CP620, Shock Compression of Condensed Matter - 2001
edited by M. D. Furnish, N. N. Thadhani, and Y. Hone
© 2002 American Institute of Physics 0-7354-0068-7/02/$ 19.00
EXPERIMENTAL ANALYSIS OF SHOCK WAVE EFFECTS IN
COPPER
Fabrice Llorca, Francois Buy, Jose Farre
CEA Valduc, 21120Is/Tille, France
Abstract. This paper proposes the analysis of shock wave effects for a high purity copper. The method
developed is based on the analysis of the mechanical behavior of as received and shocked materials.
Shock effect is generated through plates impact tests performed in the range 9 GPa to 12 GPa on a
single stage light gas gun. Therefore, as-received and impacted materials are characterized on quasi
static and Split Hopkinson apparatus. The difference between measured stresses between as received
and shocked materials allows to understand shock effects in the low pressure range of study. A specific
modeling approach is engaged in order to give indications about the evolution of the microstructure of
the materials.
INTRODUCTION
SHOCK RECOVERY TESTS
In particular explosively filled devices, materials are
subjected to high shock loading pulses, prior to the
commencement of conventional plastic flow. This
impulsive shock loading is expected to influence
subsequent material flow behavior since this loading
changes both microstructure and hardness of liner
materials. More particularly, the magnitude and time
duration effects of the shock on the subsequent
dynamic material properties will influence the ability
of modeling codes to predict metal flow. The
program presented in this paper investigates the
influence of " shock hardening " on the subsequent
stress behavior of high purity copper. This material is
selected for this study since its shock deformation
has been extensively studied [1-2-3-4-5] and is a
good candidate for studying fee materials dynamic
behavior. To accomplish this task, plate impact
recovery tests are performed in different loading
conditions in the shock pressure range from 9 GPa to
12 GPa. Comparison with numerical simulation
proves the experiment to be well monitored.
Therefore, a complete mechanical testing of as
received and post shock materials is developed as the
basis for the analysis of shock effects on elastoplastic
behavior.
Shock recovery experiments are performed using an
80 mm single-stage light gas gun. The shock
assembly is based on the assembly proposed by Gray
and Follansbee [1]. It consists of a sample 7 mm
thick and 40 mm in diameter, glued behind a cover
plate 40mm in diameter and 3.5 mm thick, which
were both fitted into a high massive momentum disk
28.4 mm thick and tapered by 7°. As in the original
system of Gray and Follansbee, the sample is
protected from spallation by backing the momentum
disk with a spall plate 5.6 mm thick. All these
elements are made of copper to ensure impedance
matching during shock loading. The sample is
surrounded by an aluminum ring with outside
diameter of 110 mm. All the system is dimensioned
to protect the samples from radial and uniaxial
release waves. Backing the assembly, a laser head is
placed on a specific support and is connected to a
Doppler Laser Interferometry system by optical
fibers. This apparatus is devoted to measurements of
the free surface velocity of the spall plate, hence
giving experimental data of the decay of shock
pressure into the assembly in view of correlating
those to numerical simulations. Piezoresistive pins
are attached to the system in order to evaluate the tilt
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microstructure modifications (evaluation of defects
density for example).
angle of the projectile. The whole assembly is fixed
at the barrel through a bronze piece and aligned
using a laser technique which gives tilt angles less
than 7 mrad. The system assembly is placed into the
target chamber in a vacuum. A steel impact cylinder,
placed at the back of the assemblies, allows the
passage of the central momentum and the spall disks
but stopped the projectile and the aluminum fixture
system. The sample is soft recovered by decelerating
into several stages of cotton drags. Copper samples
were shocked up to 12 GPa for 1 microsecond pulse
duration by impacting respectively copper (test 1),
tantalum (test 2) and copper-tantalum (test 3) flyer
systems at projectile velocities of 400 m.s"1. Typical
pictures of elements of recovered assemblies are
presented in figure 2.
MECHANICAL TESTING
Compression specimens have been electro-discharge
machined from the shock loaded samples. The
compression axis is parallel to the shock direction.
The specimens are located on two radius at 8 mm
and 16 mm in order to evaluate release wave effects.
Quasi static and dynamic tests (on Split Hopkinson
Pressure Bar apparatus) have been performed ; each
strain rate condition is repeated twice. Figures 2 and
3 show the results obtained on as received and
shocked materials. These stress strain curves are
given at ambient temperature. For modeling the as
received material behavior, the 77 K - 600 K
temperature range has been investigated. Comparing
the dispersion of the results in figures 2 and 3, it can
be deduced that hardening a) is of the same order
along the radius of the different specimens, b) is not
a function of specific loading conditions (simple
shock or sock reshock) in this range of shock
pressure,
These observations lead to the following
considerations. The radial release wave effects could
be neglected in the interpretation of results and it
seems that only residual state of microstructure
drives the post shocked behavior of copper.
b)
FIGURE 1. Recovered parts of the assembly for test 1.
a) the copper systems with samples in which compression
specimens have been machined (test 2) b) the spall plate
(test 2).
1500s-1
Numerical simulations have been performed with th
CEA Hesione code in Lagrangian version. The
elastoplastic behavior is given by an optimized
thermal activation modeling which does not take into
account any shock effect except classical plastic
deformation. Nevertheless, residual dimensions after
shock transition for the 3 tests are well calculated, it
is not known how microstructure is modified during
the shock travel. A mechanical testing program of as
received and shocked materials could give a lot of
data about the effect of shock wave effects on both
elastoplastic behavior (macroscopic flow stress) and
0
0.05
0.1
0.15
plastic deformation
FIGURE 2. Elastoplastic behaviour of the test 2 shocked
material. Effect of release waves.
