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
A COMBINED EXPERIMENTAL/COMPUTATIONAL APPROACH
FOR ASSESSING THE HIGH STRAIN RATE RESPONSE OF HIGH
EXPLOSIVE SIMULANTS AND OTHER VISCOELASTIC
PARTICIPATE COMPOSITE MATERIALS
John Corky1, Werner Riedel2, Stefan Hiermaier2, Peter Weidemaier2, Klaus Thoma2
l
Air Force Research Laboratory Energetic Materials Branch (AFRL/MNME), Eglin AFB, FL 32542-5910
FraunhoferImtitutKurrzeitdynamik, Ernst-Mach-Institut (EMI), Eckerstrasse 4, Freiburg, GE D-79194
2
Abstract, The quasistatic and dynamic mechanical properties of a viscoelastic participate composite employed
as a surrogate, cast-cure high explosive were determined from uniaxial compression experiments at strain rates
up to 107 sec"1. The results from these experiments were used to obtain parameters for a non-linear viscoelastic
material model. The viscoelasticity described by the macroscopic material model introduced in this paper affects
not only the deviatoric components of stress and strain but the volumetric components as well. The material
description is adequate for reproducing experimentally observed responses at loading rates ranging from
quasistatic to shock levels with a single set of material parameters. Parameters for an HTPB-sugar composite are
provided.
INTRODUCTION
STATE OF THE ART
The initiation of composite high explosives and
propellants has been observed in response to stress
loadings well below their shock initiation threshold.
This poorly understood phenomenom is thought to
stem, at least in part, from the dynamic mechanical
properties of this special class of particulate
composite material.
The dynamic mechanical properties of energetic
composites and their inert counterparts have been
considered largely irrelevant until recently.
Experimental characterization of these materials
has been driven mainly by sensitivity/performance
requirements (1). Their mechanical properties are
typically studied under quasistatic loading
conditions in the context of growth and exudation
concerns (2). These concerns are derived from the
creep and relaxation phenomena inherent to their
widely accepted viscoelasticity. This behavior has
been modeled extensively (3), even at the
mesoscale . Such models are considered valid only
at relatively small strains under quasistatic loading
conditions. Due to the concerns mentioned in the
introduction, dynamic material parameters have
recently emerged in the literature for a limited
number of pressed explosives and composite
propellants (4). Trends in modeling the observed
dynamic
response
emphasize a viscous
representation of interphase damage/cracking (5).
OBJECTIVES
The aim of the research described in this report is to
provide dynamic material properties data for an
inert, cast-cure, particulate composite comprising
sucrose in a polymer matrix. This composite serves
as a surrogate high explosive material.
Furthermore, a non-linear viscoelastic constitutive
model affecting the volumetric as well as the
deviatoric components of stress and strain is
introduced to describe the observed highly viscous
behavior.
705
Model representations of the dynamic bulk material
response are normally given by non-viscous (i.e.,
elastic or shock EOS) models with viscoelastic
deviatoric stress and strain components. Such
descriptions have been shown to be inadequate for
describing the strain rate dependence of the stressstrain behavior (6).
EXPERIMENTS AND RESULTS
Teflon seal was employed to eliminate extrusion of
the composite between the stamp and the steel tube
during compression. The results from representative
confined compression tests are provided in Fig. 1.
Engineering Stress vs. Strain (KS-32S)
/
o
«J
Material
£0.15
The composite in this study is an hydroxyterminatedpolybutadiene (HTPB)-based, sucrose
surrogate for the cast-cure, plastic bonded explosive
KS-32 developed and marketed by DASA TDW in
Schroebenhausen, Germany.
The sucrose
employed as the particulate filler was C&H brand
sugar.
Granular and powdered sugars were
employed in even ratios. The compositions of KS32 and its inert counterpart, designated KS-32S, are
provide in Table 1.
TABLE 1. Composition of KS-32 and KS-32S______
Component
Volume % KS-32
KS-32S
(Wt%)
(Wt%)
HTPB
27.15
15
17.42
Filler
72.85
85HMX 82.58 Sucrose
- Quasistatic (.00048 /sec)
r Test 103 (53 /sec)
- Test 110 (97 /sec)
-Test 111 (107 /sec)
0
Confined Compression Tests
Confined compression tests were performed at
strain rates ranging from quasistatic to 107 sec"1.
The tests were conducted in the same machine as
the unconfined compression tests. The 26.4 mm
diameter, 28.2 mm cylindrical test samples were
placed in a heavy-walled steel tube and pressed
using a stamp of the diameter as the test sample. A
706
0,1
0,15
Engineering Strain ( )
FIGURE 1. Engineering stress vs. engineering strain for KS32S at various strain rates.
Key learnings from confined compression tests
included:
•
•
Unconfined Compression Test
Uniaxial unconfined compression tests were
conducted using a customized servohydraulic test
system. Test samples were 50.3 mm diameter
cylinders with lengths of 100.5 mm. They were
instrumented with axial (HBM Type 20/120) and
circumferential (HBM 50/120) strain gauges. The
ratio of hoop strain to axial strain measured by
these gauges provided a value for Poisson's ratio of
0.336.
0,05
•
•
•
Nominal permanent strain (less than 0.5%) was
induced in the test items even following tests at
more than 15% strain.
At low strain rates (up to 50 sec4) the slope of
the stress-strain response of KS-32S varies
directly with strain rate.
At low strain rates, the stress-strain response
for KS-32S is bi-linear. This is attributed to
the binder dominant response at low strains and
the filler dominant response at high strains.
At high strain rates, the stress-strain response
for KS-32S is mono-modal but non-linear.
