In heterogeneous media, the scattering due to interfaces between dissimilar materials play an important role in shock wave dissipation and dispersion. In this work the influence of interface scattering effect on shock waves was studied by impacting flyer plates onto periodically layered polycarbonate/6061 aluminum, polycarbonate/304 stainless steel and polycarbonate/glass composites. The experimental results (using VISAR and stress gauges) indicate that the rise time of the shock front decreases with increasing shock strength, and increases with increasing mechanical impedance mismatch between layers; the strain rate at the shock front increases by about the square of the shock stress. Experimental and numerical results also show that due to interface scattering effect the shock wave velocity in periodically layered composites decreases. In some cases the shock velocity of a layered heterogeneous composite can be lower than that of either of its components

Hodowany, Jon

Ravichandran, Guruswami

Rosakis, Ares J.

Rosakis, Phoebus

English

Heat generation in metals during high-strain-rate plastic deformation was investigated. Experiments were designed to measure the partition of plastic work into heat and stored energy during dynamic deformations under adiabatic conditions. A Kolsky pressure bar was used to determine mechanical properties at high strain rates while a servo-hydraulic material testing system was used at low strain rates. For dynamic loading, in-situ temperature changes were measured using a high-speed infrared detector. The dependence of the fraction of plastic work converted to heat on strain and strain rate was determined for an aluminum 2024-T3 alloy and alpha-titanium. The flow stress and the fraction of plastic work converted to heat for 2024-T3 aluminum alloy were found to be a function of strain but not of the strain rate while they were found to be strongly dependent on strain rate for alpha-titanium

