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
SHOCK WAVE EFFECTS IN COPPER :
DESIGN OF AN EXPERIMENTAL DEVICE FOR
POST RECOVERY MECHANICAL TESTING
Francois Buy, Fabrice Llorca
CEA Valduc, DRMN, BP14, 21120 Is sur Tille, FRANCE
Abstract. The mechanical behavior of metals may prove high changes with strain rate and pressure
loading history. In order to investigate the effect of a shock on the ulterior mechanical behavior of
high purity copper, we set up an experimental device inspired from G. T. Gray Ill's works. This
device, based on the trapping of shock waves after a plane plate impact is validated by numerical
simulations. The aim of these simulations is the evaluation of the heterogeneity of plastic
deformation. Shock pressures up to 10 GPa have been investigated. The plastic strain levels
subsequent to the shock are between 0.08 and 0.15 in the sample.
check that no damage will affect the sample and to
estimate the deformation path the sample encounters
during the loading in terms of cumulated
deformation, strain rate and homogeneity.
INTRODUCTION
The mechanical behavior of metals depends on
the thermomechanical conditions they are submitted
to. From a macroscopic point of view , the
modeling of this behavior is rather well known for
many metals when the loading conditions don't
change during the test. In fact, the microstructural
defects such as dislocations, twins... steadily evolve
during the test in a rather gentle way, these
evolutions depending on the loading. However,
when a sudden change in the loading conditions is
observed, the microstructure evolution reveals to be
different from what it used to be in "quasi
monotonic conditions". In particular, when we
consider a shock, the changes in terms of pressure,
strain rate, temperature lead to a drastically different
behavior [1-3].
In order to investigate the effect of a shock on
the mechanical behavior of copper, we have
performed several numerical simulations with
Hesione, a CEA hydrodynamic code used in its
Lagrangian version. The goal of this work is to
NUMERICAL CONDITIONS
Geometry
The initial geometry is presented in a companion
paper [4]. The device is composed by a flying target
whose composition and velocity are described in
table 1 and by an assemblage of several elements:
+ a cover plate (copper 40 mm in diameter,
3.5 mm thick)
+ a sample (copper 40 mm in diameter, 7 mm
thick)
+ a cone shaped confinement (copper)
+ a spall plate which traps the release waves
(copper)
+ a surrounding aluminum ring to maintain the
assemblage on the launcher.
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TABLE 1. Test conditions
Test number
Tl
Gap
Impact velocity
Flyer plate
1
0. 1 mm gap around the sample
1
450 m.s"
Cu <|) 58 mm thickness 3 mm
T2
Ta (|) 55 mm thickness 3 mm
450 m.s-
0. 1 mm gap around the sample
T3
Cu 0 55 mm thickness 2 mm
Ta (|> 55 mm thickness 2 mm
400 m.sH
0. 1 mm gap around the sample
The global mesh density is 2 meshes per mm.
Three test conditions are presented in this paper (cf.
Table 1). The simulations are made in 2
dimensional axisymetrical conditions. (Fig. 1). We
have found it important to introduce a gap of
0.1 mm around the sample which is consistent with
the machining configuration to have a better
evaluation of these effects.
Constitutive equations
Several constitutive models were tested for
copper (Steinberg-Cochran-Guinan, JohnsonCook, Zerilli-Armstrong). The final result is not
significantly affected by the model. We present
results obtained with a modified Zerilli-Armstrong
constitutive law [6].
Aluminum ring 11|
(1)
Wave trap 11|
HI
Confinement 11|
Sample
The following coefficients have been optimized
from compression test in the range of temperature
77 -700 K and 10'3 to 103 s"1 [7].
1
Cover 11|
TABLE 2. ZA coefficients for copper
Flyer ! |!
C4
Co
FIGURE 1. Initial mesh
69.58 MPa
936.64 MPa
0.00176 KT
1
5.77 10'51C
Equation of state
Damage
We used a Wilkins equation of state for copper.
In the range of pressure investigated, this equation
of state of copper give the following evolutions of
particle velocity, density and temperature versus
pressure on the Hugoniot curve (fig. 2). These
evolutions are consistent with the ones given by
Steinberg [5].
In order to simulate the effect of damage, we
considered a spall stress of 1.2 GPa.
RESULTS
Figure 3 presents the evolution of pressure of a
copper plate impacting the assemblage (Tl). The
pressure level reaches 8.5 GPa. Almost all the
energy due to the impact is trapped in the back
plate. Thus, there is no tension shock wave coming
back to the sample (Fig. 4) and we can consider that
no ulterior phenomenon affects the sample after
50 us (Fig. 4 and 5)
10000
9500 ^
8500
0
100 200 300 400 500
Particle velocity (m.s )
300
8000
FIGURE 2. Hugomot curve for copper. Evolution of the density
and temperature vs. pressure.
