Modeling the effects of yarn material properties and friction on the ballistic impact of a plain-weave fabric

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<ul><li><p>pfab</p><p>.A.</p><p>A</p><p>Keywords:Ballistic impactYarn material propertiesFrictionWoven fabricFinite element analysis</p><p>Quasi-static friction was experimentally determined and incorporated into the model. Two clampededges and two free edges were used as boundary conditions to correlate the model to an experimental</p><p>of three different styles of Kevlar fabric with respect to their ballis-tic impact performance. Different levels of inter ber/yarn frictionwithin the Kevlar fabrics were achieved by removal or addition ofsurface lubricants. It was found that for a given style of fabric, the</p><p>Zeng et al. [4] developed a central difference based numericalmodel to study the effect of friction on woven fabric armor com-prised of Twaron CT716 bers. In that work [4], the authorsgrouped inter-yarn friction as low (l = 0.00.06), moderate(l = 0.060.2) and high (l = 0.21.0) based on the effect of fric-tion on the energy absorption capacity of the fabric armor. Theyshowed via detailed numerical simulations that the ballistic limitclearly increases in the low (l = 0.00.06) and moderate(l = 0.060.2) regimes, while in the high (l = 0.21.0) zone, theballistic performance only very slightly diminishes. However, theauthors of [4] surmise that increasing l = 0.2 to l = 0.6, yields little</p><p>* Corresponding author. Tel.: +1 302 831 8009; fax: +1 302 831 3619.E-mail address: (M. Keefe).</p><p>1 Present address: Department of Mechanical and Aerospace Engineering, Univer-sity of Florida, P.O. Box 116250, Gainesville, FL 32611-6250, USA.</p><p>Composite Structures 89 (2009) 556566</p><p>Contents lists availab</p><p>Composite S</p><p>sev2 Present address: The Boeing Company, Seattle, WA, USA.High-strength fabrics are often used in ballistic impact protec-tion systems where exibility and lightweight are of importance.Experiments demonstrate that interfacial friction affects the ballis-tic impact energy absorption of these fabrics [13]. Tan et al. [1]studied the ballistic performance of single layers of Twaron fabric.In their experiments, projectiles with different shapes were used toimpact onto rectangular fabric specimens clamped along twoopposite edges. Their experiments indicate that the energy ex-pended in setting the yarns into motion and pushing them out ofthe way of the advancing projectile and overcoming projectilefab-ric friction is a mechanism of energy absorption during impact.Briscoe and Motamedi [2] explored the frictional characteristics</p><p>level of friction absorbs larger amounts of energy. Bazhenov [3]investigated the effect of water on the ballistic performance of arectangular laminate comprised of 20 layers of Armos fabric. Thespecimens were attached to a plasticine foundation and struckwith projectiles possessing spherical tips. The dry laminatestopped the bullet while the wet laminate was perforated. It wasobserved that the impacted yarns in the wet laminate were notbroken indicating that the yarns moved laterally and allowed thebullet to slide through the fabric. Based on this observation, Bazhe-nov surmised that the water served as a lubricant that decreasedfriction between the bullet and the yarns.1. Introduction0263-8223/$ - see front matter 2008 Elsevier Ltd. Adoi:10.1016/j.compstruct.2008.11.012test providing yarnyarn movement. Yarns were modeled as continua with modulus and strength dom-inating along the length. Parametric studies incorporating different yarn material properties and initialprojectile velocities were then performed with the above set of boundary conditions. Results indicate thatballistic performance depends upon friction, elastic modulus and strength of the yarns. While frictionimproves ballistic performance by maintaining the integrity of the weave pattern, material propertiesof the yarns have a signicant inuence on the effect of friction. It is shown that fabrics comprised ofyarns characterized by higher stiffness and strength relative to the baseline Kevlar KM2, exhibited astronger inuence on ballistic performance. Therefore all three parameters viz., friction, elastic modulusand strength along with other variables (fabric architecture, boundary conditions, and projectile param-eters) are needed to examine ballistic performance of high-strength fabric structures.</p><p> 2008 Elsevier Ltd. All rights reserved.