Caltech Authors - Main

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
ON THE CONVERSION OF PLASTIC WORK INTO HEAT DURING
HIGH-STRAIN-RATE DEFORMATION
Guruswami Ravichandran1, Ares J. Rosakis1, Jon Hodowany2 and Phoebus Rosakis3
Graduate Aeronautical Laboratories, California Institute of Technology, Pasadena, CA 91125
2Rosetta Inpharmatics, Inc., Kirkland, WA 98034
Department of Theoretical and Applied Mechanics, Cornell University, Ithaca, NY 14853
Abstract. Heat generation in metals during high-strain-rate plastic deformation was investigated.
Experiments were designed to measure the partition of plastic work into heat and stored energy during
dynamic deformations under adiabatic conditions. A Kolsky pressure bar was used to determine
mechanical properties at high strain rates while a servo-hydraulic material testing system was used at
low strain rates. For dynamic loading, in-situ temperature changes were measured using a high-speed
infrared detector. The dependence of the fraction of plastic work converted to heat on strain and strain
rate was determined for an aluminum 2024-T3 alloy and a-titanium. The flow stress and the fraction
of plastic work converted to heat for 2024-T3 aluminum alloy were found to be a function of strain but
not of the strain rate while they were found to be strongly dependent on strain rate for a-titanium.
INTRODUCTION
When metals deform plastically, significant
amounts of heat can be generated, especially in
cases of highly localized deformation. If the
deformation process is rapid, heat generation can
lead to large temperature increases since there is no
time to conduct heat away from the deforming
metal, conditions become essentially adiabatic.
The temperature increase can cause thermal
softening in the metal and alter its mechanical
performance. Even at moderate strain rates, plastic
deformation can often be treated as essentially
adiabatic. Understanding the coupling between
plastic deformation and heat evolution is
fundamental to predicting temperature fields, and
associated thermal softening, in processes
involving high-strain-rate deformation. Examples
of applications where accurate models for heat
generation are necessary include high-speed
machining, ballistic penetration, shear banding,
dynamic void collapse and growth, and dynamic
fracture.[I"5]
Part of the mechanical energy expended during a
plastic deformation process in metals is converted
into heat, while the remainder stored in the material
microstructure. The stored energy is an essential
feature of the cold-worked state, and represents the
change in internal energy of the metal. In addition
the stored energy of cold work remains in the
material after removal of external loads. It is
generally accepted that most of the mechanical
energy is dissipated as heat during plastic
deformation. The fraction of the rate of plastic
work dissipated as heat ft is often assumed to be a
constant parameter of 0.9, for most metals.
Measurements of the ratio of stored energy to
dissipated energy have varied considerably, even
for nominally similar materials. Here we present an
experimental methodology for measuring /3 at
different plastic strains and strain rates. The
experimental results clearly show that P could
indeed be a function of these variables. The
theoretical thermodynamical foundations leading to
the observed plastic strain and strain rate
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dependence of J3 have been discussed by Rosakis et
a/>]
For elasto-plastic solids, a number of assumptions
are often made, including infinitesimal
deformations, the additive decomposition of strain
into elastic and plastic parts, a relation between
stress and elastic strain identical to that of isotropic
linear thermoelasticity, and linear Fourier heat
conduction law. These reduce the first law, or
energy balance equation, to the following
customary form under conditions of uniaxial stress,
(1)
Here 9 is absolute temperature, <j ze and &p are
the components of stress, elastic strain and plastic
strain, respectively, viewed as functions of
coordinate x and time t; subscripts indicate partial
derivatives with respect to the corresponding
variable and superposed dots denote time
derivatives. The material constants p, c, k, a, E, v
are mass density, specific heat, thermal
conductivity, thermal expansion coefficient,
Young's modulus and Poisson's ratio, respectively.
It is assumed that some of the irreversible plastic
work contributes to heat generation, while the rest
is stored as energy of crystal defects accompanying
plastic deformation, traditionally known as the
stored energy of cold work. Hence J3 in (1) is the
fraction of plastic work rate Wp — O"£p converted
into thermoplastic heating Qp = pcc^,
i.e., P = Qp jWp . Unfortunately, there seems to be
no consensus on quantitative aspects of the stored
energy of cold work. If adiabatic conditions prevail
and the thermoelastic heating Qe = -aEQze is
negligible compared to the thermoplastic heating,
(1) simplifies to pcG = Pae^ , allowing one to write
P= pc9 (2)
As a result, under adiabatic conditions, fi can be
measured from experimental records of the
temperature, stress and plastic strain versus time.
G. I. Taylor first published a series of papers on
the latent energy remaining in metals after cold
working.[7'8] Without knowledge of microstructural
mechanisms for energy storage and strain
hardening, Taylor concluded that "the fact that the
absorption of latent energy and the increase in
strength with increasing strain both cease when the
same amount of cold work has been applied
suggests that the strength of pure metals may
depend only on the amount of cold work which is
latent in them." The review article by Bever et a/.[9]
gives a comprehensive overview of various
attempts to measure the stored energy of cold work.
It also covers basic thermodynamic aspects of
plasticity and microstructural characteristics of the
cold-worked state. Mason et fl/.[IO] made the first
