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
MESOSCALE DESCRIPTIONS OF SHOCK-LOADED
HETEROGENEOUS POROUS MATERIALS*
M. R. Baer and W. M. Trott
Engineering Sciences Center
Sandia National Laboratories, Albuquerque,NM, 87185
Abstract. Recent simulations and experimental studies have revealed that dispersive waves are associated with impact on heterogeneous materials. The shock response includes fluctuating states and localization effects due to the interaction of multiple waves and deformation at material boundaries. These
features have been experimentally-observed using a line-imaging interferometer technique in impact
tests on thin porous layers of granular sugar crystals. In this work, three-dimensional numerical simulations are discussed. The focus of this study centers on interrogation of the extensive numerical data
from mesoscale simulations. Detailed wave fields are probed using imaging and filtering techniques to
determine statistical properties of the shock fields. These methods provide statistical distribution information that will lead to new continuum-level descriptions for shock-loaded heterogeneous materials.
INTRODUCTION
At the mesoscale, the shock behavior of heterogeneous materials involves multiple waves that
interact with material heterogeneities or internal
boundaries. For energetic materials, the shock sensitivity of initiation and sustained reaction is known
to be controlled by the processes occurring at the
mesoscale (1). An ensemble of crystals and binder
materials can interact to cause space-time fluctuations of the thermodynamic fields and a localization of energy to trigger reaction.
In shocked porous materials the wave fields are
three-dimensional and unsteady. Waves arise at
contact points and coalesce to produce a distribution of thermal and mechanical states. If the loading is sufficient to cause plastic deformation,
internal boundaries fold and form jets upon filling
pores. When averaged over a sufficiently large
space, a "shock" in heterogeneous material appears
to be dispersive as well as being dissipative. Rather
than a single jump state, the consolidated material
* Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the U.S. Department of
Energy under contract DE-AC04-94AL85000.
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contains a distribution of fluctuating states spanning a broad range of length and time scales. Much
of this behavior appears similar to the character of
turbulence.
Although direct numerical simulations of the
processes associated with shock-loading heterogeneous materials has revealed various features of the
wave fields, much of this new information has yet
to be incorporated in continuum-level descriptions.
To achieve this goal, data interrogation techniques
have been devised to probe the vast quantity of
four-dimensional data from detailed numerical simulations. In this work, image-processing software is
used to extract statistical properties of distribution
states during shock loading of heterogeneous material.
AN IMPACT EXPERIMENT
Time-resolved measurements often represent
averaged wave behavior because the resolution is
insufficient to capture the length/time scales associated with the mesoscale. Recently, a line-imaging
ORVIS technique has been developed to resolve the
detailed response of impact loading in a layer of
granular sugar.
0,5
To simplify the computations, the lateral width
of the granular layer is reduced to 0.75 mm which
is approximately 8 mean particle diameters. Periodic conditions at these boundaries are imposed. A
reverse ballistic computation is modeled by imposing an initial velocity condition. A shock load is
imparted to the granular column when material
stagnates at the hard wall boundary. Tracers at the
Kapton/PMMA interface monitor the conditions at
the location of the line-imaging ORVIS. All of the
relevant material parameters for the granular sugar
are given in Table 1. The Kapton and PMMA are
modeled as Mie-Grtineisen materials using the
CTH EOS database parameters. The numerical resolution was fixed at a cell size of 2 jbim requiring
120 million cells in the computations. These simulations were executed on the ASCI-Red TFLOPS
computer using 256 processors.
|i
cuvis
film
Ltf ir
Figure 1. Experimental configuration for impact on granular sugar
layer with line-imaging ORVIS particle velocity measurements.
Figure 1 displays a pictorial of the experimental
configuration. A 2.27 mm layer of granular sugar
(65% TMD) is lightly pressed into a fixture and
impacted with a Kel-F faced projectile. A 500 m/s
impact condition produces a reflected response in
the granular sugar with a mean particle velocity
estimated to be 370 m/s. Stress waves traverse the
thin granular layer and interact with a 0.23 mm
Kapton buffer layer. Transmitted particle velocities
are then measured at the Kapton/PMMA window
interface. Additional information of the test and
measurements is given in Reference 2.
Table 1. Granular Sugar EOS/Strength/Fracture Parameters
Parameter
Particle Size Distribution
46 Jim
64 ^m
91 Jim
116 Jim
138 urn
181 Jim
231 urn
338 urn
Crystal Density - p0
Sound Speed - c0
Slope of Us-Up Hugoniot - 5
Gruneisen Parameter - F0
Specific Heat - cv
Thermal conductivity - Xs
Yield Stress - Y
Poisson Ratio -v
Fracture Stress - cy
MESOSCALE MODELING
Three-dimensional numerical simulations of
the aforementioned experiment were performed
using the Eulerian CTH shock physics code (3)
including the effects of material strength and thermal dissipation. The modeling details associated
with the particle packing algorithm, material models and boundary conditions are given in Reference
4 and not repeated here.
Value
Wt. & # fraction:
0.005, 0.265
0.008,0.148
0.020,0.133
0.021,0.068
0.058,0.111
0.165,0.139
0.152,0.062
0.571,0.074
1.5805g/cm3
3.04xl05cm/s
2.05
1.04
1.38X1011 erg/gm-ev
4.86xl08erg/cm2-s-ev
1.1 Kbar
0.25
-2.0 Kbar
Figure 2 displays the initial 3D material geometry and later when all of the pores in the granular
sugar are filled. (The pore regions of the initial
granular material are assumed to be void.) Figure 2
shows a comparison of the ORVIS particle velocity
measurements to the CTH predictions. The agreement is reasonably good, particularly since the
granular geometry is only statistically represented.
