CP620, Shock Compression of Condensed Matter - 2001 edited by M. D. Furnish, N. N. Thadhani, and Y. Horie © 2002 American Institute of Physics 0-7354-0068-7/02/$ 19.00 BALLISTIC RESPONSE OF FABRICS: MODEL AND EXPERIMENTS Dennis L. Orphaf, James D. Walker* and Charles E. Anderson, Jr.+ *International Research Associates, 445 OB lack Ave., Suite E, Pleasanton, CA 94566, USA + Southwest Research Institute, Engineering Dynamics Department P.O. Drawer 28510, San Antonio, TX 78228-0510, USA Walker [1] developed an analytical model for the dynamic response of fabrics to ballistic impact. In the model the force on the bullet is a function of fabric displacement (h) along the axis of impact and the radius (R) of the fabric deformation or 'bulge". Ballistic tests against Zylon™ fabric have been performed to measure h and R as a function of time. The results of these experiments are presented and analyzed in the context of the Walker model. h/R = constant = (V/c) = (V/cf) 1/2 INTRODUCTION This assumption results in an analytical solution for the force in terms of the single variable h, as can be seen from Eqn. (1). Using Eqns. (1) and (2) along with an estimate of the amount of fabric that is "carried along" with a projectile as the fabric deforms, Walker's model successfully produces V50 data for Kevlar™ KM2 fabric for a wide range of projectile sizes and fabric areal densities, as shown in Fig. 1. In Fig. 1 V50 data have been scaled by the parameter V* = cf 8f2/3/21/3 where £f is the failure strain of the fiber, Walker [1] developed a model describing the response of fabrics to ballistic impacts. A result of this model is that for normal impacts the force on the fabric, F, is related to the axial displacement of the fabric, h, by F = ~(8/9)EfT*h3/R2 (1) where Ef is the Young's modulus of the fabric, R is the radius of the "bulge" in the displaced fabric, and T* is the "effective thickness" of the fabric. T* is equal to the pVpf where p' is the areal density of the fabric, and pf is the density of the fabric fiber. This equation agrees very well with static force-deflection data for Kevlar™ 129 sheets [1]. It is observed, at least for some fabrics, that the ratio of h/R is approximately constant during fabric deformation prior to perforation by the projectile [2], Walker finds an approximate solution for the transverse wave speed (c) at which the bulge radius increases with time: <(c f V) 1/2 (3) 2, SO 1.25 2-00 !,?$ 1,50 • 1.2$ 1*00 0,7$ (2) where V = dh/dt = the velocity of the axial fabric deformation; and cf = (E/pf )1/2, which is the bar velocity of a fabric fiber. Then self similarity is assumed, leading to: FIGURE 1. Kevlar KM2™ V50 data and Walker model fabric. 1279 TEST DATA and the abscissa-parameter X = p'Ap /mp where Ap is the presented area of the projectile and mp is the mass of the projectile. These scaling parameters are derived naturally from the model; however, it is noted that Cunniff first suggested these nondimensional parameters on the basis of dimensional arguments [3]. The model has also been successfully applied to Kevlar™ 129 [4]. Figure 2 (next page) shows the eight Imacon images from a typical test (Test 77). From these images, a spatial fiducial, and the known exposure times, the axial displacement and the radial deformation of the fabric as a function of time are determined. Test data are quite repeatable. Although tens of tests have been conducted, for clarity, Figs. 3 and 4 show the measured axial ("height") and radial fabric deformation for Test 77 along with the measurements from four additional, nominally identical, tests. In these tests, the ceramic/metal target causes the bullet to "dwell" on the target surface. This dwell, combined with the time of interaction of the bullet with the ceramic/metal target, means that the fabric does not begin to deform for several 10's of microseconds after initial impact (time zero). Additionally there is some obscuration due to the edge of the target/fabric fixture, thus the deformation of the fabric is not immediately visible when it begins. Therefore, it is approximately 45 us after impact before fabric deflections are recorded. As can be seen, except at late times when the deformation is arresting, the speed of both the axial and radial deformations are TESTS A program is in progress that involves the ballistic response of a fabric made of a relatively new fiber material. This new fiber material is PBO, poly (p-phenylene-2,6-benzobisoxazole); the specific fabric being used is called Zylon™ , made by Toyobo of Japan. Key nominal physical and mechanical properties for the PBO fibers are: pf = 1560 kg/m3, E = 169 GPa, tensile strength = 5.2 MPa, and Ef - 3.10% [3]. The Zylon™ fabrics being used in testing are composed of multiple layers or plies to obtain various areal densities. The individual plies