systematic attempt to measure the strain
dependence of the partition of plastic work during
dynamic deformations.
EXPERIMENTAL
The techniques for measuring the stored energy
of cold work can be separated into two broad
categories: (a) In-situ methods, where
measurements are made during deformation, and
(b) post-mortem methods, where the stored energy
is measured after deformation. Detailed description
of these methods can be found in the article by
Bever et al.[9]
Typically, the amount of energy given off as heat
is measured independently of the total amount of
external work. The total external work is generally
calculated from load-displacement data. Thus, the
loading device must have the means to record all
relevant forces and displacements acting on the
specimen.
The Kolsky (split-Hopkinson) pressure bar[ll'12] is
by now a well-established apparatus for the high-
strain-rate testing of metals and is shown in Fig. 1.
Many references regarding this classic technique
exist,*-12^ thus only a cursory review of the governing
equations are given here. The apparatus consists of
a striker bar, an input bar, and an output bar, all of
which are assumed to remain elastic during a test. A
specimen of length / is placed between the input
and output bars. For a sample assumed to undergo
homogeneous deformation, Kolsky[I1] showed
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Striker Bar Input Bar Output Bar
Strain Gage
Specimen
Infrared
Detector
Figure 1. Schematic of Kolsky (split Hopkinson) pressure bar with high-speed infrared thermography.
that the nominal strain rate, e (t), is given by
(3)
where £ji(t) is the time-resolved strain of the
reflected signal in the input bar and c0 is the one-
dimensional bar wave speed. The strain in the
sample can be calculated from (3) by integration.
The nominal stress, a(t), is calculated from the
load in the output bar divided by the original
sample area
(4)
where A is the undeformed area of the specimen, E
is the Young's modulus of the bar material and
ST^) is the time-resolved strain in the output bar
of cross-sectional area A0. The input and output
bars are assumed to be composed of the same
material, and of identical and uniform cross-
sectional area.
There exist several types of transducers available
for the measurement of temperature, each having
relative advantages and disadvantages. Photon
detectors measure temperature remotely, have high-
speed response, and thus are particularly suitable
for short time events. A single, photoconductive
HgCdTe detector, with maximal responsivity of 8-
12 jLim, was used for measuring temperature at high
strain rates. This wavelength range was chosen to
match the peak spectral power distribution of a
body between 300-400 K, the range of temperatures
expected during high-strain-rate deformation in a
Kolsky pressure bar. The detector-amplifier
combination used in the present study had a
bandwidth of 5 Hz to 2MHz. DC signals were
blocked by an AC-coupling capacitor located in the
preamplifier circuit, thus only dynamic temperature
changes could be resolved by the infrared detector.
Most IR optical systems are a variation of one of
the basic catoptric telescope designs. The
Newtonian system, consisting of a concave and a
flat mirror, allows for easy adjustment of
magnification, and formed the basis of the optical
system used in the present study, see Fig. 1.
Perhaps the most important experimental issue
was the calibration of the infrared detectors. For all
tests included here, an experimental approach to
calibration was adopted. The calibration specimen
heated in a furnace to raise its temperature above
the expected maximum temperature of an actual
test, and placed in a holding fixture. As the
specimen cooled, detector output and temperature
were recorded.
To obtain large plastic strains in compression, a
technique of reloading samples was used. The
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reflection of input stress waves from the free end of
the input bar can cause repeated loading of the
sample. To avoid repeated loading during one test,
a short output bar was used.[13] In this configuration,
the tensile stress wave that results from reflection
from the free end of the output bar will cause the
output bar to pull away from the sample, ending the
test before a second loading. For a given sample,
the dimensions before and after testing were
recorded. The sample was then remachined,
resulting in a virgin surface finish. The remachined
sample was then tested with a known initial value
of plastic strain. This process was repeated until the
desired value of plastic strain was attained.
RESULTS
Aluminum 2024-T3 Alloy
The engineering compressive stress versus strain
curves for the aluminum 2024-T3 alloy are shown
in Fig. 2 for two strain rates, 10~3 s"1 and 3000 s"1.
In this range of strain rates, the material behavior is
found to be rate insensitive. The fraction J3 of
plastic work rate converted to heating computed
1.0
0.8
Figure 3. Fraction of plastic work rate converted to
heating P vs. engineering plastic strain at two
different strain rates (1 s"1 and 3000 s"1) for 2024-T3
aluminum alloy.
— 3000s
-- iCrV
-1
Figure 2. Engineering stress versus engineering
strain curves at two different strain rates (10~3 s"1
and 3000 s"1) for 2024 -T3 aluminum alloy.
using (2) is shown in Fig. 3 for two strain rates, 1 s"1
and 3000 s"1. These curves represent the functional
dependence of J3 on engineering plastic strain after
yield for values of the later less than 15%. The two
curves at 3000 s"1 represent two separate tests at
that strain rate, and illustrates a measure of
repeatability of the experimental method. There
was no observed dependence of ft on strain rate.
For plastic strains between 0.05 and 0.15, only 30-
35% of plastic work was dissipated as heat.
To determine the relative partition of plastic work
at higher levels of strain in compression, the
reloading technique, described earlier, was
