River Rapids Conference Proceedings of the Society for Experimental Mechanics Series Dynamic Behavior of Materials, Volume 1 Bo Song Daniel Casem Jamie Kimberley Proceedings of the 2014 Annual Conference on Experimental and Applied Mechanics River Publishers
Conference Proceedings of the Society for Experimental Mechanics Series Series Editor Tom Proulx Society for Experimental Mechanics, Inc. Bethel, CT, USA
River Publishers Bo Song • Daniel Casem • Jamie Kimberley Editors Dynamic Behavior of Materials, Volume 1 Proceedings of the 2014 Annual Conference on Experimental and Applied Mechanics
Published, sold and distributed by: River Publishers Broagervej 10 9260 Gistrup Denmark www.riverpublishers.com ISBN 978-87-7004-897-2 (eBook) Conference Proceedings of the Society for Experimental Mechanics An imprint of River Publishers © The Society for Experimental Mechanics, Inc. 2015 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, Volume 1: Proceedings of the 2014 Annual Conference on Experimental and Applied Mechanics represents one of the eight volumes of technical papers presented at the 2014 SEM Annual Conference & Exposition on Experimental and Applied Mechanics, organized by the Society for Experimental Mechanics and held in Greenville, SC, June 2–5, 2014. The complete proceedings also includes volumes on: Challenges In Mechanics of TimeDependent Materials; Advancement of Optical Methods in Experimental Mechanics; Mechanics of Biological Systems and Materials; MEMS and Nanotechnology; Composite, Hybrid, and Multifunctional Materials; Fracture, Fatigue, Failure and Damage Evolution; and Experimental and Applied Mechanics. Each collection presents early findings from experimental and computational investigations on an important area within Experimental Mechanics Dynamic Behavior of Materials being 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 who co-sponsor and/or co-organize 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 2014 Dynamic Behavior of Materials Track successful. Livermore, CA, USA Bo Song Aberdeen Proving Ground, MD, USA Daniel Casem Socorro, NM, USA Jamie Kimberley v
Contents 1 Tensile Properties of Dyneema SK76 Single Fibers at Multiple Loading Rates Using a Direct Gripping Method...................................................... 1 B. Sanborn and T. Weerasooriya 2 Statistical Characterization of Single PPTA Fiber Tensile Properties from High Strain Rate Tests ......................................................... 5 J.H. Kim, N.A. Heckert, W.G. McDonough, K.D. Rice, and G.A. Holmes 3 Static and Dynamic Thermo-Mechanical Behavior of Ti2AlC MAX Phase and Fiber Reinforced Ti2AlC Composites ............................................... 9 Prathmesh Naik Parrikar, Huili Gao, Miladin Radovic, and Arun Shukla 4 Effects of Spherical Nanoparticle Addition on Dynamic Properties of Polyamide 11............... 15 Masahiro Nishida, Rie Natsume, Norio Fukuda, and Hiroaki Ito 5 Latest Results in Novel Inertial High Strain Rate Tests ..................................... 21 H. Zhu, F. Pierron, and C. Siviour 6 DIC in Dynamic Punch Testing....................................................... 27 J.T. Hammer, T.J. Liutkus, J.D. Seidt, and A. Gilat 7 Specimen Design to Study the Dynamic Response of an Amorphous Polymer.................... 35 Mark Foster, Robert Kaste, and Bryan Love 8 Micro-Raman Spectroscopic Evaluation of Residual Microstresses in Reaction Bonded Boron Carbide Ceramics ............................................................ 39 Phillip Jannotti and Ghatu Subhash 9 Dynamic Response of Human Wisdom Teeth and Temporary Fillers .......................... 45 J. Ren, S.H. Wang, C.C. Chiang, and L. Tsai 10 In Situ and Postmortem Measures of Damage in Polymers at High Strain-Rates ................. 53 E.N. Brown, K.J. Ramos, D.M. Dattelbaum, B.J. Jensen, A.J. Iverson, C.A. Carlson, K. Fezzaa, G.T. Gray III, B.M. Patterson, C.P. Trujillo, D.T. Martinez, T.H. Pierce, and J. Furmanski 11 Application of High Speed Imaging in Particle Dynamics Study with Explosives .................. 61 Elena Jacobs and Vilem Petr 12 Damage Assessment in Metal Plates by Using Laser Vibrometer Measurements .................. 67 Zhenhua Tian and Lingyu Yu 13 Uncertainty of Strain Gage Measurements on Kolsky Bars .................................. 73 Richard L. Rhorer 14 Full-Field Deformation Observation of Polymer Foam Subjected to Shock Loading............... 83 Silas Mallon, Addis Kidane, and Wei-Yang Lu vii
15 Explosive Blast Loading of Biosimulants Through Ballistic Protective Materials .................. 91 Patrick J. Gillich and Rachel Z. Ehlers 16 The Hugoniot Relationships for Nonlinear Elastic Substances ................................ 99 Michael Grinfeld and Pavel Grinfeld 17 Blast Performance of Foam Filled Sandwich Panels Under Extreme Temperatures ............... 107 Payam Fahr, Murat Yazici, and Arun Shukla 18 Dynamics and Shock Waves in Media with Second Order Phase Transformations ................ 113 Pavel Grinfeld and Michael Grinfeld 19 Structural Changes in Lipid Vesicles Generated by the Shock Waves: Dissipative Particle Dynamics Simulation........................................................ 121 Yelena R. Sliozberg and Tanya L. Chantawansri 20 Effect of Threaded Joint Preparation on Impact Energy Dissipation Using Frequency-Based Kolsky Bar Analysis ............................................. 127 Brian T. Werner, Bo Song, and Kevin Nelson 21 Experimental Observation of Slip Pulses During Onset of Sliding Friction ...................... 133 Vijay Subramanian and Raman P. Singh 22 Observation of Dynamic Deformation Behavior Around Interface of Bi-material Using DIC. . . . . . . . 141 Yu Oishi, Shuichi Arikawa, Satoru Yoneyama, Hiroyuki Yamada, and Nagahisa Ogasawara 23 Experimental and Analytical Investigation of Carbon Fiber Cable Damping..................... 