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 FLATTENING OF SPHERES IN POROUS
MEDIA : IMPLICATIONS FOR FLATTENED CHONDRULES
Toshimori Sekine1, Naru Hirata2, Akira Yamaguchi3, Takamichi Kobayashi1,
Hongliang He1, and Zhi-ping Tang4
1
4
Advanced Materials Laboratory, National Institute for Materials Science,
Namiki 1-1, Tsukuba 305-0044, Japan
2
National Space Development of Japan, Sengen 2-1-1, Tsukuba 305-8505, Japan
3
National Institute for Polar Research, Kaga 1-9-10, Itabashi-ku, Tokyo 173-8515, Japan
Department of Modern Mechanics, University of Science and Technology of China, Hefei, Anhui 230026, P.R.
China
Abstract. Shock deformation of spherical particles has been investigated in the model systems of fused
silica beads in porous metal powders by experimental observations and by numerical simulation for
application to chondrules flattening in some primitive meteorites. Peak shock pressure and porosity in
initial sample play an important role to deform spherical particles. A comparison of the results
between the experimental observation and the numerical simulations indicates that shock deformation
is plastic and quenchable.
INTRODUCTION
Here we investigate a model system
experimentally and at the same time simulate
shock-induced deformation of spheres by the help
of a computer code. In this paper we present the
experimental and simulated results and compare
them with the observations in meteorites.
Primitive meteorites are full of tiny igneous
spherules called chondrules, consisting mainly of
olivine and pyroxene. Chondrules were made by
some pervasive process in the early solar system
that formed melted silicate droplets [1]. Some
chondules
displays
considerable
flattening
indicating deformation of spherules. These features
are closely related to the degree of shock
metamorphism observed in the host meteorite [2, 3].
Experimental observations of shock-induced
flattening of chondrules in meteorites have been
carried out [4, 5] and revealed a linear relationship
between shock peak pressure and the degree of
flattening of chondrules. The experimental systems
are heterogeneous in terms of grain sizes and
materials and seems to be difficult to carry out a
numerical simulation of modeling for shockflattening. It is not clear whether the shock-induced
deformation can be quenched without any
significant alternation.
EXPERIMENTAL
We employed a mixture of copper powder and
fused silica beads as the starting material. The
average grain size of the copper powders is about
10 jLim. The diameter of fused silica beads ranges
briefly between 100 and 200 u,m with a mean aspect
ratio (short axis / long axis) of 0.91 ±0.08. The
mixture was pressed into a steel container at
pressures of 0.1 ~ 0.5 GPa to control the initial
porosity. The amount of beads was so small that
beads do not contact each other. The density of thus
obtained samples (~ 12mm in diameter, ~ 2 mm
thick) in the containers were 4.4 6.1 g/crri (834% porosity).
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orientations. We measured and averaged the aspect
ratios of beads. Figure 2 illustrates a deformed bead
quenched from 22 GPa, indicating asymmetrical
flattening. The ratio is summarized in Figure 6, and
a significant change can be seen at pressures of
between 22 and 31 GPa. It was not successful to
recover samples from 49 GPa.
To evaluate the effects of initial porosity of
sample, samples with higher (34 and 27 %) and
lower (8%) porosity were investigated at 22 GPa
and 32 GPa, respectively. Figures 3 and 4 illustrate
some deformed beads as a function of porosity at a
shock pressure of 31-32 GPa. It was not successful
to recover the samples with 34% porocity from
higher shock pressures. The measured aspect ratios
are shown in Figure 6.
To compare the effect of samples with different
shock impedance, we have carried out several shots
Shock recovery experiments were performed
using a 30-mm bore single-stage propellant gun.
The flyer plates were steels (SUS304) and 4 mm
thick. The peak pressure was estimated by
measured impact velocity of flyer and the
impedance match solution. The impact velocity
ranged between 0.7 and 2.0 km/sec and the pressure
ranges between 14 and 49 GPa. Recovered samples
were cut parallel to the shock compression axis and
polished in order to observe the shapes of beads by
SEM.
EXPERIMENTAL RESULTS
Figures 1 (a) to (c) show the textures of polished
sections of shocked samples with initial porosity of
about 13%. In the shocked samples copper powders
are well compacted and no pores are present. The
beads displayed flattened deformation and preferred
FIGUREl. Cross sections of post-shock samples at 14 GPa (a), 22 GPa (b), and 31 GPa (c). Fused silica beads (dark dots) are
in copper powders (light area) with an initial porosity of about 13%. Most bead diameters range between 100 and 200 (im.
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using aluminum containers with mixtures of silica
beads and aluminum powders, but it was quite
difficult to recover samples from pressures as low
as 18 GPa.
NUMERICAL SIMULATIONS
FIGURE 2. Asymmetrically deformed bead in the postsample from 2 GPa (Figure 1 .b). The bead width is about
200 Jim.
FIGURE 3. Some deformed beads in the post-shock sample
with initial porosity of 13%, recovered from 31 GPa (same
as in Fig. Ic).