employed. The calculated fi for the large strain
compression tests is shown in Fig. 4. From 0 to
0.15 plastic strain, the dependence of /? on strain
resembled that in the tests of Fig. 3. Above 0.15
plastic strain, the ability to store energy decreases
and p rapidly increases towards 1. Above 0.4
plastic strain, nearly all input work was dissipated
as heat.
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1.0
Q8
Q6
Q4
02
00
00 01 0.2 03 04 05 06
Figure 4. Fraction of plastic work rate converted to
heating p vs. engineering plastic strain from
successive loading sequences at and 3000 s"1 for
aluminum 2024-T3 alloy.
a-Titanium
The true compressive stress versus true strain
curves for the a-titanium are shown in Fig. 5 for
two strain rates, 1 s"1 and 3000 s"1. This figure
shows that the flow stress for a-titanium is clearly
dependent on the strain rate during loading. Large
strain deformations were attained on the
compression Kolsky bar by a recovery and
reloading technique similar to that used for the
aluminum. For a-titanium and other rate-sensitive
metals, extreme care must be exercised to match
strain rates between loading sequences.[13]
The partition of plastic work into heat and stored
energy was observed to be dependent on both strain
and strain rate in a-titanium. Figure 6 shows the
fraction of plastic work rate converted into heating
P plotted against engineering plastic strain during
uniaxial compressive deformation. The curves
shown here represent the value of J3 at low levels of
Figure 5. Engineering stress versus engineering
strain curves at two different strain rates for a-
titanium.
Q4
Q2
QO
1s'
QO Ql Q2
. p
Q3 Q4
Figure 6. Fraction of plastic work rate converted to
heating P vs. engineering plastic strain at two
different strain rates for a-titanium.
561
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plastic strain. At a strain rate of 1 s"1, titanium
stored a relatively large amount of energy, -35%,
just after yield. As strain increased, the ability to
store energy was reduced. At higher strain rates, a
smaller fraction of energy was stored at all strain
levels in this range. The large strain data showed
that the material cannot store energy indefinitely,
and at some critical level of plastic strain nearly all
of the energy was dissipated as heat, causing /? to
approach unity.[13]
Several features emerge concerning the relative
amount of energy dissipation in a-titanium. It is
clear that fi in titanium is a function of strain and
strain rate. Near the yield point, during the stage of
rapid dislocation multiplication, 0 was observed to
be a rapidly decreasing function of strain at both
strain rates. The relative ability of titanium to store
cold work increased with decreasing strain rate.
The theoretical basis for the dependence of J3 on
strain rate can be found in Rosakis et 0/.[6] where
the experimental results are compared with the
results of a thermodynamic theoretical model.
CONCLUSIONS
Several conclusions can be drawn regarding the
conversion of plastic work into heat, as well as the
experimental techniques[13] employed in the
investigation:
• The adiabatic, homogenous deformation in the
Kolsky (split Hopkinson) bar allowed a simple
calculation of the fraction of plastic work
converted into heat. The ratio of plastic work
rate converted into heating ft was treated as a
variable quantity and its dependence on both
strain and strain rate was investigated.
• The aluminum 2024-T3 alloy did not exhibit
strain rate dependence in flow stress over the
entire range of strain rates tested. At low levels
of plastic strain, 2024-T3 aluminum stored
more than 60% of the input plastic work. At
some level of plastic strain, it could no longer
store plastic work. After this point, ft increased
to a value near 1.0 and remained nearly
constant during subsequent plastic deformation.
The fraction of plastic work dissipated as heat
was not found to be sensitive to strain rate.
In contrast to aluminum, the flow stress of a-
titanium was strongly dependent on strain rate.
The initial flow stress increased by more than
15% between strain rates of 10"3 and 3000 s"1.
Titanium dissipated a greater proportion of
energy as heat at low strains than aluminum
2024-T3 alloy. The ability to store energy in
titanium decreased with increasing plastic
strain. The proportion of energy dissipated as
heat at fixed strain increased with strain rate.
For plastic strains above 0.3, titanium
dissipated nearly all input plastic work as heat.
ACKNOWLEDGEMENTS
The research reported here was supported by the
Office of Naval Research and the National Science
Foundation and is gratefully acknowledged.
REFERENCES
1. Clifton, R. J., Duffy, J., Hartley, K. A., and Shawki,
T. G., Scr. Met. 18,443-448 (1985).
2. Oilman, J. J., Mech. Mat. 17, 83-96 (1994).
3. Zehnder, A. T., and Rosakis, A. J., J. Mech. Phys.
Solids 39, 385-415 (1991).
4. Zhou, M., Ravichandran, G., and Rosakis, A. J., J.
Mech. Phys. Solids 44, 1007-1032 (1996).
5. Camacho, G. T., and Ortiz, M., J. Comp. Meth. Appl.
Mech. Eng. 142, 269-301 (1997).
6. Rosakis, P., Rosakis, A. J., Ravichandran, G., and
Hodowany, J., J. Mech. Phys. Solids 48, 581-607
(2000).
7. Farren, W. S., and Taylor, G. I., Proc. Roy. Soc.
Ion don A107, 422-451 (1925).
8. Taylor, G. I., and Quinney, H., Proc. Roy. Soc.
London A163, 157-181 (1937).
9. Sever, M. B., Holt, D. L., and Titchener, A. L.,
Prog. Mat. Sci. 17, 1-190 (1973).
10. Mason, J. J., Rosakis, A. J., and Ravichandran, G.,
Mech. of Materials 17, 135-145 (1993).
11. Kolsky, H., Proc. Roy. Soc. London B62, 676-700
(1949).
12. Gray, G. T., "Classic Split-Hopkinson Pressure Bar
Testing," in ASM Handbook, Vol. 8, ASM
International, Metals Park, OH, 2000, pp. 462-476.
13. Hodowany, J., Ravichandran, G., Rosakis, A. J., and
Rosakis, P., Exp. Mech. 40, 113-123 (2000).
562
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On the Conversion of Plastic Work into Heat During High-Strain-Rate Deformation