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In the sample, three different stages can be
considered :
+ a sudden rise in strain due to shock compression,
* a release that brings the sample dimensions very
close from the initial geometry,
+ two-dimensional waves that bring the sample in
its final configuration.
TABLE 3. Characteristic values of the different tests.
Peak Pressure
8.5 GPa
10 GPa
9 GPa
Shock duration
lus
lus
1.5 us
Axial deformation
in the sample
1.0%
3.0%
7.5%
In all three cases, the mean pressure in the
sample is of the same kind and thus, the axial strain
after the elastic loading and the Hugoniot is roughly
the same (4%). The subsequent unloading is also the
same but, according to the shock pressure level and
duration, the importance of the third stage is more
or less important. This level of deformation in the
third stage appears to be of the same level in the
case of a "Cu+Ta" flyer (T3) as the deformation
obtained after the compression stage. On the
contrary, in the case of the "Cu flyer" (Tl), the
influence of the radial waves on the amplitude of
the third stage is small.
FIGURE 3. Evolution of the pressure profile during the shock.
Thus, the deformation path to reach the residual
deformation is highly non monotonous. These
phenomena have been very clearly been analyzed
by Gray and al [2]. The levels of axial strain
depicted in their paper is of the same kind as the
ones we find. One has to be aware that the final
deformation does not correspond to the total plastic
deformation the sample is submitted to.
In order to check the homogeneity of the
deformation, we followed the deformation level of
lagrangian points at different diameter and thickness
position. Figure 6 shows the cumulated strain at
different positions in the sample which is the most
pertinent parameter to estimate the shock loading
effects. It can be noticed that in configurations Tl
and T2, the deformation is rather homogeneous.
However, configuration T3 exhibits high dispersion.
FIGURE 4. Mean pressure evolution through the sample (Tl).
-0.01
-0.02
-0.03
-0.04
X -005
w"
-006
-0.07
-008
-009
-0.1
FIGURE 5. Mean axial deformation in the sample.
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Tl
CONCLUSION
Thickness
3.5 mm
Thickness
6.5 mm
In this paper, we have investigated the ability to
recover a copper sample submitted to shock
pressures around 10 GPa. We have noticed that the
reflected waves do not damage the sample and that
the deformation is rather homogeneous in the
sample in the case of a single flyer plate. However,
one has to be much more careful for the
interpretation of results coming from the third
configuration.
(XL8
(U6
O.L4
CU2
0.1
0.08
0.06
0.04
We have to be aware that if this assemblage gives
good results for shock pressure around 10 GPa, it
has to be improved for higher impact velocities, the
radial waves bringing the sample to decay. Two
dimensional simulations are necessary for a good
estimation of these radial waves Numerical
simulations proves to be a very important tool for
the ulterior interpretation of post shock mechanical
testing.
0.02
0
LO 20
30 40 50 0
TimeQls)
ID 20
30 40 50 0
Timefjls)
10 20 30 40 50
Time(jls)
T2
Thickness
Thickness
O.L8
O.L6
O.L4
O.L2
O.L
0.08
ACKNOWLEDGEMENTS
0.06
The authors gratefully acknowledge JeanPhilippe PERLAT (CEA/Bruyeres le Chdtel) for his
support.
0.04
0.02
0
LO 20 30 40
Timers;)
50 0
LO 20 30 40 50 0
Time(p.s)
LO 20 30 40 50
Time (jls)
T3
REFERENCES
Thickness
O.L8
[1] L. L. Murr, Residual microstructure-mechanical property
relationships in shock loaded metals and alloys, in "Shock
Waves and High Strain-Rate Phenomena in Metals", Plenum
Press (198 l),p 607.
[2] G. T. Gray III, P.S. Follansbee, C. E. Frantz, Effect of
residual strain on the substructure development and
mechanical response of shock-loaded copper. Mat. Sci. Eng,
Alll, (1989) pp 9-16.
[3] P.S. Follansbee, G. T. Gray, Dynamic deformation of shock
prestrained copper, Mat. Sci. Eng, A138, (1991) pp 23-31.
[4] F. Llorca, J. Farre, F. Buy, Shock wave effects in copper:
Experimental analysis and interpretation for further
modeling application, this conference.
[5] D. J. Steinberg, Equation of state and strength properties of
selected metals, UCRL-MA-106439, (1996).
[6] F. J. Zerilli, R. W. Armstrong, Dislocation-mechanicsbased constitutive relations for material dynamic
calculations, J. Appl. Phys. 61 (5), (1987), pp 1816-1825 .
[7] Llorca Olb, Private communication.
O.L6
O.L4
O.L2
O.L
0.08
0.06
0.04
0.02
0
LO 20 30 40
Time(jis)
50 0
LO 20 30 40
Timers)
50 0
LO 20 30 40
Time (p.s)
50
FIGURE 6. Cumulative deformation in the sample in the three
configurations Tl, T2 and T3.
These results are of major interest for the validity
and the interpretation of the ulterior mechanical
tests.
322