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 PARADIGMS AND NEW CHALLENGES*
James R. Asay
Sandia National Laboratories
Albuquerque, NM87185
Abstract. Modern shock wave applications require prediction of material response under complex
loading conditions and are often solved with numerical simulations. Even though many of the
fundamental problems have been addressed, there are still a large number that cannot be solved from a
first-principles approach. To attain a fully predictive capability for these phenomena, it is necessary to
understand the physical processes occurring during the shock process itself and to critically examine
the fundamental postulates used to interpret shock wave phenomena. This paper examines the basic
assumptions for describing shock processes in solids.
strength of shocked materials, or the kinetics of
shock-induced phase transitions. These properties
must be evaluated experimentally for use in semiempirical theories. To realize truly predictive
capabilities, it will be necessary to develop firstprinciples theories that have robust predictive
capability. This will require critical examination of
the fundamental postulates used to interpret shockcompression processes. Another question concerns
the fundamental material processes causing the
shock transition itself. Are properties, such as
material viscosity, the controlling factors or are
kinematic effects, such as mesoscopic-scale motions
produced from local instabilities, responsible for the
observed risetimes? These and other questions must
be answered by thorough investigations. In
particular, a strong need exists to develop in-situ
diagnostics for probing these processes in real time.
It is clearly time to consider explicitly the highly
heterogeneous effects of shock compression and to
reformulate the basic conservation equations in
terms of the non-homogeneous and non-equilibrium
effects produced in the shock process. A change in
the fundamental assumptions, or a paradigm change,
is necessary to change the way we think about
shocked states and which will likely result in
significantly better continuum theories. As one
INTRODUCTION
The field of shock compression science
developed from the need to describe the highpressure response of materials in regimes
inaccessible by other methods. These requirements
led to the development of experimental and
theoretical tools for probing the transitory nature of
shock compression. The questions posed by early
investigations have been answered to a large degree,
with the result that a basic understanding now exists
for the thermophysical and mechanical properties of
shocked materials. This includes development of
highly refined continuum models, which accurately
predict most of the aggregate features of shock
compression. Even after a half-century of intensive
research, however, there are still a large number of
unresolved shock wave problems.
The resulting continuum theories have been
incorporated into a variety of numerical techniques
and used with computational methods to solve quite
complex problems. However, there are still many
outstanding problems that cannot be solved with this
approach. For example, it is still not possible to
predict shock transition times over a range of
pressures, the dynamic compressive or tensile
*Sandia is a multi-program laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of
Energy under Contract DE-AC04-94AL85000.
26
example, most treatments of solid response are
based on the elastic-plastic model with the simple
assumption that the strain tensor can be separated
into elastic and plastic components. This and
associated models do not incorporate the known
effects of mesoscopic motions and are known to be
inadequate in explaining many features of shock
compression, including loss and recovery of strength
during
shock-compression.
A
fundamental
understanding of these processes can result in
profound improvement of the continuum theories
and produce vastly improved predictive capabilities
for solving complex dynamic problems. In this
paper, the basic assumptions and evolving
capabilities that may help resolve these issues will
be briefly discussed. These challenges provide
exciting opportunities for the next-generation
researcher who is willing to do difficult physics and
chemistry research or to solve complex engineering
problems.
BASIC ASSUMPTIONS
these scales in more detail, but the main message is
that deformation in a shock wave is complex,
involves different length scales, and therefore needs
to be understood at all levels.
The simplest description of a shock involves
propagation in a fluid. There have been a large
number of papers written on this topic2'3, so only a
brief review will be given here. For planar onedimensional motion, it is assumed that the shock
wave is a transition from an initial equilibrium to a
final equilibrium state of pressure, specific volume,
and internal energy. It is further assumed that the
final fluid motion is one-dimensional. In this
approximation, sometimes referred to as the "benign
shock"4, shock compression is assumed to be
equivalent to quasi-static compression. Indeed,
shock compression data are often used to determine
the high-pressure EOS2.