149 A.K. Maji and Y. Qiu 24 Volume Damageability According to Criteria of Mechanical and Rolling Fatigue................. 155 Sergei Sherbakov 25 Developments in the Characterization of Metallic Adhesion................................. 161 D. Bortoluzzi, C. Zanoni, J.W. Conklin, and S. Vitale 26 Stress Initiation and Propagation in Glass During Ring-on-Ring Testing....................... 167 Costas G. Fountzoulas, Jeffrey J. Swab, and Parimal J. Patel 27 Investigation of Cavitation Using a Modified Hopkinson Apparatus ........................... 177 Dilaver Singh and Duane S. Cronin 28 Characterization of Structural Epoxy Adhesives .......................................... 185 Luis F. Trimin˜o, Duane S. Cronin, and Mary M. Caruso Dailey 29 Rate Dependent Response of Cross-Linked Epoxy Networks ................................. 193 Randy A. Mrozek, Mark Hindenlang, Adam Richardson, Kevin A. Masser, Jian H. Yu, and Joseph L. Lenhart 30 Dynamic Crack Propagation in Layered Transparent Materials Studied Using Digital Gradient Sensing Method................................................. 197 Balamurugan M. Sundaram and Hareesh V. Tippur 31 Fracture Toughness Testing of Advanced Silicon Carbide Ceramics Using Digital Image Correlation...................................................... 207 John Pittari III and Ghatu Subhash 32 Fracture of Pre-stressed Woven Glass Fiber Composite Exposed to Shock Loading............... 213 Silas Mallon, Behrad Koohbor, and Addis Kidane 33 A Miniature Tensile Kolsky Bar for Thin Film Testing..................................... 221 Jamie Kimberley and Jastin Paul 34 High Temperature Tension HSB Device Based on Direct Electrical Heating..................... 227 M. Hokka, K. O¨ stman, J. R€am€o, and V.-T. Kuokkala viii Contents
35 Dynamic Flow Stress Measurements for Machining Applications ............................. 235 Steven Mates, Eran Vax, Richard Rhorer, Michael Kennedy, Eric Whitenton, Stephen Banovic, and Tim Burns 36 Thermo-Mechanical Behavior of AA-2219 and AA-2195 at High Strain Rates ................... 241 Vinod Pare and Krishna N. Jonnalagadda 37 Rigid Angular Impact Responses of a Generic Steel Vehicle Front Bumper and Crush Can: Correlation of Two Velocity-Measurement Techniques ........................ 249 A. Seyed Yaghoubi, P. Begeman, G. Newaz, D. Board, Y. Chen, and O. Faruque 38 Force-Time History Assessment of a Generic Steel Vehicle Front Bumper and Crush Can Subjected to a Rigid Center Pole Impact .................................... 257 A. Seyed Yaghoubi, P. Begeman, G. Newaz, D. Board, Y. Chen, and O. Faruque 39 Damage of Two Concrete Materials due to Enhanced Shaped Charges ......................... 267 A.D. Resnyansky and S.A. Weckert 40 Influence of Free Water and Strain-Rate on the Behaviour of Concrete Under High Confining Pressure....................................................... 279 P. Forquin 41 Numerical Investigation of Impact Condition Effects on Concrete Penetration................... 285 Christopher S. Meyer 42 On the Damage Mechanisms Involved in Different Geomaterials Subjected to Edge-on Impact Experiments ....................................................... 295 P. Forquin 43 Effect of Boundary Conditions on the Thermo-Mechanical Response of Hastelloy®X Plates Subjected to Shock Loading........................................ 301 C. Anil Rajesh, P. Naik Parrikar, S. Abotula, and A. Shukla 44 Experimental Studies of the Matrix Detonating Cord Charge................................ 307 Vilem Petr and Steven Beggs 45 The Characterization of Ammonium Nitrate Mini-Prills .................................... 319 Erica Lotspeich and Vilem Petr 46 High-Strain Rate Compressive Behavior of Dry Mason Sand Under Confinement ................ 325 Huiyang Luo, Yingjie Du, Zhenxing Hu, and Hongbing Lu 47 Scale Bridging Interactions During Penetration of Granular Materials ......................... 335 M. Omdivar, Z. Chen, S. Bless, and M. Iskander 48 Experimental Investigation on Material Dynamic Behaviors Using Ultra-high-speed Cameras . . . . . . . 341 Xing Zhao, Silas Mallon, Addis Kidane, Michael Sutton, and Hubert Schreier 49 Application of 3-D Digital Image Correlation Technique to Study Underwater Implosion........... 351 Sachin Gupta, Venkitanarayanan Parameswaran, Michael Sutton, and Arun Shukla 50 Dynamic Analysis of a Plate Loaded by Explosively Driven Sand............................. 357 A.D. Resnyansky and S.A. Weckert 51 Simulating the Planar Shock Response of Concrete........................................ 369 Jeff LaJeunesse, John Borg, and Brad Martin 52 Mesoscale Simulations of Dry Sand.................................................... 379 Merit G. Schumaker, John P. Borg, Gregory Kennedy, and Naresh N. Thadhani 53 Perforation of 6082-T651 Aluminum Plates with 7.62 mm APM2 Bullets at Normal and Oblique Impacts ....................................................... 389 M.J. Forrestal, T.L. Warren, T. Børvik, and W. Chen Contents ix
Chapter 1 Tensile Properties of Dyneema SK76 Single Fibers at Multiple Loading Rates Using a Direct Gripping Method B. Sanborn and T. Weerasooriya Abstract Ultra-high-molecular-weight polyethylene (UHMWPE) fibers such as Dyneema and Spectra are seeing more use in lightweight armor applications due to higher tensile strength and lower density compared with aramid fibers such as Kevlar and Twaron. Numerical modeling is used to design more effective fiber-based composite armor. For accurate simulation of ballistic impacts, material response such as tensile stress-strain of the composite constituents must be studied under experimental conditions similar to ballistic events. UHMWPE fibers are difficult to grip using adhesive methods typically used for other fibers due to low surface energy. Based on previous studies, the ability to grip UHMWPE fibers using traditional adhesive methods depends on fiber diameter and is limited to