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
SHOCK EQUATION OF STATE AND DYNAMIC STRENGTH OF
TUNGSTEN CARBIDE
Dattatraya P. Dandekar1 and Dennis E. Grady2
!
Army Research Laboratory, Weapons Materials Research Directorate,
Aberdeen Proving Ground, Mary land 21005-5069
2
Applied Research Associates, Inc.
4300 San Mateo Blvd. NE
Albuquerque, New Mexico 87110
Abstract Tungsten carbide ceramic is a high-density material with attractive compressive and tensile
strength properties. Cercom, Inc. manufactured hot-pressed tungsten carbide ceramic was tested in the
present study. The density of this ceramic varies between 15.53 and 15.56 Mg/m3. The values of
longitudinal and shear wave velocities measured ultrasonically vary between 7.04 and 7.05 km/s, and
4.30 and 4.32 km/s, respectively. Shock wave experiments were conducted at the U.S. Army Research
Laboratory (ARL) and Sandia National Laboratory (SNL) to determine its shock-induced compressive
behavior. The results of these experiments are summarized as: (1) the Hugoniot Elastic Limit (HEL)
of this material is 6.6 ± 0.5 GPa, (2) this value of the HEL may not adequately represent the dynamic
yield strength of the material because of the substantial post-yield hardening characteristics of this
material shown by the pronounced slope of the precursor wave preceding the following final-state
shock wave, and (3) the final shock state attained in the material indicates that the shear strength is
maintained when shocked above the HEL to 80 GPa.
INTRODUCTION
MATERIAL
The attractive mechanical properties of tungsten
carbide with its high-density makes it ideally suited
for use as a protective element to mitigate shockinduced effects. The current study was initiated
with the goal of bringing together information on
the shock-induced response of a hot-pressed
tungsten carbide manufactured by Cercom, Inc.
This material is, hereafter, referred to as Cercom
WC. Specific properties of interest in this study are
hydrodynamic equation of state, and compressive
and shear strength under plane shock wave loading
of this material. Shock compression data were
obtained from a series of shock profile
measurements conducted at ARL and SNL on
Cercom WC. But the material used in the shock
wave experiments performed at ARL and SNL were
not from the same batch.
Cercom WC is a composite consisting of two
distinct materials, namely, WC (97.2% by weight)
and W2C (2.8% by weight)[l]. W2C is a byproduct
of the densification process. WC and W2C both
crystallize in hexagonal form. The theoretical
densities of these carbides are 15.7 and 17.2 Mg/m3,
respectively [2]. Both melt around 3050 K and
have similar thermal expansion coefficients. The
only other property of W2C reported is the value of
longitudinal elastic wave velocity, which is 4.94
km/s [2]. The measured values of density, elastic
longitudinal and shear wave velocities of this
tungsten carbide composite are given in Table 1.
The values of density and elastic wave velocities for
Cercom WC measured at ARL and SNL are within
the errors of measurements. Since the measured
value of the density of Cercom WC is less than the
783
TABLE 1. Properties of Cercom WC
Properties
SNL
Density (Mg/m3)
15.56
Elastic wave velocities (km/s)
Longitudinal
7.04
Shear
4.30
Bulk
4.96
Bulk modulus (GPa)
383
0.200
Poisson's ratio
disc of polymethylmethacrylate (PMMA). The
wave velocity profiles in the experiments conducted
at ARL were monitored at the center of the free
surface of the tungsten carbide target. At SNL
wave profiles were monitored at the center of the
interface of a single crystal lithium fluoride disc and
a Cercom WC target. These wave profiles were
recorded by employing the interferometry technique
(VISAR) developed by Barker and Hollenbach [3].
The impact velocities were measured by shorting
electrically charged pins located at measured
distances a few millimeters ahead of the target disc.
The planarity of impact was better than 0.5 mrad.
The precision of free surface velocity measurements
is 1%. The uncertainties in the measured values of
impact velocities are 0.5%. In all, 14 experiments
were performed on Cercom WC. Of these 14
experiments, 6 were performed at SNL.
ARL
15.53
7.05
4.32
4.98
385
0.200
reported densities of WC and W2C, it must contain
some lighter impurities with or without porosity.
We have no information about these impurities but
the void volume fraction is estimated to be around
0.01 [1].
EXPERIMENT
Plane shock wave experiments were conducted
using the ARL 100 mm light gas gun facility and
the 89 mm bore diameter single stage powder gun
facility at SNL. The maximum impact velocities
that can be achieved at these two facilities are 0.7
km/s and 2.5 km/s, respectively.
In these
experiments, a disc of either Cercom WC or 6061T6 aluminum or C-cut single crystal sapphire or xcut quartz (impactor) mounted in the projectile
impacted another Cercom WC disc (target) with a
given velocity to generate a shock compression
wave of an appropriate magnitude. In SNL
experiments, the impactor material was backed by a
RESULTS
For convenience, the experiments performed at
ARL are denoted by those which begin with
numerals in column 1 of Table 2. The experiments
performed at SNL are denoted by those starting
with letters in column 1 of Table 2. Shock
compression wave profiles recorded in a few
experiments are shown in Fig. 1. The results are
presented in terms of elastic deformation, post-yield
TABLE 2. Shock Wave Experiment Data on Cercom WC.