The relatively simple ideas of shock propagation
in fluids become much more complex in solids, as
illustrated in Figure 1. In this case, it is possible to
have folly elastic compression at low stresses where
the material does not yield. At higher stresses, the
deformation is inelastic and exhibits a rich variety of
shock features that are dominated in general by rate
dependent yielding. At low stresses a two-wave
structure is observed that is not steady in time. The
first shock is elastic and referred to as the elastic
precursor. Its amplitude, referred to as the Hugoniot
Elastic Limit (HEL), is generally not constant with
time. The second wave representing inelastic
response is usually referred to as the plastic wave,
although several investigators have shown that the
notion of a plastic "wave" is incorrect5'6'7 and that
the process is more representative of a diffusion
process. Nevertheless, in the moving coordinate
system of the first wave, the second wave can
assume steady propagation features.
For supposedly planar shock compression, the
underlying question concerns the dynamic processes
that actually occur in the shock transition and the
basic assumptions used to analyze the shock. In this
regard, I found it useful to take a specific material
and examine the predictions of specific models. This
provides perspective and insight into the
mechanisms that may be responsible for the
observations and thus on the shock process itself I
use the term "may", because without specific
measurements, we can only infer what is happening
in the shock transition. The results of this query
raise basic questions about the assumptions used to
model response at the continuum level. They also
help to identify potential diagnostics that may
further elucidate deformation mechanisms.
Material responses such as dynamic yielding or
shock-induced phase changes nucleate at
microscopic scales but the effects of initial defect
generation can quickly grow to dimensions of a
fraction of a micrometer, normally referred to as the
mesoscopic scale. There is increasing evidence that
this scale has a dominating influence on shock
response. For this reason, it is necessary to
understand material response over the full range
from the finest level, or atomic, to the microscopic,
or dislocation, to the sub-granular, or mesoscopic,
and finally to the continuum scale. Gupta1 discusses
Figure 1. Elastic-plastic wave propagation.
27
There are several basic assumptions usually
made in describing elastic-plastic response at the
continuum. These can be summarized as (1) the
deformation is homogeneous at a level large
corresponding to the source of deformation, (2) the
total strain can be separation into elastic and plastic
components with no plastic dilatation, and (3) the
mean longitudinal and lateral stresses are equivalent
to hydrostatic pressure. Using these assumptions,
the longitudinal stress is equal to the pressure plus
four thirds of the resolved shear stress. Oilman6 and
others have questioned these assumptions and in
particular have shown that the decomposition into
elastic and plastic strain is incorrect in that the
separation should involve deformation gradients.
Graham8 has also questioned the validity of
describing the anisotropic stress state as
equivalently a perturbation to the pressure state. It is
important to keep in mind that even though this
construction often represents the overall features of
the shock wave propagation, it is misleading and
diverts our thinking away from the real deformation
processes that occur.
There have been many studies, which show that
these assumptions give approximately the right
continuum response9. However, there are many
counter examples to show they are incorrect and can
give misleading conclusions about dynamic material
response.
The paper deals specifically with the following
questions: (1) is the assumption of planar motion an
adequate description of 1-D shocks?, (2) are
homogeneous, equilibrium states produced by
steady shocks?, (3) is the traditional emphasis on
mechanical deformation states sufficient to describe
real shock processes?, (4) is the risetime of a
"plastic" wave representative of deformation
mechanisms, such as viscoplastic mechanisms, and
(5) are existing solid models, e.g., the elastic-plastic
model, adequate descriptions of real response? We
will show that the state immediately behind the
shock wave is not generally homogeneous and
uniform; that the variation in material properties at
different locations throughout a shocked material
has a strong influence on material properties; that
material properties such as compressive yield
behavior can be time dependent in the shocked state,
a direct failure of the elastic-plastic model; and that
viscoplastic or other dissipative mechanisms may
not be the controlling factor for determining shock
risetime. Even the concept of a steady plastic wave
in real solids can lead to erroneous interpretations
and it may be more appropriate to think of the
process as an ensemble of stationary waves. Finally,
results will be shown to illustrate that shock-induced
local motions are highly non-planar in onedimensional experiments usually assumed to
produce pure translational motion.
SPECIFIC EXAMPLES
The advent of time-resolved measurements of
shock wave profiles opened a new regime for
probing shock deformations10 at a continuum level.
Barker and Hollenbach11 performed a classic set of
experiments on aluminum, which showed that the
HEL was nearly constant and that the plastic wave
was steady to within experimental resolution over
the stress range of 9-90 kbar. These data were
among the first to test many of the concepts of ratedependent plasticity at the continuum level. A
notable observation from these experiments was that
the risetime of the plastic wave varied roughly as the
fourth power of the peak stress. Grady12 has further
shown that this apparent fourth power dependence is
more general, applying to a wide variety of metals
and non-metals.