Zhuang, Shiming

Grady, Dennis E.

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
INFLUENCE OF INTERFACE SCATTERING ON SHOCK
WAVES IN HETEROGENEOUS SOLIDS
Shiming Zhuang1, Guruswami Ravichandran1, and Dennis E. Grady2
Graduate Aeronautical Laboratories, California Institute of Technology Pasadena, CA, USA
2Applied Research Associates, Inc., Albuquerque, NM,USA
Abstract. In heterogeneous media, the scattering due to interfaces between dissimilar materials play
an important role in shock wave dissipation and dispersion. In this work the influence of interface
scattering effect on shock waves was studied by impacting flyer plates onto periodically layered
polycarbonate/6061 aluminum, polycarbonate/304 stainless steel and polycarbonate/glass composites.
The experimental results (using VIS AR and stress gauges) indicate that the rise time of the shock front
decreases with increasing shock strength, and increases with increasing mechanical impedance
mismatch between layers; the strain rate at the shock front increases by about the square of the shock
stress. Experimental and numerical results also show that due to interface scattering effect the shock
wave velocity in periodically layered composites decreases. In some cases the shock velocity of a
layered heterogeneous composite can be lower than that of either of its components.
INTRODUCTION
With high-performance heterogeneous materials
such as fiber reinforced, woven composites and
functionally graded materials finding increasing
use in systems and structures designed to function
in the severe shock environments, the assessment
and evaluation of the response of those systems to
complex loading conditions is essential. To do so,
advanced computational methods relying on
accurate physics-based material constitutive
models are required, although such models cannot
be correctly formulated without fully
understanding the physical mechanisms of
dissipation and dispersion of shock waves
propagating in heterogeneous solids. Small-scale
heterogeneity, e.g., grain boundaries in
polycrystalline metals, fiber or particle
reinforcement in polymer and metallic composites,
could lead to scattering of waves[1^ which could
affect the rise time of a shock wave. The relative
importance of scattering increases with the severity
of the heterogeneity. Therefore, in order to obtain
an accurate physically based constitutive relation to
properly describe the dynamic response of
heterogeneous materials and assess the
performance of the composite material structures
and systems in the shock related environments, it is
critical to evaluate the role played by scattering
induced by the heterogeneous microstructure as a
shock wave propagates in the composite materials.
EXPERIMENTS
The structure of a periodically layered composite
specimen^21 is shown in Fig. 1. It consists of two
components in the form of thin disks that are
alternatively stacked and bonded together using
Hysol 0151 epoxy adhesive manufactured by
Dexter Corporation. Hereafter, the component
with larger mechanical impedance is called "hard"
layer, while the other with lower mechanical
impedance is called "soft" layer. The layered
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composite specimen is prepared by repeating the
soft and hard layers alternatively as many times as
necessary to form a specimen with the desired
thickness.
6 7
Figure 1. Schematic of shock compression
experiment and specimen configuration.
1-manganin stress gauges; 2-charged electric pins;
3-mirror surface; 4-PMMA window; 5-flyer;
6-soft layer; 7-hard layer; Vrflyer velocity.
The diameter of the disks is 38.1 mm. The soft
layer material is a commercial polycarbonate (PC)
supplied by McMaster-Carr. Two thicknesses of
sheets, 0.74 mm and 0.37 mm, are used, which are
denoted as PC74 and PC37, respectively. The hard
layer material is one of the following: 0.37 mm
thick 6061-T6 aluminum sheet (A137), 0.37 mm or
0.19 mm thick 304 stainless steel sheets (SS37 or
SS19), which are products of Allegheny Ludlum
Co., 0.55 mm thick float glass (GS55), or 0.20 mm
thick GS D-263 glass (GS20) disks from Erie
Scientific Co. Three types of composites with five
geometric configuration specimens, PC74/A137,
PC74/SS37, PC37/SS19, PC74/GS55 and
PC37/GS20, are prepared and tested under planar
impact loading. The window is a polymethyl
methacrylate (PMMA) plate of thickness 12.7 mm.
One of the window surfaces was aluminized to a
mirror surface by sputtering aluminum in a vacuum
chamber. A 0.74 mm PC buffer layer was used at
the end of composite layers before the window
layer is bonded. The mirror surface of the window
contacts the buffer layer forming an internal
mirror. The surfaces of all disks are well cleaned
to achieve good bonding between interfaces. In
order to uniformly spread the epoxy and reduce the
thickness of the glue layer, a weight was placed on
the assembled specimen to produce a stress of 50
MPa. The average thickness of the epoxy layer
bond is about 20 [im. For the PC/Glass
composites, the bonding layer can be as thin as 10
(im. The thickness of specimens is one of the
following: 3.8 mm, 7.0 mm and 10.0 mm.
The flyers are 2.87 mm or 5.63 mm thick PC
disks of 36 mm diameter, or 5.6 mm thick Al disks
of 36 mm diameter in case higher shock pressures
are desired. The flyers were accelerated to a
desired velocity through a powder gun loading
system located in the experimental Solid
Mechanics facilities, Graduate Aeronautical
Laboratories at Caltech (GALCIT). The bore of
the gun is 36 mm, and the flyer velocity achieved
by this gun ranges from 400 m/s to about 2,000
m/s. The flyer velocity is measured within 1%
uncertainty by using a light interruption fiber optic
system.
The particle velocity history on the interface
between the window and the buffer layer was
measured using a velocity interferometer, the so
called VISAR system^. In order to capture the
fine details of resonant oscillations of shock
velocity profile resulting from the interactions
between the incident shock wave and its multiple
reflection waves from internal interfaces inside
layered composites, a VISAR system with very
high velocity resolution was constructed. The
velocity fringe constant of this VISAR system is
adjustable from 85 m/s/fringe to 1,500 m/s/fringe.
Manganin gauges are also embedded between
layers of some specimens to measure the stress
history at selected internal points. Manganin
gauges (50 ohms) produced by Dynasen Inc. and
Micro Measurements Group were used in this
study.
NUMERICAL SIMULATION
The finite element code, DYNA2D, was used to
carry out axisymmetric two dimensional analysis
of the shock compression of periodically layered
composites loaded by planar impact (Fig. 1). The
size of elements in the direction of wave