smaller diameter fibers that could affect reported stress values. To avoid diameter restrictions and surface energy problems, a direct gripping method has been used to characterize Dyneema SK76 single fibers at strain rates of 0.001 s-1, 1 s-1, and 1000 s-1. In this report, the dependence of fiber diameter and gage length on failure strength is discussed as well as success rate of failures in the gage section with this gripping technique. A comparison of the tensile properties with previous studies is also explored. Keywords Single fiber • SHTB • Dyneema • UHMWPE • Tensile response 1.1 Introduction Aramid fibers such as Kevlar and Twaron are frequently used in protective armor, though ultrahigh molecular weight polyethylene (UHMWPE) fibers such as Dyneema and Spectra are desirable due to lower density at 0.97 g/cm3 compared to 1.44 g/cm3 for aramids, as well as higher tensile modulus and good resistance to chemical and physical degradation. Due to an increasing need for numerical modeling capability of different soft armor systems, constituent level material properties are required to develop simulation methods. The primary loading mode on fibers used in protective equipment is axial tension. Hence, tensile experiments must be conducted at high strain rates that mimic loading rates that are seen in an impact event. UHMWPE fibers such as Dyneema and Spectra are notoriously difficult to grip for these tensile tests due to low surface energy [1]. Several authors have reported difficulties associated with gripping UHMWPE fibers [2, 3]. The ability to grip Dyneema and other UHMWPE fibers using the standard gripping method for fibers which utilizes an adhesive to attach the fibers to a cardboard substrate is apparently dependent on fiber diameter [4, 5], which can be used successfully when diameter is limited to up to 16 μm as noted by Hudspeth et al. [5]. Hybrid methods utilizing mechanical gripping and adhesives have also shown limited success rates and some authors have indicated that fibers slip in the grips during tensile experiments [2, 3]. Though adhesive methods are effective for aramid fibers [6–10], Kim et al. [11–13] have been developing a method of direct gripping on PPTA. This direct clamping method utilizes poly methyl methacrylate (PMMA) blocks. The efficacy of this method to grip Kevlar fibers has been rigorously studied using a variety of statistical B. Sanborn (*) Oak Ridge Institute for Science and Eduction/US Army Research Laboratory, Bldg 4600, Aberdeen Proving Ground, Aberdeen, MD, USA e-mail: brett.sanborn2.ctr@mail.mil T. Weerasooriya US Army Research Laboratory, Bldg 4600, Aberdeen Proving Ground, Aberdeen, MD, USA B. Song et al. (eds.), Dynamic Behavior of Materials, Volume 1: Proceedings of the 2014 Annual Conference on Experimental and Applied Mechanics, Conference Proceedings of the Society for Experimental Mechanics Series, DOI 10.1007/978-3-319-06995-1_1, #The Society for Experimental Mechanics, Inc. 2015 1
methods at different strain rates, including high strain rates which pose additional problems such as minimizing the overall grip size to fit on the Kolsky bar apparatus [11–13]. To overcome the difficulties associated with adhesive bonding, hybrid adhesive and mechanical methods, and mechanical methods that might not provide accurate strain measurements, a gripping method similar to that proposed by Kim et al. [11–13] has been refined and used in this study to collect accurate strain histories of single fiber samples and to load specimens to failure without apparent fiber slippage from the gripping system. Furthermore, this technique is applicable to UHMWPE fibers and is not limited by the diameter of the fiber and can be utilized at high strain rates. In addition to investigating the loading rate effects on SK76 fibers, a wide range of gage lengths was used to study the effect of defect distribution in the fiber. 1.2 Experiments To study the tensile strength of Dyneema SK76 fiber under uniaxial tension, single fibers were extracted from SK76 yarns and were glued to temporary specimen holders. Diameters of individual fiber samples were measured in an optical microscope for accurate stress determination. After diameter measurements were taken, the fibers were loaded into the direct grips and clamped in place. The temporary specimen holders were clipped and removed from the experimental apparatus. Fiber samples were pulled in tension at strain rates of 0.001 and 1 s 1 using Bose Electroforce and at 1,000 s 1 using a tension Kolsky bar modified for fiber characterization. Specimens with gage lengths of 5, 10, and 50 mm were studied at quasi-static and intermediate rates and gage lengths of 5, 7, and 10 mm were studied at high strain rates to study the effect of defect distribution in the fibers. A total of ten experiments were conducted at each condition of gage length and strain rate for a total of 90 experiments. 1.3 Results Overall, the direct gripping method applied to Dyneema fibers was successful. Fibers over a range of from 14.5 to 22.3 μm were successfully gripped using this technique. One particularly large fiber sample with diameter of 35.9 0.52 μm was also successfully gripped using this technique, but was not included in the analysis due to its uncharacteristically large diameter. Tensile strength as a function of strain rate is shown in Fig. 1.1. The overall behavior of the fiber shows an increase in strength with increasing strain rate. The results show that a plateau in strength is reached at an intermediate strain rate of 1 s 1 since the failure strength of the fiber does not increase when the strain rate is increased from 1 to 1,000 s 1. The Fig. 1.1 Tensile strength as a function of strain rate 2 B. Sanborn and T. Weerasooriya