A variety of rate-dependent material models
were developed to describe these and similar
experiments. Generally, these models are based on
Maxwell construction in which the dissipative term
is described by the stress difference from
equilibrium9. These continuum models result in
good agreement with experimental data. Grady12 has
extended this concept to show that different classes
of continuum models can be described by a
generalized viscoplastic function. The main shortfall
is that these models are not predictive and generally
do not provide a complete description of loading
responses, such as unloading, multiple shock
loading, and multi-axial loading.
Various dislocation models have also been
developed to describe these data, including Johnson
and Barker13, who employed a specific dislocation
function based on the Orowan equation first used by
Taylor14 to describe elastic precursor decay. In
fitting the experimental profiles, reasonable values
of dislocation parameters were obtained, which
suggested that a microscopic description was
sufficient to describe the shock process. However,
28
this apparent agreement points out a persistent
problem that concerns the uniqueness of continuum
wave analyses. Although time-resolved shock wave
profiles provide useful information about the
macroscopic time scale of deformation, they are not
sufficient to uniquely identify actual physical
mechanisms. It is also important to note that both
continuum and dislocation models of aluminum
shock wave profiles used in all previous analyses
were based on the assumption of homogeneous
response of the shocked material on a scale large
compared to the deformation feature. The analyses
also implicitly assumed that the deformation was
one-dimensional motion on this scale.
It is clear that additional information, such as
real-time in-situ measurements of the deformation,
is needed to discriminate between the different
models. Barring this information, another approach
is to use additional waves, such as unloading or
reloading waves from the shocked state, to probe the
properties in the shocked state. Although not a direct
probe of the shock transition, this approach tests the
assumptions used to describe the shock process.
Comparison of these wave profiles with predictions
of either the elastic-plastic (E-P) or more
sophisticated models of inelastic deformation
consequently provides an independent test of the
models. Specifically, the simple elastic-plastic
model predicts that the initial unloading is elastic,
followed by plastic deformation. For reloading from
the shocked state, the expected response should be
completely plastic since the initial shock
compression produces a state on the yield surface.
These tests therefore make it possible to infer
processes occurring in and behind the "plastic"
shock.
One set of measured unloading and reloading
wave profiles15' l6 are shown in Figure 2. The
unloading wave profile shows that the release from
the shocked state deviates from the simple elasticplastic model, resulting through quasi elastic-plastic
behavior referred to as the "Bauchinger effect".
Recompression from the shocked state shows even
more deviation, since an elastic precursor to the
main second shock is observed, contrary to elasticplastic theory, which implies that further
compression should be completely plastic17. These
results can be used to determine the shear stress, TO
in the shocked state and the maximum shear
strength, tc, the material can support. The E-P model
predicts these should be equal after initial shock
compression. At low stresses (weak shocks)5, it was
found that this assumption is nearly valid. For a
single plastic shock wave, it was found that the
initial shear stress is much less than the maximum
shear strength. Detailed analyses implied that this
was not simply a rate effect, but that the yield
strength in the shocked state was time dependent or
that other processes were occurring.
"Elastic
precursor"
Plastic
Elastic - plastic
model
0.0
1.5 16
17 IM
19 2,0 21 22 23 2.4 25
2.6
Tlme(psec)
Figure 2. Unloading and reloading waves in 6061-T6 aluminum.
At that time, a plausible explanation for the
apparently anomalous behavior of the shear stress
was made that multiple reverberations of the shock
at internal grain boundaries was occurring, with the
result that the shear states were not uniform
throughout the shocked state at a sub-grain level. To
quantitatively describe this, it was assumed that the
shear stress induced behind the shock wave could be
described by a Probability Distribution Function,
PDF. Assuming a Gaussian PDF, the distribution
was adjusted until reasonable agreement could be
obtained with both the unloading and the reloading
profiles15. Although this approach produced semiquantitative agreement, we thought it to be ad hoc
and did not use it for further applications. However,
in more recent 2-D and 3-D simulations of wave
propagation in granular and polycrystalline
materials18'19, this effect is observed in numerical
simulations of shock propagation in polycrystalline
materials. The earlier results suggested that a larger
scale feature, i.e., the grain or sub-grain scale, might
29
be more important than the microscopic scale in
modeling these effects.
