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
VALIDATION OF AN ADVANCED MATERIAL MODEL FOR
SIMULATING THE IMPACT AND SHOCK RESPONSE OF
COMPOSITE MATERIALS
Richard A. Clegg1, Colin J. Hayhurst1, Hartwig Nahme2
Century Dynamics Limited, Dynamics House, Hurst Road, Horsham, West Sussex, RH12 2DT, UK
Ernst Mach Institute, Eckerstrasse 4, D-79104 Freiburg, D
Abstract. Composite materials are now commonly used as ballistic and hypervelocity protection
materials and the demand for simulation of impact on these materials is increasing. A new material
model specifically designed for the shock response of anisotropic materials has been developed and
implemented in the hydrocode AUTODYN. The model allows for the representation of non-linear
shock effects in combination with anisotropic material stiffness and damage. The coupling of the
equation of state and anisotropic response is based on the methodology proposed by Anderson et al. [2].
An overview of the coupled formulation is described in order to point out the important assumptions,
key innovations and basic theoretical framework. The coupled model was originally developed by
Century Dynamics and Fhg-EMI for assessing the hypervelocity impact response of composite satellite
protection systems [1]. It was also identified that the developed model should also offer new
possibilities and capabilities for modelling modern advanced armour materials. Validation of the
advanced composite model is firstly shown via simulations of uniaxial strain flyer plate experiments on
aramid and polyethylene fibre composite systems. Finally, practical application of the model as
implemented in AUTODYN is demonstrated through the simulation of ballistic and hypervelocity
impact events. Comparison with experiment is given where possible.
need to study these events using numerical
simulations.
This paper describes a new material model
specifically designed for simulating the shock
response and damage of anisotropic materials
subject to impact in the high to hypervelocity
regime. The model has been developed and
implemented in the hydrocode AUTODYN [4] and
couples non-linear anisotropic constitutive relations
with a Mie-Gruneisen form of equation of state [1].
The model can additionally include compaction,
orthotropic
tensile
damage
and
material
melting/decomposition effects. An overview of the
theoretical framework for the model is presented
here.
INTRODUCTION
Composite and textile armour systems are
increasingly being utilised as impact protection
materials in weight critical environments.
Applications range from protective shielding for
space vehicles against hypervelocity impacts, to
personal protective equipment of the soldier against
ballistic threat. The use of composite and textile
armour systems can result in a reduction in weight
while maintaining impact performance, or increased
impact performance for a given weight. The
limitations of performing controlled impact
experiments, especially at higher velocities, on
composite and textile materials means that there is a
685
total strain has been decomposed into volumetric,
6V, and deviatoric, £//, components.
Validation of this new composite material model
is first demonstrated here through simulations of
inverse flyer plate impact experiments on two
composite systems. Finally, practical application of
the model is demonstrated via simulation of a
hypervelocity impact on the International Space
Station Columbus module shielding.
r
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AMMHIS COMPOSITE MODEL
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The response of composite and textile materials
subject to impact is complex. Material
characterisation, impact tests and simulations
performed [1] led to the identification of the
following phenomena, which we believe are of
primary interest for composite and textile materials
subject to high velocity impact:
• Material anisotropy
• Shock response (coupling of volumetric
and deviatoric behaviour)
• Anisotropic strength degradation (damage)
• Phase changes.
• Material compaction in composite systems
which are macroscopically porous
An overview of the material model that has been
developed in AUTODYN to enable the
representation of these effects is now given. Further
details can be found in [1].
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(1)
Since the pressure is the average of the three
direct stresses, from (1) we can obtain:
PL = ~
(2)
For an isotropic Hookean material the first term
on the right-hand side is equivalent to a linear
equation of state, whilst the remaining deviatoric
strain terms would be zero. Thus for an orthotropic
material we can replace the first term with a nonlinear Mie-Gruneisen equation of state and the
remaining terms act as a correction due to deviatoric
strains.
Damage
Equation of State and Constitutive Modelling
Damage in the material is assumed to accumulate
independently in each of the material directions via
Sij. For intact material Sy- is equal to 1 and for
material fully damaged in direction ij\ 8$ is equal to
zero. Damage can evolve due to a combination of
tensile stress/strain, matrix melting and material
decomposition. Damaged material is assumed to
retain it's full intact strength if it returns to a state of
bulk compression.
In anisotropic materials, the traditional
independent approach for the solution of the
equation of state and constitutive relations in a
hydrocode is complicated because these two submodels are strongly coupled; volumetric strain leads
to deviatoric stress, and similarly deviatoric strain
leads to spherical stress. Anderson [2] has proposed
a theoretical approach for coupling together these
responses in an orthotropic material. This
methodology forms the basis of the model presented
here.
Consider a linearly elastic orthotropic material for
which the total stress, a//, can be related to the total
strain, £/,-, through the orthotropic stiffness matrix,
Cy. The coefficients of CfJ being functions of the
orthotropic elastic material constants, Eih vtj and G/y.
