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
MOLECULAR DYNAMICS SIMULATION OF SHOCK WAVE
COMPRESSION OF METALS
A.A. Selezenev, V.K. Golubev, A.Yu. Aleinikov, O.I. Butnev, R.A. Barabanov,
B.L. Voronin
Sarov Open Computer Center, Sarov, Russia 607190
Abstract. The numerous results of molecular-dynamic simulation of the melting process of some
metals in shock waves are submitted. The Hugoniot adiabats, temperature of shock heating, structure
of a shock wave front, change of structure behind a shock wave as a result of melting were determined
during the simulation of steady shock waves. The obtained results were compared to the results of
thermodynamic calculations and experimental data on shock wave compressibility, heating and
melting.
INTRODUCTION
take into account one particular feature of the
process of shock wave compression. The condensed
matter state behind the shock wave front may differ
from the state of uniform volumetric compression.
Just behind a planar shock wave front it is realized
the state of one-dimensional strain, therefore a
material elementary volume is subject to the effect
of both normal and shear stresses17. It is shown that
shear stress may influence on the parameters of
material melting9.
To determine and predict the melting point
during the shock wave loading of metals is one of
the most interesting and actual problems of shock
wave physics. Along with experimental1"4 and
theoretical5"9 methods of studying metal melting in
shock waves (SW), the molecular dynamics (MD)
modeling technique has a certain research
potential10.
For the first time the MD technique was used to
study the SW structure within solid matter that is
referenced in articles11"13. The initial intended use of
the MD technique for investigation of solid matter
melting in shock waves was made in the article14.
Solid argon was taken as a testing material. In
publications15"16 the MD technique was used to
study the melting of such metals as Al, Cu, Pd, Pt.
The dependence of melting temperature upon the
static pressure value was calculated in these works
for every metal. The numerically obtained
dependencies of melting temperature upon the static
pressure were compared with the P-U diagrams of
shock compression of metals. Based on such a
comparison there were determined the values of
pressure and temperature behind the shock wave
front at which the melting of metals took place.
However, the approach of the works15"16 does not
NUMERICAL EXPERIMENT
FORMULATION
As for the present work, the process of melting
of such metals as Al, Cu in shock waves was
studied using the method of direct molecular
modeling. The computational MD cell presented a
parallelepiped with the larger size, which was equal
to 35 periods of the crystal lattice, and the
transversal sizes that were equal to 10 periods. To
verify the reliability of the results, the part of
computations was performed using a larger cell,
with the longitudinal and transversal sizes of 150
and 10 lattice periods respectively. The Morse
potential was used for the description of interatomic
interaction.
The parameters of the potential were chosen
coming out of the condition of correspondence
374
the shock wave. The experimental results and MD
simulation results shown good agree.
To determine the melting temperature of the
shock-compressed aluminum, it was calculated the
dependence of the steady-state temperature behind
the shock wave front upon the particle velocity. The
obtained dependence is shown in Figure 1. The
characteristic salient point at the temperature
dependence corresponds to the particle velocity
value, which is remarkable for the beginning of the
aluminum melting.
8000
between computational and experimental values of
several physical properties of the materials18. It is
shown that if the metal density increases under
compression, the potential, which was obtained
using the embedded atom method, is described
quite well by the Morse potential19. That is why the
latter was chosen to describe the state of matter
behind the shock wave front. The parameters of the
Morse potential are shown in table 1. The cut-off
radius was assumed to be 22r Q .
TABLE 1. The parameters of the Morse potential
Parameters
Metals
Al
Cu
0.270
0.343
3.253
2.866
6000
1.165
1.359
- 4000
The shock wave was propagating along the
direction of the larger parallelepiped's side (i.e.
along the crystallographic direction {100}). Along
the directions perpendicular to the direction of SW
propagation there were preset periodic boundary
conditions. To calculate the parameters of the
matter state behind the shock wave front, in the
computational MD cell there were marked out
elementary volumes (containing 150-200 atoms).
Within these volumes the following parameters
were calculated: temperature, particle velocity,
pressure, and the radial distribution function. It was
demonstrated that the use of the radial distribution
function in the context of MD modeling allowed an
efficient analyzing of some features of condensed
matter restructuring behind the shock wave front20.
To determine the point of material melting in the
shock wave, it was calculated the dependence of
temperature of a shock-compressed material upon
the material particle velocity in the shock wave.
The use of modern visualization tools21 for the
MD modeling allowed creating computer films,
which serve to visualize and fix the process of
material melting in shock waves.
2000
2.0
3.0
4.0
5.0
6.0
U,km/s
FIGURE 1. Dependence of temperature upon particle velocity
for shock - compressed aluminum.
Using the MD technique, there were calculated
the radial distribution functions for aluminum under
normal conditions (dotted line), as well as for
aluminum behind the shock wave front (solid line)
with the particle velocity of 4.62. km/s, which are
shown in Figure 2.
9.0
8.0
7.0
6.0
5.0
4.0
3.0
2.0
MD SIMULATION RESULTS
1.0
In the present work there were compared the
computational and experimental22 D-U and P-U
diagrams obtained for the investigated metals. The
pressure in the shock-compressed material was
determined on the moving piston, which generated
0.0
0.0
0.5
1.0
1.5
2.0
2.5
rfa
FIGURE 2. Radial distribution functions for aluminum under
ambient conditions (the dotted line) and shock-compressed
aluminum under the pressure of 135 GPa (the solid line).
375
The results of direct MD simulation do not
contradict to well known experimental3"4 and
theoretical5'6'15 data. The thermodynamic analysis
technique was used5 to show that aluminum melting
in SW might be expected at the particle velocities of
higher than 4 km/s that corresponds to the
experimental data. It was also theoretically
revealed6'15 that the aluminum melting might be
expected in the pressure range of 120-155 GPa. The
experimental results3'4 outline the melting interval
for aluminum within the particle velocity range of
4.1-4.2 km/s. Thus the method of direct MD
simulation of aluminum melting in the shock wave
did not lead to a fixation of any tangible influence
of the stress-strain state character upon the
parameters of melting. The considered method was
also used to determine the parameters of the shock
wave induced melting for such a metal as Cu. The
MD results were compared to other well-known
experimental and theoretical data. The parameters
of the shock wave induced melting are shown in
table 2.
The form of the radial distribution functions behind
the shock wave front corresponds to the liquid state
of aluminum.
In Figure 3 there are shown the frames from the
computer film that was made on the base of
modeling results. Figure 3 reflects the configuration
of the atoms within the marked out volumes of the
MD cell when shock waves of different intensities
pass through the cell. Thus the analysis of the
obtained results shows that the melting of aluminum
in shock waves occurs in the particle velocity range
of 4.1-4.3 km/s, which corresponds to the pressure
range of 120-130 GPa and the computational
temperature about 4100 K.
U=
4 km/s
U=
4,5 km/s
Time=4
Time=6
FIGURE 3. The character of atoms distribution within the
marked out microvolumes behind SW front under preserving the
lattice structure und under the melting conditions.
TABLE 2. The parameters of the shock wave induced melting
"""---^^^ Parameters
Um, km/s
Pm,GPa
Metals
^^^^
100-130
3.6-4.3
4.3 - 4.9
130-160
4.2 - 4.5
120 - 140
125 - 150
Al
4.2-4.7
3.8
108
120-155
4.2-4.8
120-130
4.1-4.3
200 - 260
2.8-3.3
2.7-3.0
190-225
Cu
230
3.0
240-260
3.1-3.3
376
Tm, K
3100
4200
4100
5000
6500
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