Subsequent to this investigation, Swegle and
Grady employed a mixture model and included
explicit temperature effects behind the shock to
model the experimental results extremely well using
another approach.20 Specifically, they assumed that
the risetime of steady waves in aluminum are
governed by the fourth power law discussed earlier
and that the dissipative energy in the shock was
deposited locally in small regions within grains.
This effect caused a local rise in temperature due to
thermal trapping21 in these regions. They assumed at
the time that the local hot spots were produced by
shear dissipation in micro-shear bands, but a variety
of localization effects could cause such effects.
These transient hot regions can have a profound
effect on macroscopic properties such as yield
strength, which can be temporarily decreased, as
illustrated in Figure 3. Depending on the actual scale
size, which is not known a priori, they found that the
local temperature in these hot spots approaches
melting, followed by relaxation to the bulk
temperature as these regions are rapidly quenched.
In correspondence, the shear strength decreases to
near zero in the shock wave itself, followed by
recovery at times sufficiently long for thermal
equilibration. The variability shown by the bands in
the figure is due to assumed variations in shear band
thickness and separation20.
Although the atomic and microscales are
undoubtedly important contributing factors to the
shock properties, the larger scale effects appear to
dominate the macroscale response in aluminum, as
shown by the good agreement with the continuum
unloading and reloading measurements and the good
agreement with the experimental shear stress states.
Although the exact details of the mesoscopic scale
response are not known, the ability to capture the
major results of unloading and reloading from
several experiments over an extended pressure
range, without appealing to viscoplastic or
microscopic mechanisms, is attractive. These results
suggest the important point that a scale feature is
established at a mesoscopic scale by the shock itself.
These results also emphasize the need to identify the
actual mechanical and thermal effects induced in
real time during shock compression.
Variable band
-spacing & thickness
5.0
10.0 15.0 20.0
25.0
Shock Stress, GPa
Figure 3. Shear stress and maximum shear strength versus shock
pressure in aluminum. Data by AFtshuler22 are also shown.
This example further emphasizes the point that
existing models do not describe the response of
aluminum subjected to more complex loading
histories (but still simple!). In particular, the shear
strength appears to be initially low during shock
loading, followed by recovery later in time, which
implies an explicit time dependence to the yield
stress. The two interpretations discussed; i.e.,
softening due to local thermal heterogeneities or a
distribution of shear stress states due to grain
distributions, appear to explain the main features. A
common thread is that good agreement is obtained
with the data by using material descriptions that
incorporate a scale size.
It is also clear from these examples that real-time
measurements of shock induced features are needed
to discriminate between the different approaches.
Asay and Barker23 developed an interferometer
technique that allows real-time measurements of
distributions (dispersion) in particle velocity during
shock deformation. This technique provides new
information about the nature of heterogeneous
motions at a mesoscopic scale of about 100-jiim in
diameter. If the particle velocity is not uniform over
the laser-illuminated spot size, the reflected Doppler
light will contain a distribution of frequencies,
causing a loss of contrast, which can be analyzed to
determine the average particle velocity and its
variance23.
Mescheryakov and Dikov24 used this effect to
correlate material properties such as compressive,
tensile strength, and strain-rate dependence with the
degree of particle velocity dispersion in various
30
in the shocked state it is actually fluctuating from
point to point on the sample surface. Another
important observation is shown in Figure 4c, which
illustrates that the spall strength in steel can be
directly related to particle velocity dispersion.
This example illustrates the importance of grain
and sub-grain scale effects in the propagation of
shock waves in polycrystalline materials. There
have been several studies to evaluate these effects
using a numerical approach l9'25. In addition,
significant work is in progress at Los Alamos
National Laboratory using a discrete particle
approach (DM2 code) to model individual grains in
2-D motions19, as shown in Figure 5a. Impacting
0.16
0.12
(a)
(A
i 0.08
J
0.04
0
0.8
1.6
Time,
(b)
0.04
.0.02
rf
0.8
1.6
Time, \
—3E———
Au
(a)
Wtoeltr,
(b)
Figure 5. Modeling of wave propagation in copper, (a)
experimental configuration, (b) particle velocity distributions at
different times behind the shock.