are 30 by 30 weaves of 500 denier fibers. For the specific experiments here, the fabric is placed behind a ceramic/metal target. The target and fabric are forced into a steel fixture, holding the fabric tightly around the edge of the fixture but allowing the fabric to deform through a 101.6-mm (4-inch) diameter hole in the fixture. (Some tests were performed with a 152.4-mm (6-inch) diameter hole and no significant differences were noted). The impacting projectile in these tests is the 7.62-mm APM2 bullet that impacts the ceramic face of the target at nominally 850 m/s. The deformation of the fabric as a function of time following impact of the projectile against the ceramic/metal target is recorded using an Imacon 468 digital camera system. A mirror is used so that the axial and radial deformation of the fabric can be recorded simultaneously. As used the Imacon camera recorded eight images of the deforming fabric at different preset times. O.9 •£ 3.0 ,£>, .C 2.5 - £" • 0 A * • Test 62 Test 76 Test 57 Test 77 Test 56 A o * J • 0) i2.0 0 CQ 0 'C CD LJL 1.5 8 1.0 0.5 no i 8 1 D So B — — - — ... i , , . i ... i ... i ... i ... i . . ,: 20 40 60 80 100 120 140 Time ((is) FIGURE 3. Axial deformation for Zylon™ fabric. 1280 FIGURE 2. Imacon digital camera images showing both axial and radial Zylon™ deformation at eight times after impact (Test 77) (Times are: 35 JLIS, 45 ^s, 55 |is, 65 MS, 75 \is, 90 us, 125 MS, and 165 ps). ^ IU.U cc CM II 8.0 I O vT 0 • Test 62 o Test 76 A Test 57 A Test 77 m Test 56 <D 0) 3 CD .0 | A 4.0 ~ * o 1.0 _ 0.8 ° o A -" 0.6 I 0.4 "m 0.2 8 a 2.0 0 "„ j^ " n CO IL. ° • fto.u /I _ I n ft - An 0 20 40 • Test 62 0 Test 76 A Test 57 A Test 77 • Test 56 I————————I B 1.2 A ^ CO 0 _ _ • •^ \ ft 0 j 8 >• o . A.4-»t!-*~- ~ -_ , ,- 1.4 £ 60 80 100 120 20 Time (us) 40 60 80 100 120 140 Time (fis) FIGURE 4. Diameter of Zylon™ fabric deformation versus time. FIGURE 5. The ratio of deformation height to radius versus time for Zylon™. about constant. The slopes for the axial and radial deformation, respectively, are or a little more, and then achieves an approximately constant value of about 0.6-0.7 for times between 60 us and 110 us. dh/dt = V « 300 m/s (4a) 500 m/s. (4b) dR/dt DISCUSSION Figure 5 shows the ratio h/R calculated from the measured data shown in Figs. 3 and 4. For these tests with Zylon™ fabric, the ratio h/R is not constant during the entire deformation response. As indicated by the dashed line, the ratio h/R from 45 us to -70 us appears to decrease from about 1, Fabric deformation, as measured by h/R, is not constant during early portions of the deformation history, although somewhat later h/R does become constant. Walker [1] modeled the fabric as an extended system of orthogonal springs. As 1281 initially formulated the model has no provision for the crimp or "slack* associated with a woven fabric, such as tested here. It is hypothesized that inclusion of this slack would result in a nonconstant and lower transverse wave velocity, c, at early times until the slack is removed. By Eqn. (3) this would in turn result in a non-constant h/R. Thus, if this hypothesis is correct, the ratio h/R would decrease from some value associated with the removal of the slack and then achieve a constant, or nearly constant, value after the slack has been removed. There is much yet to be learned about the response of fabrics to ballistic impacts. The work reported here is intended as a contribution to this effort. Additional experiments and analysis are in progress. Walker has already extended his model to include fabrics with resin, with excellent results [4]. Work is also in progress to include the effects of slack in Walker's model. of the U.S. Army Soldier Biological and Chemical Defense Command and Steve Wax of DARPA for their guidance and support. The efforts of Don Grosch and the ballistic testing crew at Southwest Research Institute are also gratefully acknowledged. REFERENCES 1. Walker, J. D., "Constitutive Model for Fabrics with Explicit Static Solution and Ballistic Limit", Proc. 18th Int. Symp. on Ballistics, Vol. 2, pp. 1231-1238, Technomic Publishing Co., Lancaster, PA, 1999. 2. Cunniff, P. M., "An Analysis of the System Effects in Woven Fabrics Under Ballistic Impact," Textile Res. J., 62(9), 495-509, 1992. 3. Cunniff, P. M., "Dimensionless Parameters for Optimization of Textile-Based Body Armor Systems," Proc. 18th Int. Symp on Ballistics, Vol. 2, pp. 1303-1310, Technomic Publishing Co., Lancaster, PA, 1999. 4. Walker, J. D., "Ballistic Limit of Fabrics with Resin", Proc. 19th Int. Symp. on Ballistics, Vol. Ill, pp. 1409-1414, Interlaken, Switzerland, 7-11 May, 2001. ACKNOWLEDGMENTS This work was performed under U.S. Army Contract No. DAAD16-00-C-9260. The authors would like to thank Janet Ward and Phil Cunniff 1282
© Copyright 2025 Paperzz