</p><p>velocity required to perforate increased while the residual velocitydecreased with increasing levels of friction. Fabric with a higherAvailable online 28 November 2008Impact of a rigid sphere onto a high-strength plain-weave Kevlar KM2 fabric was modeled usingLSDYNA focusing on the inuence of friction and material properties on ballistic performance.Modeling the effects of yarn material proon the ballistic impact of a plain-weave</p><p>M.P. Rao a,1, Y. Duan a,2, M. Keefe b,*, B.M. Powers c, TaCenter for Composite Materials, University of Delaware, Newark, DE 19716, USAbDepartment of Mechanical Engineering, University of Delaware, Newark, DE 19716, UScUS Army Research Laboratory, Aberdeen Proving Ground, MD 21005, USA</p><p>a r t i c l e i n f o</p><p>Article history:</p><p>a b s t r a c t</p><p>journal homepage: www.elll rights reserved.erties and frictionric</p><p>Bogetti c</p><p>le at ScienceDirect</p><p>tructures</p><p>ier .com/locate /compstruct</p></li><li><p>2. Modeling the ballistic impact onto a plain-weave fabric</p><p>A commercially available explicit nonlinear FEA code, LSDYNA,is used to model the ballistic impact of a rigid sphere onto a singlelayer of a high-strength fabric. Fig. 1 shows the initial geometry ofthe impact event: a 0.627 g, 5.35 mm diameter rigid steel sphereimpacting at normal incidence onto the center of a 50.8 mm 50.8 mm square plain-woven fabric panel of areal density 180 g/m2</p><p>with 34 yarns per inch in the warp and ll directions. The projectileis constrained to move in the direction normal to the XZ plane.The edges of the fabric are perpendicular to the warp/weft yarnswith two edges clamped, two edges free. The projectile and fabricparameters are chosen based on tests performed at the ArmyResearch Laboratory (ARL), Aberdeen Proving Ground, Maryland,</p><p>Fig. 1. Initial geometry of the simulated impact event.</p><p>Structures 89 (2009) 556566 557difference, but more importantly, determine that the optimumfriction coefcient range for Twaron CT716 woven fabrics is0:1 6 l 6 0:6:</p><p>Tan and Ching [5] developed a nite element model using barelements to model the ballistic impact of a rigid sphere onto aplain-woven fabric structure made of Twaron CT716 yarns. Whilethe above study was successful in reducing the size of the problem,it did not account for the effect of changing material properties ofthe yarns coupled with friction. Barauskas and Abraitiene [6]developed a coupled shell and membrane element based nite ele-ment model of multi-layer fabric packages (MLFP) of plain-wovenpara-aramid Twaron CT709 yarns under ballistic impact from alead bullet. They showed that for the particular case modeled,acceptable results for wave propagation and residual projectilevelocities were obtained in comparison with full detailed nite ele-ment simulations. While they did not explore the interplay be-tween material properties and friction, they were successful insimulating the ballistic event between the lead projectile and astructure comprised of multiple layers of woven fabric. Naik andShrirao [7] developed a simplied analytical model to investigatethe ballistic impact of plain-woven E-glass/epoxy and twill-wovenT300 carbon/epoxy composite structures. The plain-woven E-glass/epoxy composite characterized by higher volumetric density, modeII dynamic critical strain energy release rate and ber failure en-ergy was shown to have a higher ballistic limit. However, theydid not distinguish whether material properties or weave architec-ture had a greater contribution toward the observed ballistic per-formance. Tabiei and Ivanov [8] developed a computationallyefcient micro-mechanics based material model for braided com-posites to interface with LSDYNA. While their model accountsfor yarn reorientation and interlocking, the spatially varying crimpof the yarns is approximated to be constant. The membrane shellelements based nite element model developed in [8], signicantlyreduces the size of the problem, and produces results in excellentagreement with experimental data. Yet, their study does not ad-dress the interaction between friction and material properties withrespect to ballistic performance.</p><p>The experimental work presented in [13] clearly shows thatinterfacial friction plays a critical role in the ballistic impact of fab-rics. However, the mechanisms through which friction takes effectare not well understood. In previous papers by Duan et al. [9,10], anite element analysis (FEA) model was created to simulate theballistic impact of a rigid sphere onto a square panel of plain-wo-ven fabric. Projectilefabric and yarnyarn friction were taken intoaccount as well as yarn failure. The effect of friction on the fabricenergy absorption and the mechanisms through which frictionplays a role were deduced from that modeling effort. However,friction was only parametrically modeled as either very large ornot present and material properties were meant to show trends,but not represent actual materials. Further work by the authors[11] utilized material properties from actual Kevlar woven fabricand compared to experiments. However, in the above cited works[911], the effect of yarn material properties on the ballistic perfor-mance of woven fabrics has not been addressed. As such, it is pos-tulated that friction along with yarn material properties couldinuence the ballistic performance.</p><p>Therefore, the present work endeavors to address the effects ofboth yarn material properties and friction. The effects of paramet-ric variation of yarn mechanical properties viz.; elastic modulusand stress-to-failure are studied along with the effect of friction both yarnyarn and projectilefabric. A novel pull-out test meth-od is developed to compare static to dynamic friction and theseexperimental results are used in this work. These studies further</p><p>M.P. Rao et al. / Compositedemonstrate the inter-relationship of variables when studying bal-listic impact and the importance of modeling when trying tounderstand this complex phenomenon.Fig. 2. Details of the quarter symmetric 3D nite element mesh of the initialgeometry shown in Fig. 1.