propagation is about 130 urn and the aspect ratio of
the elements was chosen to be as close to 1 as
possible. The interface between layers was treated
as a frictionless slide line. The increase in
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thickness of the specimen due to the adhesive
bonding between layers is treated as an increase in
the thickness of the PC layer since the physical and
mechanical properties of the epoxy adhesive are
very close to those of the PC. The standard
DYNA2D artificial viscosity is used for all
materials. During simulations, only glasses are
treated as elastic material for the stress range of
interest in this study[4l For all other homogeneous
PC, Al and SS components, PC or Al flyers, and
PMMA window, Gruneisen equation-of-state and
isotropic elastic plastic hydrodynamic constitutive
relations were employed to model the response of
individual materials.
RESULTS AND DISCUSSION
Experimental results indicate that periodically
layered composites support steady structured shock
waves[2l With the increase of shock loading
strength (pressure), the slope of the shock front
increases. At the same time, the amplitude of
oscillations in the wave profile also increases (Fig.
2). The larger the impedance mismatch between
the components, the smaller the slope of the shock
front, indicating larger dispersion (Fig. 3). When
the interface density increases, the rise time of the
shock front becomes shorter, indicating an increase
in the nonlinearity property of the composite.
Note, in the legend of Figs. 2 and 3, h and w are
specimen and flyer thickness, respectively, Vf is
flyer velocity and x is the distance from the impact
face.
The experimental Hugoniots of PC/GS and
PC/SS composites are compared with the
predictions of Meyers^ and Dremin's^ mixture
models, as well as 2-D numerical simulation
results, in Figs. 4 and 5, respectively. It is seen that
the shock velocity of a composite can be lower
than that of either of its components. The
calculated relations between the strain rate of the
shock front and the shock stress for periodically
layered composites are shown in Fig. 6. It is noted
that for layered composites, the strain rate at the
shock front increases by about the square of the
shock stress, while in homogeneous media such as
metals, the strain rate of the shock front increases
by the fourth power of the shock stress[7],
indicating much larger shock viscosity in the
composites due to the scattering effect of interfaces
on the shock wave.
is
CO
, Al flyer h =10.50 mm
x=3.55mm,
w =5.59 mm
Vf=K)79m/s,
h =10.62 mm
x=3.41mm,
w =2.87 mm
'Vf=567m/s,
h =10.4 3mm
x=3.41mm,
w=2.87mm
2 3 4 5 6
Time (jis)
Figure 2. Influence of loading strength on
measured shock stress profiles for PC74/GS55
composite.
0.6
Q.4
•B0.2
0.0
PC74/AI37
Vf=D60m/s
h =6.59 mm
w=2.87mm
PC74/SS37
Vf=D56m/s
h =6.46 mm
w =2.87 mi
5
Time
Figure 3. Influence of interface mechanical
impedance mismatch of composites on measured
shock particle velocity profiles.
I3
0 2
03
'm » » -Glass imm"- m """Polycarbonate
"•^•Dremin's model —————Meyers'model
• PC37/GS20,exper. O PC37/GS20,numer.
A PC74/GS55,exper. O PC74/GS55,numer.
0.0 0.2 0.4 0.6 0.8
Particle velocity (km/s)
1.0
Figure 4. Comparison of PC/GS composite
Hugoniots between experiments and predictions of
mixture models and 2-D numerical simulations,
and their homogeneous components.
711
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Numerical analysis reveals that due to the
interaction of multiple reflection of waves within
the layers and the incident shock wave, i.e., the
scattering of the shock wave due to interface, the
pressure and particle velocity in the layered
composites are not uniformly distributed during the
shock compression, even if the steady shocked
state is achieved. The pressure in the hard layer is
lower, while the particle velocity is higher, in
comparison to their corresponding values in the
adjacent soft layer. The difference of pressures and
particle velocities between the hard and soft layers
and the amplitude of the resonant oscillations on
the shock profiles, as well as the oscillation
duration, are influenced by both the mismatch of
their mechanical impedance and the geometric
structure of the composite. Furthermore, the
phases of velocity and pressure profiles of steady
- - - -304steel ^— - -Polycarbonate
^m^^"«•Dremin's model —————Meyers' model
O PC37/SS I9,numer. • PC37/SS 19,exper.
<> t PC74/SS3t7,i]umer.i t 4 _ PC74/S£37,exper.
0.0 0.2 0.4 0.6
Particle velocity (km/s)
0.8 1.0
Figure 5. Comparison of PC/GS composite
Hugoniots between experiments and predictions of
mixture models and 2-D numerical simulations,
and their homogeneous components.
10
a PC74/SS37
0 PC74/GS55
4 PC37/SSI9
• PC74/AI37
* PC37/GS20
1 .E+05 1 .E+06 1 .E+07
Strain rate (1/s)
1 .E+08
Figure 6. Shock stress vs. strain rate for the
layered composite.
wave are not synchronous as they are in the
homogeneous media[2l
The influence of internal interfaces on shock
wave propagation is through the scattering
mechanism, i.e., multiple reflection of waves in the
layers and their interaction with the shock wave.
Due to interface scattering both the shock wave
velocity (Figs. 4 and 5) and the shock front strain
rate (Fig. 6) of the composites decrease. The
decrease of shock front strain rate indicates a
increase in the effective shock viscosity of the
composites. Since ignoring the interface scattering
effect the existing mixture models can only, at best,
reasonably predict the response of the composites
under strong shock loading conditions. In order to
fully describe the response of a heterogeneous
composite to shock compression loading, accurate
physics-based constitutive relations need to be
formulated taking into account the scattering effect
induced by the heterogeneous microstructure.
ACKNOWLEDGMENTS
The research reported here was supported by the
Solid Mechanics program at the Army Research
Office (Dr. M. A. Zikry, Program Manager) and is
gratefully acknowledged.
REFERENCE
1. Grady, D.E., Ravichandran, G., and Zhuang,
S., in Proceedings of the AIRPAT Conference,
Honolulu, Hawaii, edited by Manghani, M.,
Oxford University Press (1999).
2. Zhuang, S., Shock wave propagation in
periodically layered composites, Ph.D. Thesis,
California Institute of Technology (2002).
3. Barker, L.M. and Hollenbach, R.E., J. Appl
Phys. 43,4699 (1972).
4. Wackerle, J., J Appl. Phys. 33, 922 (1962).
5. Meyers, M.A. Dynamic behavior of materials,
John Wiley & Sons, Inc., New York (1994).
6. Dremin, A.N. and Karpukhin, I.A., Zh. Prikl
Mekhan. i Teck. Fiz. 1, No.3 (1960).
7. Swegle, J.W. and Grady, D.E., J.Appl. Phys.
58, 692 (1985).
712
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Influence of Interface Scattering on Shock Waves in Heterogeneous Solids

