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 PROPAGATION PROCESS IN EPOXY SYNTACTIC
FOAMS
J. Ribeiro, J. Campos, I. Plaksin and R. Mendes
Laboratory of Energetics and Detonics, Mechanical Engineering Department
Faculty of Sciences and Technology of theUniversity ofCoimbra
Polo II3030 Coimbra, PORTUGAL
Abstract. The Shock Wave Propagation Process [SWPP] in epoxy syntactic foams [SF] (Hollow Glass
Micro Spheres [HGMS] within an epoxy binder) with a nano-second temporal and micrometer spatial
resolution is presented and discussed. Samples with three different characteristic HGMS sizes were
studied (42, 92 and 135 jim). For the samples with characteristic HGMS size of 92 jim, the effects of the
density (0.64, 0.81 and 0.92 g/cm3) and of the loading pressure (20.0 and 9.6 GPa) were also analyzed.
The obtained results show the effects of self-organization (synergetic/cooperative) in the initial phase of
the SWPP, associated to a layer-by-layer collapse of HGMS, and in the following phase of propagation,
associated to the cellularization of the SW front. Specific experimental results, showing the SWPP in
one or two layers of HGMS, and numerical simulations (LS-DYNA 2D), of the pore collapse process in
one layer of HGMS, were also performed in order to clarify the mechanisms of SW propagation.
INTRODUCTION
resulting from the localization of energy and suggest
that a shock wave [SW] in heterogeneous media
cannot be seen as a propagation of a simple jump
discontinuity at a certain velocity like it is classically
presented.
In St. Petersburg, Y. Mescheryakov4 and T.
Khantouleva5 emphasize the stochastic character of
the phenomena and advocate a statistic approach to
deal with it. They developed a theory based on the
concept of the velocity distribution function, stating
that the average particle velocity determines the
macroscale behavior while the particle velocity
dispersion and the asymmetry of the velocity
distribution function determine the mesoscopical
effects like shear banding and/or mesorotation,
being all these three last quantities, average particle
velocity, velocity dispersion and asymmetry
assessable by experimental ways. According to them
the transfer of energy between the macro and the
meso scales is related with the transfer of kinetic
energy [KE] from the average motion of the media
In the past few years the scientists working in the
area of the shock compression of condensed matter
are attempting to fill the gap of knowledge existing
between the atomistic and macroscale-equilibrium
descriptions of the shock wave propagation process
[SWPP] in heterogeneous materials. This feature is
addressing the theoretical, numerical and
experimental investigation in the area to a mesoscale
level which is the length scale of the heterogeneities
- pores, particles, grains or crystals - existing in the
majority of the interesting materials with
technological applications.
Numerical simulations at this scale level are
being made for PBX - based on HMX compositions at Sandia National Laboratories
(USA) by M. Baer et al., since, at least, 19981'2.
Main conclusions of these simulations point to the
appearing of space-time fluctuations in the
thermodynamic fields, behind the shock front,
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were: for an initial density of 0.64 g/cm3 three
different characteristic HGMS diameters were
considered: d50=42, d50=92 and d5o=135 jim. For the
samples prepared with d50=92 jam HGMS, two other
initial densities were considered, 0.81 and 0.92
g/cm3. Typical thickness of the studied samples,
depending on the characteristic size of the HGMS,
ranging from 2 to 25 diameters of the HGMS.
All the samples were shock loaded using PBX,
based on RDX, cylindrical explosive charges. For
the samples with initial density of 0.64 g/cm3 and
d50= 92 |nm, Nitromethane [NM] cylindrical
explosive charges were also used. The level of the
SW pressure evaluated at the end of the inert barrier
that was always placed between the bottom of the
explosive charge and the top of the sample to be
loaded was: 20.0 GPa for the PBX and 9.6 GPa for
the NM. A schematic representation of the
experimental set-up used to perform this study is
shown in Fig. 1. As it can be seen there, in each
experiment the samples were placed below the inert
barrier and, below them, oriented toward the
incoming SW, were placed the optical fiber strips
that will allow the visualization - and registration in
an electronic streak camera - of the light emitted
during the process of the SW propagation
throughout all the thickness of the samples. Usually,
in order to evaluate the intensity of the SW
transmitted throughout the samples, a set of layers of
Kapton - Polyimide - was placed between the
bottom surface of the samples and the top of the
optical fiber strips. A typical streak record obtained
with the configuration shown in Fig. 1 can be seen in
Fig. 2. It corresponds to a simultaneous shock
loading, using PBX cylindrical charges, of samples
(with a thickness of 350 ^m), prepared with HGMS
with the same characteristic size (d50 = 92 jim), but
presenting different densities. It is possible to
observe, for each of the porous samples, an initial
long
and
non-homogeneous
light
zone,
corresponding to the SW propagation within the
sample, followed by strips of light, almost equal
spaced, corresponding to the SW propagation in the
set of the Kapton layers, placed after the samples.