(c)
3
I
the polycrystalline sample against a rigid wall forms
a reverse shock wave, as illustrated. Several notable
features are apparent in this simulation. First, a
microstructure corresponding to the grain size is
observed. Associated with this is a non-planar shock
front and highly rotational flows behind the shock
front. The simulation also illustrates that the
longitudinal particle velocity is not uniquely
defined, but has a discrete variation near the shock
front at the grain identified as "A" that persists for
states well behind the shock front (grains "B" and
"C"). Note that the dispersion in velocity at C is
nearly of Gaussian form. The main results from
these calculations are (1) that shocks in
polycrystalline materials are not planar, and (2) that
there is a scale effect to the deformation which is
related to the grain size. The scale effect is
observed to be associated with a rotational motion
of mass points within grains that has some features
of mesoscale eddies or the beginnings of turbulent
motions. These results are in qualitative agreement
with experimental results on aluminum by Lipkin
Free surface velocity, m/s
Figure 4. Particle velocity dispersion in metals, (a) wave profile
in al. (b) dispersion velocity in Al. (c) spall strength versus
velocity dispersion in Fe. Top curve is pullback velocity; the
bottom is dispersion.
polycrystalline metals. In their experiments, a laser
beam was focused on a polycrystalline sample to
determine the average free surface velocity and its
variation. The resulting average particle velocity and
the dispersion of particle velocity for the elastic,
plastic and pullback signals observed in aluminum
are shown in Figures 4a and 4b. In particular, a large
dispersion of particle velocity is obtained at the
onset of yielding and near the top of the plastic
wave. The magnitude of dispersion decays during
unloading and becomes large again during the
spalling process. The implication is that although
the average particle velocity appears to be constant
31
and Asay15 and in semi-quantitative agreement with
the experimental results of Mescheryakov et al.24.
Recent additional calculations by Yano and
Hone 26 illustrate the effects of shock pressure on
the local gradients near the shock front25'26.
Specifically, the degree of "shock front roughness",
i.e., the local velocity variations and the rotational
motions, appears to decrease as the stress increases.
An important implication is that measurement of
shock risetime with a continuum gauge can give
varying results, depending on gauge dimensions.
Furthermore, the results shown in Figure 5
emphasize a critical need to understand the details
of shock deformation at the mesoscale in order to
develop better continuum models. Undoubtedly, the
microscopic features of plastic deformation also
contribute to the mesoscopic response, but local
rotational motions and velocity distributions must be
accounted for in realistic continuum models27' 28.
This conclusion agrees with the ad hoc assumptions
used by Lipkin and Asay15 to model shear states in
shocked aluminum, but within a solid mechanics
framework. Refinement of the approach holds
considerable promise for changing the fundamental
paradigms used in modeling approaches.
To understand these processes in more detail,
Baer 9 is studying shock propagation in granular
materials, such as sugar, that are elucidating features
of the deformation not heretofore considered. In
particular, he is attempting to identify scalar
invariants of the shock-induced flow that can be
translated into continuum models. In his recent
simulations29, a shock wave was generated in a
three-dimensional sample of 65% dense sugar
sample containing representative grain distributions.
A hydrodynamics code was used to simulate the
propagation of the shock motion created by
impacting this sample into a rigid plate, as shown in
Figure 629.
Figure 6 shows the resulting pressure and
temperature fields induced by the shock. As
observed, there is considerable variation, which
must be quantified in order to link mesoscopic scale
response to continuum models. Baer has made
significant progress in this endeavor by synthesizing
large sets of numerical output, typically fewgigabyte files, to determine the spatial and temporal
distributions in shock and thermodynamic variables.
PfWMA
.Pressure
Kapton
sugar
Temperature
(a)
(b)
Figure 6. (a) Numerical configuration used for 3-D modeling a
granulated sugar mixture, (b) pressure and temperature variations.
The results for particle velocity distributions, or
probability distribution functions (PDFs), are
illustrated in Figure 7, which shows the distribution
in longitudinal, vz, and lateral , v xy , particle
velocities for a micron-thick layer at the mid-plane
of the sugar sample for times of 500 ns, 800 ns, and
1000 ns after impact. In the first frame, the wave has
not yet reached the mid plane. At 800 ns, the wave
has passed the mid-plane, inducing a distribution in
the longitudinal velocity, but the average velocity
has still not achieved the boundary condition value
(zero velocity). Even at 1000 ns, the longitudinal
velocity still has a considerable spread, which is
nearly Gaussian. Similarly, the lateral velocity
develops a distribution about zero, which is not
predicted for strictly one-dimensional motion of the
shock. Presumably, the lateral velocity averaged
over the complete volume of the sample for all times
would be exactly zero, since the initial loading is 1D. Note also that even late in time, lateral motions
on the mid-plane are appreciable.