</p></li><li><p>using .22 caliber Type F shot against neat plain-woven 600 de-nier Kevlar KM2 fabric [11].</p><p>Since the impact system has symmetry with respect to the XYplane and the YZ plane, only a quarter of the entire system needsto be modeled. As in the previous papers by the authors [911], thefabric is modeled at a yarn level of resolution. The warp and llyarns are modeled as transversely isotropic elastic continua andcombined to form the fabric weave structure. Fig. 2 shows the de-tails of the nite element mesh for the plain-woven fabric. Meshsensitivity studies indicated that the chosen mesh density was ableto capture both the longitudinal and transverse wave responses ofthe impact event. The fabric thickness is 0.23 mm and the yarncrimp wavelength is 1.49 mm. The material constants for thetransversely isotropic Kevlar KM2 yarns are dominated by thelongitudinal tensile modulus (E11 = 62 GPa) [12] assuming the1-direction to be along the ber axis. In these studies, the trans-verse elastic moduli (E22 and E33) and shear moduli (G12, G13, andG23) are assumed to be two and three orders of magnitude smallerthan E11, while the Poissons ratio are set as m12 = m13 = m23 = 0, sincethe yarns are collections of loose individual bers. The density of</p><p>the yarn is modied from the density of Kevlar KM2 bers usinga simple tightest packing approach and assuming the Kevlar KM2</p><p>bers in the yarns have a circular cross-section: a simple geometryof packing circles creates a tightest volume ratio of 0.91, leading toqyarn = 1310 Kg/m3, as opposed to qber = 1440 Kg/m3. Since theelastic modulus along the ber direction (E11) is much larger thanthe transverse and shear moduli, the von Mises stress at a materialpoint is approximately equal to the stress in the ber direction. Thestress in the ber direction is a linear function of the strain in thatdirection. Therefore, the maximum von Mises stress failure crite-rion is roughly equivalent to a maximum strain failure criterion,which has been used by other researchers for the investigation ofyarns [1416]. Consistent with the studies of Cheng et al. [13],the failure of Kevlar KM2 yarns is triggered if the maximum prin-cipal stress along the longitudinal direction r1P 3.4 GPa.</p><p>2.1. Experimental friction measurement</p><p>Quasi-static yarn friction tests and yarn pull-out tests are usedto characterize the friction behavior between Kevlar KM2 yarns. A</p><p>or t</p><p>558 M.P. Rao et al. / Composite Structures 89 (2009) 556566Fig. 3. Test xture and setup fFig. 4. (a) Photograph of the Kevlar KM2 fabric employed during ballistiche yarn pull-out experiments.experiments. (b) Schematic representation of the yarn pull-out test.</p></li><li><p>simple system for pulling one yarn against another with knownloads allows a direct measurement of yarnyarn friction coef-cients, and yarn pull-out tests, uniquely performed using a non-woven tail on the pulled yarn, allow incorporation of the geome-try effects of the weave into the friction modeling. Fig. 3 shows atest xture developed previously at ARL for yarn pull-out tests.This xture uses springs to provide a pre-load along the width ofthe fabric while using a standard force-displacement device to per-form the load vs. displacement measurements of a yarn pull-outfrom the fabric. Fig. 4a shows a 600 denier Kevlar KM2 test sam-ple with the modied yarn tail. Different specimens, characterizedby the dimensions indicated in Fig. 4b, were used to perform indi-vidual pull-out tests. Using an approach similar to Coulomb fric-tion, one could write:</p><p>f lF 1</p><p>Fig. 5. Yarn pull-out force measured as function of crosshead displacement forvarying magnitudes of the applied pre-load, F.</p><p>Fig. 6. Average static and kinetic forces obtained from the yarn pull-out testsperformed with the baseline Kevlar KM2 fabric.</p><p>Fig. 7. Schematic representation of the friction device designed to me</p><p>M.P. Rao et al. / Composite Structures 89 (2009) 556566 559where f is the pull-out force, F is the applied pre-load perpendicularto the pull-out force, and l is a coefcient of friction between theindividual Kevlar KM2 yarns.</p><p>Fig. 5 shows typical results for various pre-loads in the widthdirection corresponding to a Kevlar KM2 specimen. Five speci-mens were employed to obtain ve sets of data similar to the re-sults in Fig. 5. The static and kinetic forces for each data set wereaveraged as shown in Fig. 5, and these averages (along with max-imum and minimum bounds) are reported in Fig. 6 as functions ofapplied pre-load. It is clear from Fig. 6 that individual linear rela-tionships could be employed to predict both the average kineticand static forces of friction in terms of the applied pre-load.</p><p>The above linear trend line equations can be written as:</p><p>fs msF...</p></li></ul>