Note that to facilitate the coupling of the
deviatoric and volumetric material response the
MODEL VALIDATION - IFPT
Fhg-EMI have conducted composite material
characterisation experiments [1] and [6], as part of
composite model development and validation
programs. The main dynamic test used in this work
was the inverse flyer plate experiment. The flyer
consists of the composite specimen backed by a
686
The results of the Dyneema UD-HB25 inverse
flyer plate tests and simulations are shown in Figure
2. Only simulation results for the new model are
shown, the A2 parameter (8) having again been
derived through calibration to the first Hugoniot
plateau. Good correlation with experiment is
observed.
metallic plate (either C45 steel or aluminium) whilst
the target witness plate is C45 steel. A laser velocity
interferometer VISAR is used to record the rear side
velocity of the target plate. The results of these
experiments were used to aid the model
development process and to provide input data for
the composite equation of state. Results of these
experiments, and equivalent numerical simulations
for Kevlar-129/Epoxy and Dyneema UD-HB25
composites are presented here.
The results of the Kevlar/Epoxy inverse flyer
plate tests and simulations are shown in Figure 1.
Simulation results based on a linear orthotropic
modelling assumption and using the coupled
anisotropic model are presented. For the linear
orthotropic model, the material constants were
derived from material characterisation tests [1]. For
the coupled orthotropic model, the same linear
orthotropic model constants were used in
conjunction with an equation of state of polynomial
form. The parameters for this equation of state were
derived iteratively through numerical experiments
such that the first plateau in velocity observed in the
inverse flyer plate tests, at approximately
0.0005msec, matched that of the experiment for the
three velocities shown in Figure 1. Once this match
was achieved, the remainder of the velocity trace
matched with the experiment.
Time (ms)
FIGURE 2. Dyneema polyethylene composite Inverse Flyer
Plate Experiments and Simulation Comparisons for three impact
velocities.
HYPERVELOCITY IMPACT
Simulations of hypervelocity impacts on the
Columbus module shielding system of the
International Space Station have been conducted
using AUTODYN-2D and 3D at 3km/s, 6.5km/s
and llkm/s with the advanced composite material
model data described above. The models use SPH
for the projectile and all parts of the shield system
except for the backwall, which is modelled using
Lagrange finite elements. The models are able to
predict the main aspects of the shielding material
response. Calculated shielding damage in the first
bumper and in the Nextel and Kevlar/Epoxy layers
correlates well with experimental results. For
example, the simulation of a 6km/s impact of a
15mm diameter aluminium projectile predicts
backwall damage consistent with the experimental
observations as shown in Figure 3.
Experiment
Simulation + Shock Effects
Simulations. Linear EOS
0.000
0.001
0.002
0.003
0.004
0.006
0.007
0.008
0.009
0.010
FIGURE 1. Kevlar-129/Epoxy Inverse Flyer Plate Experiments
and Simulation Comparisons for three impact velocities.
687
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T
FIGURE 3. Alenia/EMI Test A8611, 15mm diameter projectile, 6.5km/s. Simulation results showing material response and failure.
CONCLUSIONS
A new composite material model has been
implemented in AUTODYN-2D and 3D. In
particular the model can couple anisotropic material
stiffness, strength and damage with the non-linear
shock response of composites.
The new composite material model has been
shown to reproduce the shock propagation
phenomena observed in uniaxial flyer plate
experiments for two very different composite
materials. The model has also been validated
against hypervelocity impact experiments.
AKNOWLEDGEMENTS
The authors wish to thank M. Lambert of
ESA/ESTEC for supporting the initial composite
model development work. Acknowledgement also
goes to our co-workers at Fhg-EMI during the
development of the model. Thanks also go to A.
Diederen (TNO), M Jacobs (DSM) and P. Kelly
(DCTA) for collaboration
modelling work.
in
the
Dyneema
REFERENCES
1.
Hiermaier SJ, Riedel W, Hayhurst CJ, Clegg RA, Wentzel
CM. "Advanced Material Models for Hypervelocity Impact
Simulations", ESTEC Contract 12400/97/NL/PA(SC) Final
Report, July 1999.
2. Anderson CE, Cox PA, Johnson GR, Maudlin PJ., Comp.
Mech., vol. 15, 201-223 (1994).
3. Schafer F. "Hypervelocity Impact Test Campaign Columbus APM-COF Phase 2- Report No. 1", EMI Report
EMI-HVITC 003forAlenia Aerospazio, August 1997.
4. Birnbaum, N.K., M.S. Cowler, 1987. "Numerical Simulation
of Impact Phenomena in an Interactive Computing
Environment" in Proc. Impact Loading and Dynamic
Behaviour of Materials Conference IMPACT '87, Bremen,
Germany, May 1987.
5. Clegg RA, Hayhurst CJ, Leahy JG, Deutekom M.
"Application of a Coupled Anisotropic Material Model to
High Velocity Impact Response on Composite Textile
Armour", in Proc. 18th Intl. Symp. on Ballistics, San
Antonio, Texas, USA, Nov. 1999.
6. Hayhurst, CJ. et al....."Development of Material Models for
Numerical Simulation of Ballistic Impact onto Polyethylene
Fibrous Armour", in Proc. PASS, Sept. 2000