More details of this calculation can be found in
Baer's paper29, but it is instructive to comment
briefly on the temperature distributions since they
are important in thermodynamic calculations. Baer
shows that the temperature PDF for this problem has
very interesting features, which includes four
distinct regions: (1) a precursor region, (2) a bulk
region, which represents bulk response, (3) a hot
spot region due to local jetting, and (4) a gradient
region, which will be important for regions of
32
A typical result30 obtained on sugar is shown in
Figure 8, which indicates that spatial irregularities in
particle velocity persist for long times behind shock,
in agreement with the numerical simulations by
Baer.
reactivity growth in energetic materials. Although
an exact correspondence cannot be made, it is
interesting to note that a small fraction of material in
his simulations is at high temperature, which is in
qualitative agreement with the thermal model of
Swegle and Grady20. It is also apparent that these
temperature variations will significantly influence
most thermodynamic or phase transition properties
in non-reactive materials.
(a)
800ns
1000ns
(b)
Figure 8. Experimental technique for Line VISAR
measurements, (a) experimental setup, (b) typical velocity result
obtained on sugar.
The particle velocity records from a Line VISAR
can be integrated to provide spatial displacements
versus time along a projected line on the target,
which for sugar shows a distinct periodicity to the
displacement that is finer than the grain scale.
Furthermore, these features appear to be nearly
independent of time, in agreement with the concept
of a scalar invariant of the motion proposed by Baer.
In addition, the experimental results are in semiquantitative agreement with predictions of the 3-D
granular calculations by Baer29. Baer is continuing
these studies in order to investigate the possibility of
scalar invariants that can be used in developing
generalized continuum models. This approach is
similar that used to predict distributed shear stresses
in aluminum15.
The observations from
numerical and
experimental measurements on granular materials
can be summarized as follows. The common feature
for "planar" shock propagation in either
polycrystalline metals or granular sugar is that shock
wave variables, such as pressure, particle velocity
and density, are not distinct values behind the shock,
but are distributed in 3-D space and time. Initial
studies indicate that these distributions are nearly
invariant in time but further work is needed to
clarify this. For planar loading of a granular or
polycrystalline material, numerical studies to date
indicate that large transverse components of velocity
are produced, giving rise to localized rotations that
V
L _ n
A ——23*——-
0.0 0.4
-0.2 0.0 0.2
Vz (km/s)
VX,Y (km/s)
Figure 7. Probability distribution functions of particle velocity
for shock propagation in sugar.
As mentioned, it is necessary to develop better
diagnostics for in-situ. real-time measurements of
deformation states. Although the velocity dispersion
technique described earlier provides information
about the magnitude of the distribution, it contains
no information about the spatial nature. A recent
extension of the VISAR has recently been
developed that provides information about both the
magnitude and the spatial distribution of velocity
dispersion. The technique has been referred to as a
Line Imaging Velocity interferometer and
alternatively as a Line ORVIS or a Line VISAR30'31.
The technique is applied by projecting a line of laser
light onto the target, in contrast to a regular VISAR
that uses a bulls-eye pattern of focused light
typically 100 f^m in diameter. During target motion,
fringes displace along the line in proportion to the
local corresponding particle velocity at that point
and are recorded by a streak camera30.
Measurements have been made with the technique
for line lengths ranging from a fraction of one
millimeter to about 20 mm. Typically, for a ~200um line, the spatial resolution is about 20 microns.
33
are reminiscent of turbulent effects that may
produce localized stress concentrations, including
grain fracture and thermal hot spots. The
temperature distributions persist for long periods of
time after the material has been shock compressed.
Similarly, pressure and density variations persist for
long times after the shock. Given these variations, it
is important to investigate the resulting effects on
other property measurements, such as equations of
state, that are routinely made to high precision. In
addition, these heterogeneous effects are likely
responsible for apparent anomalies, such as phase
transitions8, optical properties4'32'33, electrical
properties4, and energetic materials29.