This was attributed largely to the observed
viscoelasticity of the polymeric binder in
another series of confined compression tests.
At higher strain rates, the stress-strain response
does not always vary directly with strain rate.
This was attributed to mesoscale effects. As
shown in Figure 2, post test inspection of a
sample (Test 110) where this exceptional
behavior occurred, revealed damage of the
particulate filler. No discernible damage was
observed in samples which conformed to the
direct relationship between strain rate and the
resulting stress strain relationship.
The constants in Eq. (2) are v, E0 , t|, EI and K.
Definitions/values for KS-32S are given in Table 2.
TABLE 2. Non-Linear VE Model Parameters for KS32S
Parameter
Value
Poisson's Ratio, v
Young's Modulus, E0 (kPa)
0.336
69823
10
4xl05
1
T|
Maxwell Coefficient, EI (kPa)
Relaxation Time X (msec)
Test 110KS-32S#10
(97 sec5)
FIGURE 2. Micrographs (100X) of KS-32S: Fractured sugar
crystals are visible in sample loaded at 97 sec4,
Inverse Flyer Plate Impact Tests
In the inverse flyer plate impact test, the sample
being characterized and a backing plate comprising
a well-characterized aluminum are accelerated
using a compressed air or powder gun. As they exit
the gun barrel, a carefully aligned witness plate is
encountered. Impact velocity is measured by short
circuiting pins. The rear surface velocity of the
witness plate is measured using lasar
interferometry. The shock EOS parameters for KS32S derived from these tests are given in Eq. (1).
Us= 1553 + 3.45up (m/s)
The first two parameters were determined directly
from unconfined and confined compression tests,
respectively.
The remaining parameters were
obtained from simulations of confined compression
tests.
The material model employing these
parameters was implemented as a subroutine in the
commerical hydrocode AUTODYN™.
As
implemented, up to four Maxwell elements may be
employed. Here, only one element was used.
Engineering Stress vs. Position for KS-32S
(1)
SIMULATIONS AND RESULTS
This paper introduces a non-linear viscoelastic
(VE) material model for polymer-based particulate
composites. The strain rate dependence described
by the model affects the volumetric components of
stress cr and strain €kk as well as the deviatoric
components eyD. As shown in Equation (2), the
model is based on a Hookean description of an
isotropic elastic material and a Maxwell description
of viscoelasticity. The experimentally observed
non-linearity of the stress-strain response is
represented by a time t dependent compression term
(current volume V(t) over initial volume V ) (7).
3(1-2v)
1
k
J
(2)
Position (mm)
FIGURE 4. Comparison of KS-32S confined compression test
results and simulations with non-linear VE model
The results of simulations for the confined
compression test employing the parameters
provided in Table 2 are shown in Figure 4 along
with experimental results. The strain rate
dependence of KS-32S observed experimentally for
the quasistatic test and the test at 3.04 m/s
(107 sec"1) is nicely replicated. The stiffness of the
response at the intermediate strain rate condition
was over predicted in the simulation. The results of
simulations for the inverse flyer plate impact test
using parameters for KS-32S are shown in Figure 5
along with experimental results from two different
impact velocities. Also shown are results of
707
simulations employing the non-viscous shock EOS
given in Equation (1).
X-Velocity at Tail (mis)
Free Surface Velocity vs. Time for KS-32S
Shock EOS Non-Linear Viscoelastic Model
—Test 2286 (417 mfe)
—-Test 2238 (198 m/s)
«-Shock EOS {417 m/s)
—m- Shock EOS (198 m/s)
E Model (417 m/s)
E Model (198 m/s)
Time (msec)
FIGURE 6. Comparison of inverse impact penetrator test
results with simulations employing non-linear viscoelastic model
FIGURE 5. Experimental results (bold line) and simulations of
inverse flyer plate tests at two different impact velocities using
shock EOS (squares) and non-linear VE model (circles).
The simulations with both models slightly under
predict the free surface velocity corresponding to
the Hugoniot state in the material (i.e., the first
plateau) as well as subsequent release states. Still,
the primary features of the velocity profiles are
retained.
VALIDATION OF NON-LINEAR VE MODEL
Inverse impact penetration experiments were
conducted to provide experimental data from a
dynamic application representative of those for
which a particulate composite material might be
employed. A 60 mm x 60 mm cylindrical, pure
aluminum target impacted a stationary penetrator at
a velocity of 335 m/s. The C45 steel penetrator had
a length of 150 mm and a diameter of 15 mm with
an ogive radius of 60 mm. The fill cavity had a
diameter of 12 mm, a depth of 120 mm, and a 3 mm
conical internal tip. There was no liner material
isolating the fill material from the penetrator casing.
The tail end of the projectile was not sealed. The
free surface velocity of the fill material was
measured as a function of time using laser
interferometry to monitor the position of a thin
aluminum disk affixed to its surface.
The experimental results for the measured free
surface velocity of the KS-32S filler and the
simulation results employing the non-linear viscoelastic material model are compared in Figure 6.
708
The simulation employing the viscoelastic material
model provided a response similar to that measured
in the experiments.
CONCLUSIONS
The dynamic mechancial response of a cast-cure
particulate composite based on HTPB was described. A non-linear viscoelastic material model
affecting the volumetric as well as the deviatoric
stress-strain components has been introduced. The
model has been shown to reproduce the results of
material characterization experiments at strain rates
ranging from quasistatic to 104 sec"1 and was
validated in simulations of inverse penetrator
impact tests without parameter fitting. Material
characterization tests (also of aluminized
compositions) at intermediate strain rates are
prescribed.
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3.
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