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.
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** * *
*
*
Discrete Meso-Dynamic Method (DM 2 ) has
been applied to model the deformation of the beads
embedded in porous powders such as copper and
aluminum powders.
The details of the method has been published
elsewhere [4]. We have investigated the
deformation of the beads as a function of time, and
impact velocity. To make a simple configuration,
the assembly of a flyer of SUS304 (0.5mm thick), a
mixture of metal powder and beads (0.4 mm thick),
and container (0.9 mm thick) are used at impact
velocities of 0.7, 1.0 and 1.5 km/sec.
in the first series of calculations for fused silica
beads in a porous copper powders (18% porosity),
the aspect ratios decrease with increasing impact
velocity (peak shock pressure). They do not change
at times of 0.2 and 0.4 jisec after impacted, as
shown in Figure 5.
However, beyond about 0.5u,m later after
impacted, the ratio returns to nearly one, suggesting
that the deformed beads rebound. The time for
beads to start to rebound corresponds to the arrival
time of the refraction wave originated from the back
of a flyer plate. A second series of calculations for
the beads in porous aluminum powders (18%
porosity) indicate that the obtained aspect ratio is
quite similar to the results for the copper powder.
The distribution of porosity around a bead seemed
to be very important to the initial stage of
deformation.
The simulated changes of aspect ratio before
rarefaction wave arrives are indicated in Figure 6,
to compare with the experimental observations.
The results are consistent with the experimental
observations although the simulation indicates
rebounding deformation after subjected to pressure
release. Additional simulation on the effect of
different containers was carried out at a pressure of
14 GPa. The mean aspect ratio of beads at 0.2 jusec
after impacted is 0.86 in a steel container and 0.83
in aluminum container, and beads in latter container
indicate to rebound faster and greater.
FIGURE 4. Some deformed beads in the post-shock
sample with initial porosity of 34%, recovered from 32 GPa.
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DISCUSSION
0.2
0.4
Time (jjs)
Our present experimental and simulation results
indicate that beads in porous metal powders change
the aspect ratio by shock compression.
The
change of the aspect ratio is a plastic deformation
and can be quenchable. The distribution of pores
contacting on each bead may play an important role
for the initial deformation. The shock pressure is
also a key factor to the change of the aspect ratio.
Nakamura et al. [5] and Tomeoka et al. [6] have
carried out experiments on Allende and Murshison,
respectively. Their data indicate that the mean
aspect ratio of chondrules increases linearly with
increasing shock pressure up to about 30 GPa.
The change of the aspect ratio is much greater in
natural samples, and it can be recognized at a lower
onset pressure of about 10 GPa. This may be due
to a higher porosity of the natural meteorites. The
porosity of Allend and Murchison meteorites are
-23% and -26%, respectively. The distribution of
pores also may affect. If it is heterogeneous, then
the stress distribution is also heterogeneous and
more shear stress is expected during shock
compression.
If the beads are subjected to
heterogeneous pressure, the flattening should not be
observed. Shock loading is uniaxial compression,
and provides a chance for beads to flatten. The
degree depends on factors such as peak pressure,
porosity, and so on, as indicated by both the present
experimental observations and simulations.
0.6
FIGURE 5. Simulated changes of the aspect ratio of beads
as a function of time. Solid curve is for fused silica beads
in porous copper powders, and broken curve for the beads in
porous aluminum powders 0.5 mm thick steel flyer impacts
on a 0.4 mm thick sample backed on steel plate at 1.5
km/sec.
porosity (%)
REFERENCES
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1. Hewins, R.H., Jones, R.H., Scott, E.R. (eds),
Chondrules and the Protoplanetary Disk, Cambridge
University Press, Cambridge, 1996.
2. Martin, P.M. and Mills, A.A., Earth Planet. Sci. Lett.
51, 18-25(1980).
3. Sneyd, D.S., McSween, H.Y., Sugiura, N., Strangway,
S.W., Meteoritics 23, 139-149 (1988).
4. Tang, Z.P., Horie, Y., and Psakhie, S.G., "Discrete
Meso-Element Modeling of Shock Processes in
Powders," in High-Pressure Shock Compression of
Solids IV, edited by L. Davison, Y. Horie, and M.
Shahinpoor, New York 1997, pp. 143-175.
5. Nakamura, T., Tomeoka, K., Sekine, T., and Takeda,
H., Meteoritics 30, 334-347 (1995).
6. Tomeoka, K., Yamahana, Y., and Sekine, T.,
Geochim. Cosmochim. Ada 63, 3683-3703 (1999).
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30
Pressure (GPa)
FIGURE 6. Summary of the change of aspect ratio of
beads as a function of shock pressure. Solid circles are
beads in copper powders with initial porosity of 13-15%.
Open circle is for beads in 34% porosity of copper powders
and open square for beads in 8% porosity of copper
powders. Crosses and open triangles are for simulated
results on beads in 15% porosity copper powders and
aluminum powders in steel containers, respectively.
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