SUMMARY AND FUTURE DIRECTIONS
We've discussed the effects of nonhomogeneous deformations of shock compression in
polycrystalline materials.
As implied by the
observed yield behavior of aluminum that may be
partially due to a distribution of shear states, the
computationally predicted distribution of states in
particle velocity, density and temperature, may
likely influence all physical phenomena traditionally
studied in shock physics. The effects of
heterogeneous
deformation
on
mechanical
properties have been emphasized in this paper,
although there are likely many other dynamic
properties that are also influenced. A few of these
are summarized in the following paragraphs.
In phase transition studies, there has been a longstanding issue about why some transitions proceed
extremely rapidly in dynamic experiments but are
sluggish in static experiments8. The iron transition is
a well-known example. When this was first
identified in shock wave experiments at LANL in
195434, Bridgman was skeptical about these results
and expressed concern whether traditional
deformation mechanisms could result in the fast
transition kinetics observed8. Recent MD atomic
level and particle mesoscopic-level calculations at
Los Alamos National Laboratory are shedding light
on the role of defects and non-homogeneous
motions in the transformation18'19. The principal
conclusion is that the transformation appears to
initiate within defect regions induced by the shock
and grow from these regions.
Another example includes porous materials that
are often used to determine off-Hugoniot properties,
34
especially the thermal component of the EOS.
However, recent 3-D computer simulations for
porous granular sugar by Baer29 illustrate that the
state behind the shock front is definitely not in
equilibrium over relatively long times. Furthermore,
the shock compression states are characterized by
distributions in thermodynamic properties that
persist for long periods of time. These effects raise
serious concerns as to whether meaningful
thermodynamic properties can be accurately
determined by shock loading of porous materials. A
systematic study of the actual distributed states
produced by shock compaction and the states
expected from thermodynamic properties should be
undertaken using 3-D simulations.
Numerous other examples can be cited, including
anomalous emissions observed in transparent
materials above their yield point, electrical
conductivities, chemical reactions and so on. In
addition to the usual problem of correcting for
strength effects, it is useful to keep in mind whether
non-homogeneous response will be a problem in
obtaining accurate thermodynamic data from shock
wave experiments.
Continuum measurements continue to be the
mainstay of shock physics work, but it is becoming
increasingly clear that present models are far from a
predictive capability. Combining continuum
property measurements with other mesoscopic scale
information, such as real-time PDF measurements of
the important variables would be powerful for
understanding the processes and replacing the
existing continuum models. Developing the right
experimental and computational tools to accomplish
this goal is probably one of the most challenging
problems that the shock community faces, but it is
absolutely essential that this problem be addressed
as soon as possible. Otherwise, we will continue to
use the inadequate models developed decades ago.
As modeling abilities improve, it will become
necessary to include microscale and perhaps atomic
scale effects into mesoscale models. Significant
progress has already been made in the initial steps of
this work27'28.
For the most part, shock wave experiments have
been limited to planar loading conditions. This type
of experiment does not really give much information
about the full anisotropic stress tensor, especially if
the gauges themselves are essentially onedimensional. If we are to extend the present model
12. D.E. Grady, J. Mech. Solids 10, 2017-2032, 1998.
13. J.N. Johnson and L.M. Barker, J. Appl. Phys. 40,
4321-4334, 1969.
14. J.W. Taylor, J. Appl. Phys. 36, 1965.
15. J. Lipkin and J. R. Asay, J. Appl. Phys., 48, 182
1977.
16. J. R. Asay and L.C. Chhabildas, Shock Waves and
High-Strain-Rate Phenomena in Metals: Concepts
and Applications, Marc A. Meyers and Lawrence E.
Murr, Plenum Publishing Corporation, NY, 1981.
17. G.R. Fowles, J. Appl. Phys., 32, 1475-1487, 1961.
18. B.L Holian and P.S. Lomdahl, Sci. 280, 2085, 1998.
19. K. Yano and Y. Horie, Phys. Rev. B, 59, 1999.
20. J.W. Swegle and D. E. Grady, Metallurgical
applications of shock-wave and high-strain-rate
phenomena, Eds. Lawrence E. Murr, Karl P.
Staudhammer and Marc A. Meyers, NY, 1986.