The oscillations in the light intensity are very clear
for all the samples and for the samples with initial
densities of 0.64 and 0.81 g/cm3, they present a
remarkable regularity.
to the individual mesoparticles with a decrease of
the average velocity and an increase on the
dispersion.
I. Plaksin et al3 has been devoting his attention to
the mesoscale details of the detonation wave [DW]
propagation in PBX explosives for more than 5
years. The used experimental method allows the
visualization of the light emitted during the DW
propagation free from the boundary effects with a
time and a spatial resolution of 0.6 ns and 250 ^m.
Fluctuation of the light emission with 35±5 ns of
duration and with a changing spatial dimension have
been observed with this method. It is believed that
the nature of these fluctuations is a consequence of
the PBX own heterogeneity. Based on this idea it is
said that in the initial phase of HE crystal ignition
the characteristic dimension of the fluctuations in the
DW is in the order of the HE crystal size and within
the DW propagation the scale of the fluctuations
increase as a result of a synchronization/synergetic
effect.
Recognizing the importance of the subject and
trying to contribute for the clarification of these
emerging theories we have proposed6 the system
resulting from the mixture of a polymeric binder
with hollow glass micro-spheres [HGMS] - known
in the bibliography as syntactic foams [SF] and
which presents, as an essential feature, the
possibility to control the number, the size and even
the relative position of the pores - as an ideal media
for the study of the mesoscopic details of the SW
propagation in heterogeneous materials. Using a
modified version of the optical method developed by
I. Plaksin et al. in the Laboratory of Energetics and
Detonics it was already possible to observe
oscillations in the light emitted during the shock
propagation process on thin - 1000 \im of thickness
- polyester SF samples, with a nanosecond temporal
and a micrometer spatial resolution6. Trying to
clarify the nature of these oscillations we have
decided to study now the SWPP in epoxy SF
samples prepared with mono-sized HGMS.
EXPERIMENTS
Five different groups of SF samples have been
used for that propose, being each one of them
characterized by a unique pair of its initial density
and HGMS mean diameter (d50). The studied groups
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with NM. It can also be said that the degree of
regularity in the light oscillation appears to be
bigger in the sample shock loaded with PBX than in
the sample shock loaded with NM.
L OUTPUT
KAPTON LAYERS
FIGURE 1. Schematic representation of the experimental set-up
used - with small variations - in the majority of the presented
experiments
FIGURE 3. Streak record for four SF samples shock loaded with
PBX. Effect of the HGMS characteristic diameter on the light
emission patters
FIGURE 2. Typical streak record for four SF samples shock
loaded with PBX. Effect of the initial density - HGMS
concentration - on the light emission patterns
FIGURE 4. Streak record for four SF samples shock loaded with
PBX. Effect of the initial density - HGMS concentration - on the
light emission patterns
In the streak record presented in Fig. 3 is
possible to observe the effect of the characteristic
size of the HGMS on the patterns of the light
oscillations. It is clear that the reduction in the
characteristic size of the HGMS have as a
consequence a reduction in the period of oscillation.
The SW propagation in a sample prepared with nonsieved HGMS is also shown in that streak record.