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0
0.05
0.1
plastic deformation
variable. A shock wave is a very high strain rate
loading which leads the microstructure of a material
to a very specific internal state. It is well known that
on homogeneous and high purity fee materials,
strength is mostly related to dislocations density
evolution when other mechanisms like twinning are
not activated. It has been demonstrated, on
aluminum, that mechanisms creation of dislocations
are rate sensitive [6]. For a given strain level, this is
one good reason to explain how, after shock loading,
the dislocations density is larger than that generated
during a classical Hopkinson test for example. The
strain rate is divided by a factor 100 or 1000 which
could not be neglected on dislocations creation rate
during plastic deformation. This mechanism on fee
materials is well known to conduct to a large
hardening effect while in bcc materials the
consequences are opposite. In general and from an
experimental point of view, these " strain rate history
effects" on viscoplastic behavior of metals are
classically studied through strain rate jump tests.
0.15
FIGURE 3. Elastoplastic behavior of the shocked
materials (Tests 1, 2 and 3). Experimental results for the
16 mm radius specimens.
DISCUSSION
Nevertheless, if the hardening is compared to the
behavior of the as received material, it could be
associated, at 1500 s"1, to strain levels of 0,14 and
0,16 for tests 1 and 2 (see figure 4).
It is possible to make a quantitative investigation of
shock effects on microstructure through the next
approach. We consider the following stress evolution
with dislocations density (proposed in [6] in the case
of aluminum) :
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
For a monotonic test in the region of the athermal
plateau for copper, it can be deduced that dislocation
density is related to plastic deformation through the
next expression :
0.18
plastic deformation
FIGURE 4. Stress equivalence between as-received and
preshocked materials (Tests 1 and 2) for dynamic tests
conditions.
p =
-ex/71-
We try to demonstrate that, for tests 1 and 2,
considering parameters Mn and ka as constants, it is
possible to consider that the effect of shock wave is
only reported on the modification of the initial
dislocations density. Optimization of the as received
athermal plateau gives Mn =1.33 1015, ka =2.3. Table
1 summarizes the optimization results for the tests Tl
and T2 on the athermal plateau.
Because of copper thermophysical properties
(density, specific heat ...), temperature rise during
dynamic tests can be neglected for strain levels less
than 0,5.Since the modification of the elastoplastic
behavior of the material is related to the residual
plastic strain levels after shock loading, it is not
possible to describe it through macroscopic plastic
deformation : it needs to consider a microstructural
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athermal plateau for both as received and shocked
copper behaviors has shown that dislocations density
might have been multiplied by a factor ten. A
complete model based on the principle of the
Evolution of Defects Density approach proposed in
[8] for aluminum is actually determining, mixing
classical monotonous compression tests but also
jump tests. From our point of view, this physical
model is capable of predicting shock wave effects (in
this game of shock pressure levels) without any
arbitrary fitting of any parameters. As an extension
of this first work, we attempt to extend the shock
pressure range to 30 GPa in order to examine the
capability of this methodology to be applied to the
introduction of other microstructural deformation
mechanisms, twinning for example.
Table 1. Coefficients of the evolution law of dislocations
density for the athermal conditions (sTi the macroscopic
plastic deformation measured after shock passage at
16 mm radius, 8*T,the plastic deformation corresponding to
the dislocations density - see in figure 2).
Shocked (Tl)
Pti=L87 1015
E\i=0.156
sT1=0.0954
As received
p0=1.28 1014
Shocked (T2)
pT2=2.33 1015
s\2=0.208
8^=0.166
Compared to values founded in literature for fee
materials [7], these ones are well correlated, and the
shock effect induces a multiplication by a factor
twenty of the initial dislocations density (or defects
density). Figure 5 puts in evidence the accuracy of
the stress law to represent the experimental stress strain curves in the conditions of the athermal
plateau.
ACKNOWLEDGEMENTS
Test 2
The authors gratefully acknowledge Patrice
ANTOINE, Jacques MATHIAS for conducting the
impact tests, Sophie LAMALLE and Carine
MATHIEU for their contribution to the quasi static
and dynamic tests.
1
REFERENCES
Testl
Post shock wave equivalent state
0.05
0.1
plastic deformation
[1] PS Follansbee, GT Gray III, Materials Science
and Engineering, A138, pp 23-31, 1991.
[2] WH Gourdin, DH Lassila, Materials Science and
Engineering, A151, pp 11-18, 1992.
[3] GT Gray III, PS Follansbee, Impact Loading &
Dynamic Behaviour of Materials, Gesellschaft
Verlag, Oberusel, pp 541-548, 1988.
[4] GT Gray III, PS Follansbee, CE Frantz, Materials
Science and Engineering, Al 11, pp 9-16, 1989.
[5] GM Weston, NM Burman, 13th International
Symposium on Ballistics, WM7/1-WM7/9, 1992.
[6] J.R. Klepaczko, Proceedings of the IMPACT87
International Conference on Impact Loading and
Dynamic Behaviour of Materials, Bremen, 1987.
[7] J. Farre, C. Mathieu, Eurodymat 2000, Phys. 10,
pp 45-50, 2000.
[8] J. Farre, Private communication.
0.15
FIGURE 5. Representation of the experimental stress strain curves by the athermal law deduced from the EDD
model for as-received and shocked copper.
CONCLUSIONS
In this paper, it has been shown that the specific
experimental assemblies earlier proposed by Gray
and Follansbee [1] are well adapted to the study of
shock wave effects of copper around 10 GPa. Results
are in good agreement wit those founded by these
authors on this fee. material. We have confirmed that
plastic deformation could not classically explained
shock hardening effect and that it is necessary to
introduce a internal state variable for the modeling of
the large modification of the material microstructure.
From a modeling point of view, a short study on the
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