Granular sugar is represented as an ensemble
of crystals with a predetermined unpressed particle
size distribution (5). A closely-packed geometry is
created using a MC/MD method with eight classes
of particle sizes forming an initial configuration
with a density of -65% TMD. Incorporated into
this model are the Kapton and PMMA layers of the
gauge package.
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useful in developing improved continuum-level
models of shocked heterogeneous materials.
The velocity-time profiles at the Kapton/PMMA
interface indicate complex transverse mode structure in addition to a ~120 ns rise time. Both experiment and computations exhibit early peaks in the
particle velocity followed by the late-time mean
velocity of ~ 250 m/s.
In this approach, four dimensional data is rendered as planes of gray-scale contours. For example, consider the field of temperatures from a direct
numerical simulation as shown in Figure 3. The
370 m/s
Transverse
cut
65%
contours
800 us
0.5 kmte Iippacl CTH. caJc.
(spatM average)
Figure 3. Gray-scale contours of temperature field at the midplane
transverse cut plane.
spatial and temporal image planes of information
contain a 256 array of pixel intensities spanning a
linear range of temperatures. A pixel count per
gray-scale intensity yields the distribution of states.
This information is directed related to a probability
density function (PDF). Furthermore, the set of
spatial or temporal planes forms the basis for an
ensemble average of the PDF.
Figure 2. Top displays initial and compacted 3D material crosssections from numerical simulation and bottom is a comparison of
particle velocities at the measurement plane.
DATA INTERROGATION
Various bands of the PDF can be masked to
identify characteristics of the field of interest. Then
image data is sampled to assemble relevant statistics such as mean size, area, fractal dimension, etc.
Although the line-imaging ORVIS measurements provide insightful information on transmitted wave behavior, the wave fields in the shocked
granular material are richly filled with important
statistical information related to the fluctuating
thermal and mechanical states. However, interrogating the massive quantity of numerical data in
these transient three-dimensional parallel computer
simulation is a computational intensive task. In this
study, image-processing software, such as ImagePro Plus (6), is used to extract statistical information relevant for averaging and filtering the fields
Figure 4 displays a representative PDF from an
ensemble of temperature contours. Four divisions
of the temperature distribution are identified: I - a
precusor range associated with elastic stress waves,
II - bulk response in which much of the mechanical
load is supported, III - a thermal gradient range
near grain boundaries and IV - the tail portion of
the distribution associated with the localization of
energy into "hot-spots". For reactive materials,
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region IV serve as the trigger of reaction and III is
the range associated with the growth of reaction.
I II
III
IV
300. 320. 340. 360. 380. 400.
SUMMARY AND CONCLUSIONS
This study has focused on probing numerical
simulations to extract statistical information needed
to define better continuum descriptions of shockloaded heterogeneous materials. Image-processing
software has been used as a means of data-mining
ensembles of contour planes of information from
direct numerical simulations. Representative PDF's
of temperature has suggested four aspects of the
shock response. Work is in progress to provide statistical information of additional mechanical and
thermodynamic fields such as those associated with
stress, strain and velocity fluctuations. Future study
will explore how these distributions are related to
the stochastic geometry and properties of the initial
state of the material. Ultimately, this state distribution information will be used in the development of
a new paradigm for modeling shocks in heterogeneous materials.
420. 440. 460. 480. 500.
Temperature [K]
Figure 4. Representative temperature PDF's displaying the four
ranges of the temperature field.
1
>385K
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
- * • • - 340-385 K
-•—310-340 K
-o—300-31 OK
ACKNOWLEDGEMENTS
We would like to thank David Kethison for help with
the image-processing. We also thank Steve Sheffield and
Rick Gustavsen (LANL) for sharing their sugar EOS and
shock Hugoniot data.
1000
500
Time after impact [ns]
1500
REFERENCES
1 Bowden, P.P. and Yoffe, A.D., Initiation and Growth
of Explosions in Liquids and Solids, Cambridge
University Press, Cambridge, 1952.
2 Trott,W.M., Chhabildas,L.C, Baer, M.R. and Castaneda,
J.N., "Investigation of Dispersive Waves in Low-Density
Sugar and HMX Using Line-Imaging Velocity
Interferometry," (this volume).
3 McGlaun, J.M., Thompson^.L., and Elrick, M.G.,
"CTH: A Three-Dimensional Shock Wave Physics
Code," Int. J. Impact Eng., Vol 10, 351-360, 1990.
4 Baer, M.R., "Computational Modeling of Heterogeneous
Reactive Materials at the Mesoscale", Shock
Compression of Condensed Matter -1999, edited by M.
D. Furnish, L. C. Chhabildas and R. S. Hixson, June,
1999.
5 Trott,W.M., et a/., "Dispersive Velocity Measurements
in Heterogeneous Materials", Sandia National
Laboratories, SAND2000-3082, December, 2000.
6 Image-Pro Plus v4.2, Media Cybernetics, Silver Springs,
MD., 1999.
Figure 5. Ensemble-averaged volume fraction for each region of
the temperature distribution.
Having identified the various regions of the
temperature PDF, masks for each of the four parts
are superimposed on the contour images, separated
from the original image and the statistics are resampled. Figure 5 displays the time evolution of the
volume fraction of shocked material corresponding
to each part of the temperature distribution function. At this impact condition, roughly 10% of the
material contains localized high temperatures forming "hot-spots". The gradient range is seen to be
represented by approximately 25% of the volume,
hence, the sum of the two parts of the distribution
displaces a volume similar to that of the initial
porosity.
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