Guruswami Ravichandran

Crossref

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
INFLUENCE OF INTERFACE SCATTERING ON SHOCK
WAVES IN HETEROGENEOUS SOLIDS
Shiming Zhuang1, Guruswami Ravichandran1, and Dennis E. Grady2
Graduate Aeronautical Laboratories, California Institute of Technology Pasadena, CA, USA
2Applied Research Associates, Inc., Albuquerque, NM,USA
Abstract. In heterogeneous media, the scattering due to interfaces between dissimilar materials play
an important role in shock wave dissipation and dispersion. In this work the influence of interface
scattering effect on shock waves was studied by impacting flyer plates onto periodically layered
polycarbonate/6061 aluminum, polycarbonate/304 stainless steel and polycarbonate/glass composites.
The experimental results (using VIS AR and stress gauges) indicate that the rise time of the shock front
decreases with increasing shock strength, and increases with increasing mechanical impedance
mismatch between layers; the strain rate at the shock front increases by about the square of the shock
stress. Experimental and numerical results also show that due to interface scattering effect the shock
wave velocity in periodically layered composites decreases. In some cases the shock velocity of a
layered heterogeneous composite can be lower than that of either of its components.
INTRODUCTION
With high-performance heterogeneous materials
such as fiber reinforced, woven composites and
functionally graded materials finding increasing
use in systems and structures designed to function
in the severe shock environments, the assessment
and evaluation of the response of those systems to
complex loading conditions is essential. To do so,
advanced computational methods relying on
accurate physics-based material constitutive
models are required, although such models cannot
be correctly formulated without fully
understanding the physical mechanisms of
dissipation and dispersion of shock waves
propagating in heterogeneous solids. Small-scale
heterogeneity, e.g., grain boundaries in
polycrystalline metals, fiber or particle
reinforcement in polymer and metallic composites,
could lead to scattering of waves[1^ which could
affect the rise time of a shock wave. The relative
importance of scattering increases with the severity
of the heterogeneity. Therefore, in order to obtain
an accurate physically based constitutive relation to
properly describe the dynamic response of
heterogeneous materials and assess the
performance of the composite material structures
and systems in the shock related environments, it is
critical to evaluate the role played by scattering
induced by the heterogeneous microstructure as a
shock wave propagates in the composite materials.
EXPERIMENTS
The structure of a periodically layered composite
specimen^21 is shown in Fig. 1. It consists of two
components in the form of thin disks that are
alternatively stacked and bonded together using
Hysol 0151 epoxy adhesive manufactured by
Dexter Corporation. Hereafter, the component
with larger mechanical impedance is called "hard"
layer, while the other with lower mechanical
impedance is called "soft" layer. The layered
709
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composite specimen is prepared by repeating the
soft and hard layers alternatively as many times as
necessary to form a specimen with the desired
thickness.
6 7
Figure 1. Schematic of shock compression
experiment and specimen configuration.
1-manganin stress gauges; 2-charged electric pins;
3-mirror surface; 4-PMMA window; 5-flyer;
6-soft layer; 7-hard layer; Vrflyer velocity.
The diameter of the disks is 38.1 mm. The soft
layer material is a commercial polycarbonate (PC)
supplied by McMaster-Carr. Two thicknesses of
sheets, 0.74 mm and 0.37 mm, are used, which are
denoted as PC74 and PC37, respectively. The hard
layer material is one of the following: 0.37 mm
thick 6061-T6 aluminum sheet (A137), 0.37 mm or
0.19 mm thick 304 stainless steel sheets (SS37 or
SS19), which are products of Allegheny Ludlum
Co., 0.55 mm thick float glass (GS55), or 0.20 mm
thick GS D-263 glass (GS20) disks from Erie
Scientific Co. Three types of composites with five
geometric configuration specimens, PC74/A137,
PC74/SS37, PC37/SS19, PC74/GS55 and
PC37/GS20, are prepared and tested under planar
impact loading. The window is a polymethyl
methacrylate (PMMA) plate of thickness 12.7 mm.
One of the window surfaces was aluminized to a
mirror surface by sputtering aluminum in a vacuum
chamber. A 0.74 mm PC buffer layer was used at
the end of composite layers before the window
layer is bonded. The mirror surface of the window
contacts the buffer layer forming an internal
mirror. The surfaces of all disks are well cleaned
to achieve good bonding between interfaces. In
order to uniformly spread the epoxy and reduce the
thickness of the glue layer, a weight was placed on
the assembled specimen to produce a stress of 50
MPa. The average thickness of the epoxy layer
bond is about 20 [im. For the PC/Glass
composites, the bonding layer can be as thin as 10
(im. The thickness of specimens is one of the
following: 3.8 mm, 7.0 mm and 10.0 mm.
The flyers are 2.87 mm or 5.63 mm thick PC
disks of 36 mm diameter, or 5.6 mm thick Al disks
of 36 mm diameter in case higher shock pressures
are desired. The flyers were accelerated to a
desired velocity through a powder gun loading
system located in the experimental Solid
Mechanics facilities, Graduate Aeronautical
Laboratories at Caltech (GALCIT). The bore of
the gun is 36 mm, and the flyer velocity achieved
by this gun ranges from 400 m/s to about 2,000
m/s. The flyer velocity is measured within 1%
uncertainty by using a light interruption fiber optic
system.
The particle velocity history on the interface
between the window and the buffer layer was
measured using a velocity interferometer, the so
called VISAR system^. In order to capture the
fine details of resonant oscillations of shock
velocity profile resulting from the interactions
between the incident shock wave and its multiple
reflection waves from internal interfaces inside
layered composites, a VISAR system with very
high velocity resolution was constructed. The
velocity fringe constant of this VISAR system is
adjustable from 85 m/s/fringe to 1,500 m/s/fringe.
Manganin gauges are also embedded between
layers of some specimens to measure the stress
history at selected internal points. Manganin
gauges (50 ohms) produced by Dynasen Inc. and
Micro Measurements Group were used in this
study.
NUMERICAL SIMULATION
The finite element code, DYNA2D, was used to
carry out axisymmetric two dimensional analysis
of the shock compression of periodically layered
composites loaded by planar impact (Fig. 1). The
size of elements in the direction of wave
propagation is about 130 urn and the aspect ratio of
the elements was chosen to be as close to 1 as
possible. The interface between layers was treated