Despite the clear differences for the samples
prepared with sieved HGMS, even in this situation is
possible to observe a certain degree of regularity. In
Fig. 4 is possible to observe the effect of the
pressure in the patterns of the light oscillation for
samples prepared with HGMS presenting a
characteristic size of 92 jim and an initial density of
0.64g/cm3 shock loaded with PBX and NM. Both
samples present clear regular oscillations in the light
intensity being the period of oscillation slightly
smaller for the case of the sample shock loaded with
PBX when compared with the one shock loaded
DISCUSSION AND CONCLUSIONS
The obtained results show space-time
oscillations in the light intensity emitted by the
shocked media, characterized by noticeable and
surprising regularity, over wide shock front area,
from 8 to 20 times the characteristic diameter of the
used HGMS. The nature of these oscillations is
certainly related with the samples heterogeneity
because its period changes with the concentration
and characteristic size of the pores - HGMS - and
with the loading pressure. The surprising part of the
results came from the regularity presented by the
oscillations. This regularity does not have a
complete correspondence in the distribution of the
HGMS in the volume of the polymeric matrix and
cannot be explain also by the scattering of the light.
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It is believed that the principal reason for this
behavior is the cooperative/synergetic effect, like
that proposed by I. Plaksin for the PBX explosives,
which in this case tends to slow down the shock
front in the inter-pore space transferring part of
shock front KE to closure of the pores.
A clear manifestation of this behavior can be
seen in the streak record presented in the Fig. 5. It
refers to the SW propagation in a sample with a
maximum of two HGMS (d50=92 jam) layers. The
HGMS are acting like a net in a turbulent flow,
making a redistribution of the KE and smoothing out
the irregularities of the input SW.
FIGURE 6. Simulation of the collapse of a HGMS from a
idealized layer of a po = 0.64 g/cm3 and dso = 92 urn SF sample.
Fringes of radial velocity - horiz. direction in the picture
[cm/us]. Positive velocity from left to right.
REFERENCES
1. Baer, M., Kipp M., and van Swol F.,
"Micromechanical Modeling of Heterogeneous
Energetic Materials", in Eleven International
Symposium on Detonation, pp. 788-797.
2. Baer,
M.,
"Computational
Modeling
of
Heterogeneous Reactive Materials at The Mesoscale",
Shock Compression in Condensed Matter-1999,
edited by M. D. Furnish, L. C. Chhabildas, and R. S.
Hixson, AIP CP 505, New York, 2000, pp. 27-33.
3. Plaksin, I., Campos, J., Mendes, R., Ribeiro, J., and
Gois, J., "Pulsing Behaviour and Corner Turning
Effect of PBX", in Eleven International Symposium
on Detonation, pp. 679-685.
4. Mescheryakov, Y., "Mesoscopical Effects and Particle
Velocity Distribution in Shock Compressed Solids",
Shock Compression in Condensed Matter-1999, ed.
by M. D. Furnish, L. C. Chhabildas, and R. S. Hixson,
AIP CP 505, New York, 2000, pp. 1065-1070.
5. Khantouleva, T., "Non-Local Theory of High-Rate
Processes in Structured Media", Shock Compression
in Condensed Matter-1999, edited by M. D. Furnish,
L. C. Chhabildas, and R. S. Hixson, AIP CP 505,
New York, 2000, pp. 371-374.
6. Ribeiro, J., Campos, J., Plaksin, L, and Mendes, R.,
"Process of Shock Wave Attenuation Inside a Hollow
Glass Microshpere/Polymeric Composite Material"
Shock Compression in Condensed Matter-1999,
edited by M. D. Furnish, L. C. Chhabildas, and R. S.
Hixson, AIP CP 505, New York, 2000, pp. 559-562.
FIGURE 5. Streak record of the shock wave propagation process
in a sample with two, one and zero layers of HGMS.
Trying to understand the mechanism of transfer
of KE in these cases, 2-D numerical simulations of
the collapse of a sphere - within a layer - have been
performed using the LS-DYNA2D. The results,
which can be seen in the Fig. 6 for the case of a SF
sample with an initial density of 0.64 g/cm3
(d50=92|im), show that the particle velocity is
affected by the release waves coming from the
internal surface of the sphere, changing its direction
toward the center of the pore, and contributing for a
redistribution of the energy over the SW front. By
this way the KE is being removed from the back of
the shock front that sweeps around the first HGMS,
and when this front reaches the second layer doesn't
have the strength enough to promote their collapse.
Only after the complete collapse of the first HGMS
will be possible for the shock front to proceed with
the collapse of the second HGMS. This mechanism
of redistribution of KE tend to induce a organized,
layer-by-layer, regime of propagation even if such
degree of regularity or organization cannot be found
in the distribution of the HGMS in the binder
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