failure strength of Dyneema does not depend on the gage length of the fiber since no change in strength was observed at shorter gage lengths. Future work should include shorter gage lengths to further probe this observation. The results of this study show higher failure strengths compared to the study by Hudspeth et al. [5] on Dyneema SK76, but compare well with published data by Dyneema [14] and a study by Russell et al. on SK76 fibers and yarns [3]. In general, the stress–strain behavior of the Dyneema fiber is increasingly linear with increasing strain rate [3, 15, 16]. The average behavior of 5 mm gage length samples is shown in Fig. 1.2. Error bars represent one standard of deviation of strength at each strain value. At low rates, the primary deformation mode of the Dyneema UHMWPE fiber is creep [3, 17–19]. Creep was also noted on non-ballistic grades of Dyneema such as SK66 [20] and SK65 [21]. In each case the creep component increases with decreasing strain rate. The increase in linearity of the stress–strain curve is also seen when experiments at different temperatures are conducted [20] suggesting that the mechanism of failure at low temperatures is similar the mechanism of failure at high strain rates. References 1. Lin SP, Han JL, Yeh JT, Chang FC, Hsieh KH (2007) Surface modification and physical properties of various UHMWPE fiber reinforced modified epoxy composites. J Appl Polym Sci 104:655–665 2. Umberger PD (2010) Characterization and response of thermoplastic composites and constituents. Master’s thesis 3. Russell BP, Karthikeyan K, Deshpande VS, Fleck NA (2013) The high strain rate response of ultra high molecular weight polyethylene: from fibre to laminate. Int J Impact Eng 60:1–9 4. Cochron S, Galvez F, Pintor A, Cendon D, Rosello C, Sanchez-Galvez V (2002) Characterization of fraglight non-woven felt and simulation of FSP’s impact in it. R&D 8927-AN-01 5. Hudspeth M, Nie X, Chen W (2012) Dynamic failure of Dyneema SK76 single fibers under biaxial shear/tension. Polymer 53:5568–5574 6. Lim J, Zheng JQ, Masters K, Chen WW (2010) Mechanical behavior of A265 single fibers. J Mater Sci 45:652–661 7. Lim J, Chen WW, Zheng JQ (2010) Dynamic small strain measurements of Kevlar ® 129 single fibers with a miniaturized tension Kolsky bar. Polym Test 29:701–705 8. Lim J, Zheng JQ, Masters K, Chen WW (2011) Effects of gage length loading rates, and damage on the strength of PPTA fibers. Int J Impact Eng 38:219–227 9. Cheng M, Chen W, Weerasooriya T (2005) Mechanical properties of Kevlar KM2 Single fiber. J Eng Mater Technol 127:197–203 10. Sanborn B, Weerasooriya T (2013) Quantifying damage at multiple loading rates to Kevlar KM2 fibers due to weaving and finishing. ARL-TR-6465. June 2013 11. Kim JH, Heckert AN, Leigh SD, Rhorer RL, Kobayashi H, McDonough WG, Rice KD, Holmes GA (2014) Statistical analysis of PPTA fiber strengths measured under high strain rate condition. Compos Sci Technol 98:93–99 12. Kim JH, Heckert NA, McDonough WG, Rice KD, Holmes GA (2013) Single fiber tensile properties measured by the Kolsky bar using a direct fiber clamping method. In: Proceedings of society for experimental mechanics conference. Lombard, IL 13. Kim JH, Heckert NA, Leigh SD, Kobayashi H, McDonough WG, Rice KD, Holmes GA (2013) Effects of fiber gripping methods on the single fiber tensile test: I. Non-parametric statistical analysis. J Mater Sci 48:3623–3673 Fig. 1.2 Stress–strain response at multiple strain rates. Note the increase in linearity for the same gage length with increasing strain rate. The curves in these plots represent the average behavior of ten experiments 1 Tensile Properties of Dyneema SK76 Single Fibers at Multiple Loading Rates Using a Direct Gripping Method 3
14. Dyneema Comprehensive Fact Sheet (2008) January 2008. REF: CIS YA100 15. Cansfield D, Ward I, Woods D, Buckley A, Pierce J, Wesley J (1983) Tensile strength of ultra high modulus linear polyethylene filaments. Polym Commun 24:130e1 16. Schwartz P, Netravali A, Sembach S (1986) Effects of strain rate and gauge length on the failure of ultrahigh strength polyethylene. Text Res J 56(8):502–508 17. Wilding MA, Ward IM (1978) Tensile creep and recovery in ultra-high modulus linear polyethylenes. Polymer 19:969–976 18. Wilding MA, Ward IM (1978) Creep and recovery in ultra-high modulus polyethylene. Polymer 22:870–876 19. Wilding MA, Ward IM (1984) Creep and Stress-relaxation in ultra-high modulus linear polyethylene. J Mater Sci 19:629–636 20. Govaert LE, Bastiaansen CWM, Leblans PJR (1993) Stress–strain analysis of oriented polyethylene. Polymer 34(3):534–540 21. Liu X, Yu W (2005) Evaluation of the tensile properties and thermal stability of ultrahigh-molecular-weight polyethylene fibers. J Appl Polym Sci 97:310–315 4 B. Sanborn and T. Weerasooriya
Chapter 2 Statistical Characterization of Single PPTA Fiber Tensile Properties from High Strain Rate Tests J.H. Kim, N.A. Heckert, W.G. McDonough, K.D. Rice, and G.A. Holmes Abstract Single [poly (p-phenylene terephalamide)] PPTA fiber tensile strengths were measured under quasi-static and high strain rate loading conditions, and poly (methyl methacrylate) (PMMA) and rubber as gripping materials were used to investigate gripping effects for the tests. To incorporate the strength distributions of single PPTA fibers into a rate dependent stochastic strength model, it is important to estimate uncertainties of the model parameters as well as the best-fittingdistribution for the parameter estimation. We demonstrated the appropriateness of a Weibull model for the tensile strengths obtained by the quasi-static test and preliminary results for the corresponding Weibull shape parameters with approximately 20 % parameter confidence intervals. These results will be used to characterize of the strengths obtained by the high strain rate test using the Weibull model. Keywords Single fiber tensile test • PPTA fiber • Statistical analysis • High strain rate • Direct fiber grip 2.1 Introduction Soft body armors have been used to protect the human body from the ballistic