fig. 2.3a indicates the presence of significant void like features on the surface and along the length of the fiber. Void like features are also observed on the surface of the compressed fibers. The normalized contact width (b/r) and compressed width (w/r) growth is shown in Fig. 2.4. At maximum load the compressed width has increased by a factor of 4.5. It is also seen both 2b and 2w plateau at higher load levels to approximately four and a half fiber diameters. Negligible elastic recovery or reduction in width growth is observed during unloading. The elastic modulus in transverse compression is determined using an analytical solution based on the Hertzian contact for a transversely isotropic fiber given by eqs. 2.1 [6] and 2.2 [7]. The experimental measurements are fitted into eqs. 2.1 and 2.2 to as shown in Fig. 2.5a using the properties in Table 2.1(v31 and v12 in Table 2.1 are assumed values). The analytical solution compares well with the experimental results until about 2 % nominal strains where material softening and damage may be on setting. A transverse modulus of 2.37 GPa and a Hertzian elastic limit of 2 % is determined. Fig. 2.1 Schematic of single fiber transverse compression 8 S. Sockalingam et al.

Fig. 2.2 QS experimental (a) one load unload cycle on different fibers (b) multiple load unload cycle on the same fiber Fig. 2.3 SEM images of deformed fibers at nominal strain levels (a) 0%(b) 22%(c) 51 %(d) 71% 2 Transverse Compression Response of Ultra-High Molecular Weight Polyethylene Single Fibers 9

Fig. 2.4 Normalized 2b and 2w Fig. 2.5 (a) Nominal stress strain (b) normalized cross sectional area Table 2.1 Transversely isotropic properties of Dyneema SK76 ρ (g/cm3) D (μm) E3 (GPa) ν31 ν12 E1 (GPa) Hertzian elastic limit True elastic limit 0.97 17.0 116.0 0.60 0.40 2.37 2% 0.5 % 10 S. Sockalingam et al.

u ¼ 4F π s11 s2 13 s33 0:19þsinh 1 r= b ð2:1Þ b2 ¼ 4Fr π 1 E1 ν2 31 E3 ð 2:2Þ where, F—load per unit length along the fiber longitudinal direction u—platen displacement L—length of the compressed fiber r—radius of the fiber b—contact half width E1—Young’s modulus in 1–2 plane of transverse isotropy E3—longitudinal Young’s modulus in the fiber direction w—compressed half width s11 ¼ 1 E1 s12 ¼ ν12 E1 s13 ¼ ν13 E1 s33 ¼ 1 E3 The intrinsic material behavior is isolated from the total response by defining true stress as σ ¼ F 2weff where the effective widthweff ¼ wþb 2 . The original fiber cross section is assumed to be a circle and the compressed fiber cross section is assumed to be a rectangle. The compressed cross sectional area is estimated using 2weff 2r u ð Þ. The normalized compressed apparent cross sectional area is found to increase to a maximum of 1.83 times the original area at 46 % nominal strain and then plateau at higher strain levels as shown in Fig. 2.5b. A more detailed study is required to understand the increase in cross sectional area. The true strain is obtained by equating the internal energy to the external work done given by eq. 2.3. The true strains are computed incrementally using trapezoidal rule to evaluate the integrals in eq. 2.3. ð V V0 ð εeff 0 σeff dεeff dV ¼ð u 0 Fdu ð2:3Þ The true stress strain response obtained by imposing a constant volume along with a linear elastic behavior with a stiffness of 2.37 GPa is shown in Fig. 2.6. The true elastic limit of 0.5 % is identified as the point at which the instantaneous stiffness is lower than the elastic stiffness of 2.37 GPa. The single fiber transverse compression experiment is modeled using a quarter symmetric finite element (FE) model shown in Fig. 2.6b in the commercial FE code LS-DYNA. The fiber is modeled as a nonlinear inelastic continuum material with a user defined constitutive model [5] UMAT. The yield stress-effective plastic strain required as input to the model is determined by subtracting the elastic portion of the true stress-strain curve (Fig. 2.6a). The UMAT force displacement predictions are much better correlation to the experimental results compared to a linear elastic behavior with stiffness of 2.37 GPa. However the model under predicts contact area compared to the experiments as shown in Fig. 2.6d. This deviation may be attributed to the increase in fiber cross sectional area observed in the experiments which is a topic for future studies. 2.4 Conclusions This paper presented the quasi-static transverse compression response of UHMWPE Dyneema SK76 ballistic fibers. The fibers exhibit nonlinear inelastic behavior under large compressive strains. The true stress strain behavior of the fiber is determined by removing the geometric nonlinearity using the measured contact area. The true elastic limit of these fibers in transverse compression is found to be 0.5 % and the Hertzian elastic limit is found to be 2 %. The numerical FE model 2 Transverse Compression Response of Ultra-High Molecular Weight Polyethylene Single Fibers 11

predictions using true stress-strain curve is found to be in a much better correlation to the experimental force displacement response compared to a linear elastic assumption. Both virgin and compressed fibers are found to possess void like features on the fiber surface. Further investigation is required to better understand the increase in apparent fiber cross sectional area during transverse compression. Acknowledgements Research was sponsored by the Army Research Laboratory and was accomplished under Cooperative Agreement Number W911NF-12-2-0022. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Laboratory or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation herein. References 1. Krishnan, K., Sockalingam, S., Bansal, S., Rajan, S.: Numerical simulation of ceramic composite armor subjected to ballistic impact. Compos. Part B41(8), 583–593 (2010) 2. McDaniel, P.B., Deitzel, J.M., Gillespie, J.W.: Structural hierarchy and surface morphology of highly drawn ultra high molecular weight polyethylene fibers studied by atomic force microscopy and wide angle X-ray diffraction. Polymer 69, 148–158 (2015) 3. Sockalingam, S., Gillespie Jr., J.W., Keefe, M.: Dynamic modeling of Kevlar KM2 single fiber subjected to transverse impact. Int. J. Solids Struct. 67–68, 297–310 (2015) 4. Cunniff, P.M.: Dimensionless parameters for optimization of textile-based body armor systems. In: Proceedings of the 18th International Symposium on Ballistics, November, San Antonio, pp. 1303–1310. Technomic, Lancaster, PA (1999) Fig. 2.6 (a) True stress strain behavior (b) FEmodel (c) comparison of model and experiments (d) normalized contact and compressed width 12 S. Sockalingam et al.

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