21. D. E. Grady and J. R. Asay, J. Appl. Phys. 53, 7350,
1982.
22. L.V. APtshuler, M.N. Pavlovskii, V.V. Komissarov,
and P.V. Makarov, Combustion, Explosion and
Shock Waves, 55, 92-96, 1999.
23. J. R. Asay and L. M. Barker, J. Appl. Phys., 45,
2540-2546,1974.
24. Yu. I. Meshcheryakov and A. K. Dikov, Sov. Phys.
Tech. Phys. 30,348-350, 1985.
25. M. A. Meyers and M. S. Carvalho, Materials Science
and Engineering, 24, 131-135, 1976.
26. Horie, private communication, 2001
27. P. V. Makarov, Physical Mesomechanics /, 57, 1998.
28. V. E. Panin, Yu. V. Grinyaev, T. F. Elsukova, and A.
G. Ivanehin, Izvestiya Vysshikh Uchebnykh
Zavedenii, Fizika, 6, 5-27, 1982.
29. M.R. Baer, this conference.
30. W. M. Trott, J. N. Castaneda, J. J. O'Hare, M. R.
Baer, L. C. Chhabildas, M. D. Knudson, J. P. Davis,
and J. R. Asay, Dispersive velocity measurements in
heterogeneous materials. SAND2000-3082, 2000.
31. K. Baumung et al, in Laser and Particle Beams.
Cambridge University Press, 14, 181-209, 1986.
32. P.J. Brannon, C. Konrad, R.W. Morris, E.D. Jones
and J. R. Asay, J. Appl. Phys. 54, 6374-6381, 1983.
33. David Hare, this conference
34. J.W. Taylor, Shock Waves in Condensed Matter 1983, ed. J. R. Asay et al., 1984.
35. Yu. Mescheryakov, S.A. Atroshenko, V. B. Vasilkov
and A. I. Chernyshenko, Shock Compression of
Condensed Matter, ed. S.C. Schmidt et al., 1991.
for solids to a more realistic description, we must
define experiments that exercise the lateral
components of stress. These might include planar
compression-shear or off-axis impact. I believe there
is much to learn by studying combined states of
loading, such as shock followed by unloading or
reloading, ramp loading, ramp followed by
shocking, etc. These additional complexities allow
a test of the assumed state produced by the initial
process and will be needed to develop fully
validated material models for use in the next
generation computer codes.
Several investigators have recently emphasized
that taking the next step in material modeling will
require detailed studies at the mesoscopic
level19'27'28'29'35. Personally, I believe this is the right
approach, that it is the most challenging problem in
shock physics today, and that it is also one of the
most exciting challenges for the shock physics
community. I believe the challenge of developing
the appropriate tools and using them to understand
the actual shock deformation mechanisms at
multiple levels will draw new talents to the field.
REFERENCES
1.
Y.M Gupta, Shock Compression of Condensed
Matter-1999, M.D. Furnish, L.C. Chhabildas, R. S.
Hixson (eds), 3-10, North Holland, 2000.
2. L. Davison and R.A. Graham, Physics Reports, 55,
1979.
3. G.W. Swan, G. E. Duvall and C.K. Thornhill,, J.
Mech. Phys. Solids, 21, 215-227, 1973.
4. R.A. Graham, Solids Under High-Pressure Shock
Compression: Mechanics, Physics, and Chemistry,
Springer-Verlag, New York, 1993.
5. D. C. Wallace, Phys. Rev. B, 22, 1495-1502, 1980.
6. J. J. Gilman, Fundamental Issues and Applications of
Shock-Wave and High-Strain-Rate Phenomena, K.P.
Staudhammer, L.E. Murr, and M.A. Meyers
(editors), Elsevier Sciences Ltd, 2001.
7. Y. Hone, private communication, 2001.
8. R.A. Graham,," High Pressure Science and
Technology, Part 1, Eds. S.C. Schmidt et al,
American Institute of Physics, 1993.
9. W. Herrmann and R J. Lawrence, J. Eng. Mat.
Tech., 7,84, 1978.
10. L.C. Chhabildas and G.A. Graham, Amer. Soc. of
Mech. Engineers, NY, AMD 18, 1-18, 1987.
11. L.M. Barker, in Behavior of Dense Media Under
High Dynamic Pressures. Gordon & Breach, N.Y,
483, 1968.
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