impact. The impact and perforation of fabrics in the body armors depend on several parameters including the material properties of the yarns, fabric structure, the projectile velocity etc. When a projectile strikes a fabric of body armor, longitudinal and transverse waves propagate from the impact zone, and these create fiber deformations in several different directions indicating tension along the fiber’s axis, transverse compression, and fiber deflection. Numerous studies have been carried out on the impact behaviors of soft body armors during ballistic events, however, most of the studies on the influence of materials tensile properties on ballistic performance are conducted using the quasi-static properties [1]. Until recently, most fiber strengths obtained by single fiber tensile tests have been performed under many orders of magnitude slower loading conditions compared to ballistic impact. In order to measure fiber strengths under loading rates comparable to those of ballistic impact, a miniaturized Kolsky bar has been developed [2] and a direct fiber gripping method to increase test throughput has been adopted after a comparison study for gripping methods [3, 4]. Fiber strengths obtained by the single fiber tensile test typically exhibit large variation, so statistical analyses are often carried out to model dispersions of strength data. Many Weibull analyses for single fiber strengths obtained under the quasistatic loading conditions have been carried out; however fiber strengths for high strain rates tests are rarely reported. J.H. Kim • W.G. McDonough • G.A. Holmes (*) Materials Science and Engineering Division (M/S 8541), National Institute of Standards and Technology, Gaithersburg, MD 20899, USA e-mail: gale.holmes@nist.gov N.A. Heckert Statistical Engineering Division (M/S 8980), National Institute of Standards and Technology, Gaithersburg, MD 20899, USA K.D. Rice Materials Measurement Science Division (M/S 8102), National Institute of Standards and Technology, Gaithersburg, MD 20899, USA Official contribution of the National Institute of Standards and Technology; not subject to copyright in the United States. B. Song et al. (eds.), Dynamic Behavior of Materials, Volume 1: Proceedings of the 2014 Annual Conference on Experimental and Applied Mechanics, Conference Proceedings of the Society for Experimental Mechanics Series, DOI 10.1007/978-3-319-06995-1_2, #The Society for Experimental Mechanics, Inc. 2015 5
Main objectives of this study are investigating stochastic the behavior of single PPTA fiber strengths obtained under the quasi-static and high rate loading tests. We focus on the Weibull distribution to model the strength dispersions, after examining distributions graphically. 2.2 Stochastic Fiber Fracture Model A stochastic fiber fracture model using the two-parameter Weibull distribution has been proposed to predict ultimate strengths of various types of fibers [5]. The average tensile strength (σf) of the individual fibers with a length (L) can be given by: σf ¼γ L L0 1=β Γ 1þ 1 β , ð2:1Þ whereγ andβare the Weibull scale and shape parameters respectively, andГis the gamma function. Г(1 + 1/β) 0.95 0.03 in the case of the Weibull shape parameter β values varying from 5 to 30 [5]. L0 is a reference length (1 mm in this study). Equation (2.1) is typically used for estimating fiber strengths obtained by quasi-static tests. Assuming the same linear elastic behaviors of the fibers until rupture for both quasi-static and high strain rate loadings, the relation of the Weibull parameters between quasi-static and high strain rate tests as a function of strain rate can be given by [6]: βs ¼βh γs ¼ 1þE _ε _εref 0 @ 1 A 2 4 3 5 1þε _ε _εref 0 @ 1 A 2 4 3 5 γh 8> >< >>: ð2:2Þ where the subscripts s and h represent quasi-static and high strain rate loading conditions, and _ε and _εref represent the input strain rate and the reference strain rate (i.e. the strain rate for quasi-static loading) respectively. The ratio of the mean strengths for the two cases is γs L L0 1=βs Γ 1þ1 βs =γh L L0 1=βh Γ 1þ1 βh . So if two cases (i.e., quasi-static and high strain rate) are adequately modelled by the two-parameter Weibull and the shape parameters are essentially equivalent, then the ratio simplifies to the ratio of the scale parameters. 2.3 Experimental Procedure 2.3.1 Single Fiber Tensile Tests PMMA [poly (methyl methacrylate)] and rubber were used as clamp materials for the single fiber tensile tests to investigate gripping effects. The authors will utilize the term “PMMA and rubber grips” to refer a fiber grip made by two different materials set. For the quasi-static loading, a single fiber was clamped in the grips of a screw-driven machine with approximately 1 mN of pretension using a weight. Open/close motions of the grips were controlled by a pneumatic controller. Strain-to-failure was obtained by the displacement of the actuator, and the tensile stress was obtained by the force history and the cross sectional area of the fiber. Fiber lengths of 2, 5, and 10 mm were chosen to be the gauge lengths respectively. For the high rate loading, the miniaturized Kolsky bar was used in conjunction with a quartz-piezoelectric load cell due to very small transmitted force signal through a single PPTA fiber. A laser optical system [7] was used to measure the displacement of the Kolsky bar. A thin laser line generated by 100 mW laser illuminates a target that is attached to the gripping area of the Kolsky bar. The intensity of the refocused beam from the laser line is increased as the end of the bar moves in uniaxial tension and the relation between the bar location and the laser intensity is used to calibrate the laser intensity. Fiber lengths with 2, 5, and 8 mm were used as the gauge lengths of the high rate tests. Both tensile test results as a function of strain rate will be demonstrated in the presentation. 6 J.H. Kim et al.