as a frictionless slide line. The increase in
710
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thickness of the specimen due to the adhesive
bonding between layers is treated as an increase in
the thickness of the PC layer since the physical and
mechanical properties of the epoxy adhesive are
very close to those of the PC. The standard
DYNA2D artificial viscosity is used for all
materials. During simulations, only glasses are
treated as elastic material for the stress range of
interest in this study[4l For all other homogeneous
PC, Al and SS components, PC or Al flyers, and
PMMA window, Gruneisen equation-of-state and
isotropic elastic plastic hydrodynamic constitutive
relations were employed to model the response of
individual materials.
RESULTS AND DISCUSSION
Experimental results indicate that periodically
layered composites support steady structured shock
waves[2l With the increase of shock loading
strength (pressure), the slope of the shock front
increases. At the same time, the amplitude of
oscillations in the wave profile also increases (Fig.
2). The larger the impedance mismatch between
the components, the smaller the slope of the shock
front, indicating larger dispersion (Fig. 3). When
the interface density increases, the rise time of the
shock front becomes shorter, indicating an increase
in the nonlinearity property of the composite.
Note, in the legend of Figs. 2 and 3, h and w are
specimen and flyer thickness, respectively, Vf is
flyer velocity and x is the distance from the impact
face.
The experimental Hugoniots of PC/GS and
PC/SS composites are compared with the
predictions of Meyers^ and Dremin's^ mixture
models, as well as 2-D numerical simulation
results, in Figs. 4 and 5, respectively. It is seen that
the shock velocity of a composite can be lower
than that of either of its components. The
calculated relations between the strain rate of the
shock front and the shock stress for periodically
layered composites are shown in Fig. 6. It is noted
that for layered composites, the strain rate at the
shock front increases by about the square of the
shock stress, while in homogeneous media such as
metals, the strain rate of the shock front increases
by the fourth power of the shock stress[7],
indicating much larger shock viscosity in the
composites due to the scattering effect of interfaces
on the shock wave.
is
CO
, Al flyer h =10.50 mm
x=3.55mm,
w =5.59 mm
Vf=K)79m/s,
h =10.62 mm
x=3.41mm,
w =2.87 mm
'Vf=567m/s,
h =10.4 3mm
x=3.41mm,
w=2.87mm
2 3 4 5 6
Time (jis)
Figure 2. Influence of loading strength on
measured shock stress profiles for PC74/GS55
composite.
0.6
Q.4
•B0.2
0.0
PC74/AI37
Vf=D60m/s
h =6.59 mm
w=2.87mm
PC74/SS37
Vf=D56m/s
h =6.46 mm
w =2.87 mi
5
Time
Figure 3. Influence of interface mechanical
impedance mismatch of composites on measured
shock particle velocity profiles.
I3
0 2
03
'm » » -Glass imm"- m """Polycarbonate
"•^•Dremin's model —————Meyers'model
• PC37/GS20,exper. O PC37/GS20,numer.
A PC74/GS55,exper. O PC74/GS55,numer.
0.0 0.2 0.4 0.6 0.8
Particle velocity (km/s)
1.0
Figure 4. Comparison of PC/GS composite
Hugoniots between experiments and predictions of
mixture models and 2-D numerical simulations,
and their homogeneous components.
711
Downloaded 27 Mar 2006 to 131.215.225.175. Redistribution subject to AIP license or copyright, see http://proceedings.aip.org/proceedings/cpcr.jsp
Numerical analysis reveals that due to the
interaction of multiple reflection of waves within
the layers and the incident shock wave, i.e., the
scattering of the shock wave due to interface, the
pressure and particle velocity in the layered
composites are not uniformly distributed during the
shock compression, even if the steady shocked
state is achieved. The pressure in the hard layer is
lower, while the particle velocity is higher, in
comparison to their corresponding values in the
adjacent soft layer. The difference of pressures and
particle velocities between the hard and soft layers
and the amplitude of the resonant oscillations on
the shock profiles, as well as the oscillation
duration, are influenced by both the mismatch of
their mechanical impedance and the geometric
structure of the composite. Furthermore, the
phases of velocity and pressure profiles of steady
- - - -304steel ^— - -Polycarbonate
^m^^"«•Dremin's model —————Meyers' model
O PC37/SS I9,numer. • PC37/SS 19,exper.
<>
 t PC74/SS3t7,i]umer.i t 4 _ PC74/S£37,exper.
0.0 0.2 0.4 0.6
Particle velocity (km/s)
0.8 1.0
Figure 5. Comparison of PC/GS composite
Hugoniots between experiments and predictions of
mixture models and 2-D numerical simulations,
and their homogeneous components.
10
a PC74/SS37
0 PC74/GS55
4 PC37/SSI9
• PC74/AI37
* PC37/GS20
1 .E+05 1 .E+06 1 .E+07
Strain rate (1/s)
1 .E+08
Figure 6. Shock stress vs. strain rate for the
layered composite.
wave are not synchronous as they are in the
homogeneous media[2l
The influence of internal interfaces on shock
wave propagation is through the scattering
mechanism, i.e., multiple reflection of waves in the
layers and their interaction with the shock wave.
Due to interface scattering both the shock wave
velocity (Figs. 4 and 5) and the shock front strain
rate (Fig. 6) of the composites decrease. The
decrease of shock front strain rate indicates a
increase in the effective shock viscosity of the
composites. Since ignoring the interface scattering
effect the existing mixture models can only, at best,
reasonably predict the response of the composites
under strong shock loading conditions. In order to
fully describe the response of a heterogeneous
composite to shock compression loading, accurate
physics-based constitutive relations need to be
formulated taking into account the scattering effect
induced by the heterogeneous microstructure.
ACKNOWLEDGMENTS
The research reported here was supported by the
Solid Mechanics program at the Army Research
Office (Dr. M. A. Zikry, Program Manager) and is
gratefully acknowledged.
REFERENCE
1. Grady, D.E., Ravichandran, G., and Zhuang,
S., in Proceedings of the AIRPAT Conference,
Honolulu, Hawaii, edited by Manghani, M.,
Oxford University Press (1999).
2. Zhuang, S., Shock wave propagation in
periodically layered composites, Ph.D. Thesis,
California Institute of Technology (2002).
3. Barker, L.M. and Hollenbach, R.E., J. Appl
Phys. 43,4699 (1972).
4. Wackerle, J., J Appl. Phys. 33, 922 (1962).
5. Meyers, M.A. Dynamic behavior of materials,
John Wiley & Sons, Inc., New York (1994).
6. Dremin, A.N. and Karpukhin, I.A., Zh. Prikl
Mekhan. i Teck. Fiz. 1, No.3 (1960).
7. Swegle, J.W. and Grady, D.E., J.Appl. Phys.
58, 692 (1985).
712
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Classic Split-Hopkinson Pressure Bar Testing,&quot;

Ion don A107,

London A163,

London B62,

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Influence of Interface Scattering on Shock Waves in Heterogeneous Solids

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