1279.PDF

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)
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(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.
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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.
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FIGURE 3. Axial deformation for Zylon™ fabric.
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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).
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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
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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
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