2.4 Results and Discussion In this section, the procedures of the statistical analyses for the tensile strength data are briefly described and the statistical analysis results are summarized for each step. 2.4.1 Non-parametric Analysis of the Tensile Strengths The fiber tensile strengths obtained by PMMA and rubber grips were compared graphically using kernel density plots. The kernel density estimate is defined as f yð Þ¼X n i¼1 K y Yi ð Þ h n o nh , ð2:3Þ with K, h, Yi, and n denoting the kernel function, the window width, the ith data point and the number of data points, respectively. The histogram is a simple kernel density estimator where h corresponds to the bin width, but typically the kernel density plot can show the underlying structure in the data more clearly than a histogram, particularly for modest sample sizes. Kernel density plots provide indications of such features as (1) the center of the data, (2) the spread of the data, and (3) the skewness of the data. Because of these advantages, we used it for estimating the strength distributions graphically. Figure 2.1 shows the kernel density plots of the tensile strengths for the PMMA and rubber grip tests using 2 mm fibers under the quasi-static loading condition. Similar widths of the kernel density plots for both grip tests indicate comparable strength distributions for the tests, but with possibly distinct modes of peak locations. 2.4.2 Distributional Fits: Parameter Estimates and Confidence Limits Since the parameters of the two-parameter Weibull distribution are used in estimating average fiber strengths, one should estimate the Weibull parameters and uncertainties (confidence intervals) for the parameter estimates. The cumulative distribution function of the two-parameter Weibull distribution is given by: F¼1 exp L L0 x γ β !, ð2:4Þ where x is fiber strength and other parameters are the same with those in Eq. (2.1). Although the Weibull plot is frequently used to estimate the parameters, we used maximum likelihood (ML) method. Since the Weibull shape parameter is Fig. 2.1 Kernel density plot for the fiber strengths obtained by PMMA and rubber grips 2 Statistical Characterization of Single PPTA Fiber Tensile Properties from High Strain Rate Tests 7
correlated to the dispersion of the data, we focus on the shape parameter and its confidence interval. The shape parameters for the strength data (Fig. 2.1) obtained by the ML method varied from six to eight with confidence intervals approximately 20%. 2.4.3 Assessing Goodness of Fit The two-parameter Weibull distribution is typically used to analyze dispersions of fiber strength data without investigating goodness of fit. A primary analytical method to assess goodness-of-fit is the Anderson–Darling (AD) test. Using PPTA fibers similar to the fibers used in this study, fiber strengths with 2 mm were previously measured for the PMMA grip under the quasi-static loading condition. A–D tests were carried out, which rejected the best-fitting assumption for the two-parameter Weibull distribution (1.2 A–D and 0.76 critical values). More goodness-of-fit analyses are being carried out with the PPTA fibers for the PMMA and rubber grips and will be presented in the future. 2.5 Concluding Remarks Single PPTA fiber strengths were measured using the PMMA and rubber grip methods under quasi-static and high strain rate loading conditions. To validate a model, an important procedure is to confirm the best-fitting distribution as well as the parameter estimates. Since we are investigating dispersions of fiber strengths obtained by the high rate tests which are rarely reported in literatures, a procedure for assessing the strength distributions with the two-parameter Weibull is demonstrated for each step. Detailed statistical investigations for the strengths will be used to characterize PPTA fiber tensile properties as a function of loading rate and gripping method. References 1. Cheeseman BA, Bogetti TA (2003) Ballistic impact into fabric and compliant composite laminates. Compos Struct 61:161–173 2. Cheng M, Chen W, Weerasooriya T (2004) Mechanical properties of Kevlar KM2 single fiber. Int J Solids Struct 41:6215–6232 3. Kim JH, Heckert NA, Leigh SD, Kobayashi H, McDonough WG, Rice KD, Holmes GA (2013) Effects of fiber gripping methods on the single fiber tensile test: I. Non parametric statistical analysis. J Mater Sci 48:3623–3637 4. Kim JH, Heckert NA, Leigh SD, Rhorer RL, Kobayashi H, McDonough WG, Rice KD, Holmes GA (2012) Statistical analysis of PPTA fiber strengths measured under high strain rate condition. Compos Sci Technol 98(2014):93–99 (10 1016/j Compscitech 2012 03 021) 5. Vanderzwaag S (1989) The concept of filament strength and the weibull modulus. J Test Eval 17:292–298 6. Xia YM, Yuan JM, Yang BC (1994) A statistical-model and experimental-study of the strain-rate dependence of the strength of fibers. Compos Sci Technol 52:499–504 7. Lim J, Chen WNW, Zheng JQ (2010) Dynamic small strain measurements of Kevlar 129 single fibers with a miniaturized tension Kolsky bar. Polym Test 29:701–705 8 J.H. Kim et al.
