Keywords:Ballistic impactYarn material propertiesFrictionWoven fabricFinite element analysis
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
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
Zeng et al.  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 , 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  surmise that increasing l = 0.2 to l = 0.6, yields little
* Corresponding author. Tel.: +1 302 831 8009; fax: +1 302 831 3619.E-mail address: firstname.lastname@example.org (M. Keefe).
1 Present address: Department of Mechanical and Aerospace Engineering, Univer-sity of Florida, P.O. Box 116250, Gainesville, FL 32611-6250, USA.
Composite Structures 89 (2009) 556566
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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 . Tan et al. 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  explored the frictional characteristics
level of friction absorbs larger amounts of energy. Bazhenov 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.
2008 Elsevier Ltd. All rights reserved.
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
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
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2. Modeling the ballistic impact onto a plain-weave fabric
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
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,
Fig. 1. Initial geometry of the simulated impact event.
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:
Tan and Ching  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 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  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  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 , 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.
The experimental work presented in  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 utilized material properties from actual Kevlar woven fabricand compared to experiments. However, in the above cited works, 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.
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 th