Chapter 3 Static and Dynamic Thermo-Mechanical Behavior of Ti2AlC MAX Phase and Fiber Reinforced Ti2AlC Composites Prathmesh Naik Parrikar, Huili Gao, Miladin Radovic, and Arun Shukla Abstract Ti2AlC MAX phase samples were processed by using Spark Plasma Sintering from commercially available Ti2AlC powder. Static and dynamic loading was performed by Universal Testing Machine and Split Hopkinson Pressure Bar (SHPB) respectively. The SHPB apparatus was modified to investigate the dynamic fracture initiation toughness. High speed photography was used to determine the fracture initiation time and the associated failure load. To widen applications, 20 vol % fiber of NextelTM-610 and NextelTM-720 have been added for the reinforcement of Ti2AlC, respectively. The results reveal that the peak compressive failure stress in dynamic conditions decreases with increasing temperatures, from 1,645 MPa at 25 C to 1,210 MPa at 1,200 C. The fracture experiments show that the dynamic fracture toughness is higher than the quasi-static value by approximately 35 %. The fracture toughness decreases with increase in temperature. The post mortem analysis of the fracture surfaces conducted using Scanning Electron Microscopy revealed that kinking along with intergranular cracking and delamination play important role in deformation of Ti2AlC. Compared to pure Ti2AlC, compressive fracture strength of 20 vol% Ti2AlC/720f and Ti2AlC/610f composites were enhanced by 39.7 and 32.6 % under static loading. Keywords MAX phase • Thermo-mechanical loading • Fracture toughness • Constitutive behavior • Kink bands • Titanium aluminum carbide 3.1 Introduction TheMn+1AXn (MAX) phases are a class of nanolayered, machinable, early transition ternary metal carbides and/or nitrides [1]. Because of the structural similarity between MAX phases and their corresponding MX structure, they share lot of properties while some properties are significantly different from their MX counterparts [2, 3]. Ti2AlC is a MAX phase that has attracted a lot of attention as it is machinable, electrically conductive, lightweight and resistant to thermal shock, oxidation and creep [4–7]. Different methods of fabrication of Ti2AlC and its composites for high temperature applications [4, 8, 9]. The material characterization of MAX phases has been limited to quasi-static loading regimes. TheKI values are reported to be in a large range from 4 to 16 MPa m1/2 are probably attributed to the different grain size, the shape and dimension of the sample, sample impurities, different testing methods, and experimental conditions [10–13]. In this study experiments were conducted to investigate the effect of different strain rate and temperature on the material characteristics. An experimental investigation of the stress strain characteristics of Ti2AlC under quasi-static and dynamic loading was conducted at room and elevated temperatures. The peak compressive stress decreases with increasing P. Naik Parrikar • A. Shukla (*) Department of Mechanical, Industrial and Systems Engineering, University of Rhode Island, Kingston, RI 02881, USA e-mail: shuklaa@egr.uri.edu H. Gao Mechanical Engineering Department, Texas A&M University, College Station, TX 77843, USA M. Radovic Mechanical Engineering Department, Texas A&M University, College Station, TX 77843, USA Materials Science and Engineering Department, Texas A&M University, College Station, TX 77843, USA B. Song et al. (eds.), Dynamic Behavior of Materials, Volume 1: Proceedings of the 2014 Annual Conference on Experimental and Applied Mechanics, Conference Proceedings of the Society for Experimental Mechanics Series, DOI 10.1007/978-3-319-06995-1_3, #The Society for Experimental Mechanics, Inc. 2015 9
temperature. The fracture initiation toughness was instigated as a function of temperature. The dynamic fracture toughness is higher than the quasi-static value by approximately 35 %. Also, the fracture toughness decreases with increasing temperature. 3.2 Material Fabrication Commercial Ti2AlC powders (Kanthal AB, Sweden) was used to process all samples in this study. Bulk Ti2AlC samples with a diameter of 50 mm were processed at 1,300 C for 15 min with a constant load of 100 MPa by Spark plasma sintering system. The relative density of bulk Ti2AlC was measured above 98 % according to ASTM D792. All of specimens tested in this study were electron-discharge machined from disc. Two kinds of alumina fiber-reinforced Ti2AlC MAX phase composites have been successfully fabricated to improve static and dynamic behavior of Ti2AlC via colloidal processing, called Ti2AlC/720f and Ti2AlC/610f composites. To widen applications at high temperature, 20 vol% fiber, including NextelTM 610 and NextelTM 720, have been added for the reinforcement of Ti2AlC, respectively. 3.3 Quasi-Static Characterization The quasi-static compression tests were performed using Materials Testing Systems 810 with 100 kN load cell. Strain was measured using a high-temperature extensometer. The specimens had a diameter of 5 mm and thickness of 8 mm. Fixed displacement rate was used to yield 10 4 s 1 strain rate. K-type thermocouple in contact to Silicon carbide spacer was used to monitor the temperature. 3.4 Dynamic Characterization A Split Hopkinson Pressure Bar (SHPB) apparatus developed by Kolsky [14] was used to study the dynamic behavior of Ti2AlC. The striker bar, incident bar and transmission bar, in the SHPB setup were all made out of Maraging steel. Incident and transmission bars have a diameter of 12.5 mm and a length of 2,133 and 1,524 mm respectively. The striker bar is propelled using an air-operated gun. The specimens had a diameter of 6.35 mm and thickness of 3.18 mm. A lead pulse shaper of thickness 1 mm was placed at the impact end of the incident bar as shown in Fig. 3.1. Two impedance matched tungsten-carbide (WC) inserts were placed between the two bars and the specimen was sandwiched between the inserts. The inserts were used to reduce stress concentration in the specimens and to prevent indentation of the specimens into the bars. Molybdenum disulfide was used to lubricate the specimen insert interface to minimize the effects of friction. Two strain gages were mounted diametrically opposite to one another on the surfaces of the incident and transmission bar to provide time-resolved measures of the axial elastic strain pulses in the bars. The strain signals are recorded using a Vishay 2301A signal-conditioning amplifier that is connected with an oscilloscope. Using one-dimensional wave theory, the strain and stress in the specimen can be determined from the reflected and transmitted strain pulses, respectively, as σs ¼Eb Ab As εt tð Þ ð3:1Þ Fig. 3.1 Schematic representation of SHPB setup 10 P. Naik Parrikar et al.
εs ¼ 2cb Ls ð t 0 εr tð Þdt ð3:2Þ Where σs and εs are stress and strain in the specimen, εr and εt are the time resolved strain values of reflected and transmitted pulses, cb is the longitudinal bar wave speed, Eb is the Young’s modulus of the bar material, Ab is the crosssectional area of the bar, and As is the cross-sectional area of the specimen and Ls is the thickness of the specimen. Figure 3.2 shows the pulses recorded during an experiment at an average strain rate of 400 s 1. The strain gage on the incident bar measures the incident and the reflected pulses. The lead pulse shaper gives a linear ramp in the incident pulse as seen in the figure. A drastic fall in the transmitted pulse marked by “+” is observed and this corresponds to catastrophic failure of the specimen. The point marked by “o” on the reflected pulse also corresponds to failure of the specimen. Beyond this point the magnitude of reflected pulse rises due to free forward motion of the incident bar end and is not representative of specimen strain. The high temperature experiments were carried at 400 s 1 from room temperature to 1,200 C. An induction coil heater was used in conjunction with the SHPB setup. The Ti2AlC specimens are electrically conductive and get heated by electromagnetic induction using coiled loops around the specimen. The WC inserts prevented sharp temperature gradient in the bars and also protected the strain gages mounted on them. 3.5 Fracture Toughness The single edge notched specimens for fracture toughness experiments were machined by electron discharge machining using a wire of 0.1 mm diameter. Figure 3.3 shows the details of specimen geometry. 3.6 Quasi-Static Fracture Initiation Toughness The quasi-static fracture initiation toughness was investigated using a three-point bending experiment as shown in the Fig. 3.4. The experiments were conducted at, 25, 500 and 900 C temperatures. The specimen was heated to the desired temperature using an induction heating system before applying load. The experiments were conducted under a fixed loading rate of 1 mm/min at room temperature. To avoid the creep effect during elevated temperature, a loading rate of 5 mm/min was used. ° 0 200 400 600 −4,000 −3,000 −2,000 −1,000 0 1,000 2,000 3,000 4,000 Transmitted Pulse Reflected Pulse Time (μs) Strain gage on incident bar Stain gage on transmitted bar Strain (με) Incident Pulse Fig. 3.2 Typical pulses recorded during an experiment 3 Static and Dynamic Thermo-Mechanical Behavior of Ti2AlC MAX Phase and Fiber Reinforced Ti2AlC Composites 11
3.7 Dynamic Fracture Initiation Toughness A modified split Hopkinson pressure bar (SHPB) apparatus with induction heating system is used to investigate the dynamic fracture initiation toughness of Ti2AlC. The modified SHPB apparatus mainly consists of an incident bar, striker bar and pressure gun. The incident bar and striker bar are made from T6061 aluminum. The strains in the incident bar are measured using two semiconductor strain gages that are attached in the middle of the bar diametrically opposite to one another. During loading, the specimen is sandwiched between the incident bar and the rigid frame. For an elevated temperature experiment, the bar is first kept apart and the specimen is heated to the desired temperature (usually about 20–50 C higher than the test temperature) and later the bar is manually brought into contact with the specimen. The temperature of the specimen is monitored by using thermocouple, which is spot welded onto the specimen. Once the specimen is in contact with the incident bar, the striker bar is propelled towards the incident bar using an air-operated gun. The impact generates a compressive stress wave in the bar which propagates toward the bar/specimen interface. When the wave reaches the specimen, some of the wave is reflected back and part of the wave is transmitted into the specimen. The load history at the specimen/bar interface is obtained from the recorded strain data using a one dimensional elastic wave theory given by the following equation: F tð Þ¼ εi tð Þþεr tð Þ ½ EA ð3:3Þ Where F is the force, εi and εr are the incident and reflected strain pulses, E is the Young’s modulus, and A is the cross sectional area of the bar. When the time of fracture is sufficiently long, the dynamic stress intensity factor can be calculated from the input load as: KI tð Þ¼ F tð Þ B ffiffiffifffiiW p f a W ð 3:4Þ B=4.5 mm S=36 mm W=9 mm a=4 mm Fig. 3.3 Single edge notched specimen Fig. 3.4 Three point bend experimental setup 12 P. Naik Parrikar et al.
Where KI is the stress intensity factor, B the specimen thickness, W the specimen width, a the initial crack length and f(a/W) is the geometric factor. The dynamic fracture initiation toughness (KID) corresponds to the stress intensity factor at the time of crack initiation, i.e. KID ¼KI(tinitiation). High speed photography was incorporated to identify the time corresponding to the load required to initiate the crack. Photron SA1 high-speed digital camera was used at a frame rate of 450,000 fps with an image resolution of 128 32pixels. The camera was synchronized to ensure that the images and strain gage data could be correlated and that the total time from the beginning of the load to the fracture initiation could be evaluated. 3.8 Results and Discussion Figure 3.5 shows the true compressive stress-strain curves of Ti2AlC during quasi-static and dynamic loading at various temperatures. The dynamic experiments were conducted at an average strain rate of 400 s 1. The specimens exhibit catastrophic failure at all the temperatures tested under dynamic loading. The peak compressive stress in the high strain rate experiments varies from 1,645 MPa at room temperature to 1,210 MPa at 1,200 C. The peak compressive stress decreases with increase in temperature. In the quasi-static experiments at the strain rate of 10 4 s 1 the peak compressive stress decreases with increasing temperature and at 900 C a brittle to ductile transformation is observed. The quasi-static and dynamic fracture initiation toughness of Ti2AlC was investigated as a function of temperature. The quasi-static fracture initiation toughness at room temperature (25 C) was 4.03 MPa m1/2 and decreased to 2.23 MPa m1/2 at 900 C. Dynamic fracture initiation at room temperature was 5.46 MPa m1/2 and 5.18 MPa m1/2 at 900 C. The fracture initiation toughness is rate dependent; it is higher at dynamic loading as compared with quasi-static loading. The fracture toughness decreases with increase in temperature. The post mortem analysis of the fracture surfaces conducted using Scanning Electron Microscopy. 3.9 Conclusion Experimental investigation of constitutive behavior and fracture toughness of Ti2AlC was conducted at room and elevated temperatures. The material exhibits positive strain rate sensitivity exhibiting higher stress with increasing strain rate. Brittle to plastic transformation was observed under quasi-static loading at 900 C. Under dynamic loading conditions the failure remains brittle in nature even at temperature of 1,200 C. The peak compressive stress decrease with increasing temperatures. Fracture toughness shows rate dependence and decreases with increasing temperature. Acknowledgment Authors would like to acknowledge CMMI, National Science Foundation, Grant No. 1233887 and 1233792 at University of Rhode Island and Texas A&M University. 0 1 2 12 15 18 21 24 0 300 600 900 1,200 1,500 1,800 Room Temp. 500 C 1,000 C 1,200 C Room Temp. 500 C 700 C 900 C 1,000 C 1,100 C True Stress (MPa) True Strain (%) Dynamic Quasi-static Fig. 3.5 True compressive stress–strain curve of Ti2AlC at various temperatures 3 Static and Dynamic Thermo-Mechanical Behavior of Ti2AlC MAX Phase and Fiber Reinforced Ti2AlC Composites 13
RkJQdWJsaXNoZXIy MTMzNzEzMQ==