Thickness (mm)
Elastic compression
Experiment/
Impact
Impactor
Impactor
Target Velocity
Stress Mass
material
(GPa) velocity
(km/s)
(km/s)
3.15
3.14
6.79
0.0620
504/WC
0.6130
0.0672
2.02
507/S
3.14
0.2962
7.33
2.02
514-1/S
3.15
6.35
0.058
0.5067
514-2/WC
3.14
0.069
7.55
6.43
0.5067
516/Q
0.99
0.0591
0.5004
6.47
6.48
517/WC
3.14
6.84
6.48
0.0625
0.1848
102/WC
4.00
3.49
0.0319
6.00
0.0648
3.44
0.0314
103/WC
4.00
6.00
0.0644
WC-8/WC
6.20
6.2
6.18
1.660
0.0566
WC-12/A1
1.51
0.362
0.0392
6.19
4.30
WC-13/A1
1.50
6.19
5.90
0.0539
0.454
WC-14/WC
6.35
6.32
6.2
1.239
0.0566
WC-15/WC
6.2
6.35
3.00
0.0566
1.210
WC-16/WC
6.2
6.30
6.34
0.824
0.0566
784
Density
(Mg/m3)
15.67
15.68
15.66
15.68
15.66
15.67
15.60
15.60
15.68
15.64
15.68
15.68
15.68
15.68
Inelastic compression
Stress Mass
Plastic
(GPa) velocity
velocity
(km/s)
(km/s)
0.306
5.43
27.6
9.3
0.088
5.79
15.2
0.165
5.29
23.7
0.253
5.56
Density
(Mg/m3)
16.41
15.74
15.98
16.22
5.10
9.1
0.092
15.75
6.22
5.98
5.93
5.74
81.6
0.830
17.92
59.2
57.5
38.
0.620
0.605
0.412
17.30
17.27
16.69
1
1
f
w
1
1
1
1
o
D
5
1
-
^rri! —;
1
i 'cr" °
Jl
0.0
0.2
°
D
""a
——•—— WC8
Lf
0
^^
__*__WC14
- -«-— WC16
——*—— 504
- - - - a - - - - 514-2
0.4
0.6
0.8
1.0
1.2
Time(]Lis)
Timers)
FIGURE 2. Precursor characteristics of Cercom WC
FIGURE 1. Shock wave profiles in Cercom WC
feature, inelastic deformation, and its nature.
post-yield behavior of Cercom WC.
Elastic Compression
The wave profiles showed initial break
corresponding to stresses between 6.2 and 7.6 GPa
(Fig. 1). This break is identified as the HEL for the
Cercom WC. The decay of the elastic precursor
with target thickness is not evident from the results
of these experiments. The average value of the
HEL is 6.6 ± 0.5 GPa. Since the precision of
measurements of particle and free surface velocity
is 1%, the large statistical uncertainty associated
with the average value of the HEL is likely to be
arising from variability in the material itself.
Details of the precursor wave indicating the
dynamic strength property of Cercom WC is shown
in Fig. 2. This figure shows a substantial post-yield
hardening in Cercom WC following the elastic
precursor and preceding the attainment of final
shock-induced state. These wave profiles cannot
discriminate between the relative roles of pressure
hardening or deformation hardening in the observed
Inelastic Compression
Shock wave following the elastic precursor
travels in the elastically deformed Cercom WC with
velocity between 5.1 and 6.2 km/s. These values
of shock velocities are larger than the bulk sound
wave velocity in Cercom WC at the ambient
condition, i.e., 4.96-4.98 km/s (Table 1). This
suggests that the inelastic deformation proceeds
plastically in this material. Since an adequate
presentation of results of inelastic deformation
requires knowledge of appropriate hydrodynamic
compression of the material, it is dealt with next.
The hydrodynamic compression of Cercom
WC is obtained from the shock compression data on
tungsten carbide reported by McQueen et al. [4].
Tungsten carbide material used in their experiments
contained 5 weight percent of cobalt as a binder
material. The density of the material was 15.01
Mg/m3. The values of longitudinal and shear wave
velocities were reported to be 6.89 km/s and 4.18
785
km/s, respectively. The calculated values of bulk
sound wave speed and Poisson's ratio are 4.92 km/s
and 0.209, respectively. These values are not very
different from the measured values of sound speeds
for Cercom WC given in Table 1. Thus, the
calculated hydrodynamic compression of Cercom
WC based on the results of McQueen et al. [4]
experiments should represent its compression
faithfully. A careful analysis of their data taking
into account the fact that hydrodynamic equilibrium
in their tungsten carbide was not attained in their
experiments until the pressures in excess of 70 GPa
were reached yield the following linear relation
between shock velocity (Us) and particle velocity
(Up):
Us = 4.93+1.309 Up.
Hydrodynamic
ARL
SNL
80
60
I
40
CO
20
(1)
The value of correlation coefficient for the
above linear relation is 0.999, and the 95%
confidence intervals of the intercept (C0) and the
slope (s) in relation (1) are ±0.05 km/s and ±0.083,
respectively. Further, the value of C0 agrees well
with the value of the bulk sound wave velocity,
4.92 km/s, at the ambient condition.
The hydrodynamic compression of Cercom
WC calculated by using the value of its bulk
modulus 384 GPa with s= 1.309, and experimentally
determined shock Hugoniot of Cercom WC are
shown in Fig. 3. It shows that this material
continues to retain shear strength under plane shock
wave propagation when shocked to 80 GPa. The
value of shear stress sustained by Cercom WC at
the HEL obtained from the Hugoniot data and the
hydrodynamic compression curve is 2.4 GPa. This
compares well with the elastic value of shear stress,
i.e., 2.5 ± 0.2 GPa. It appears that the magnitude of
shear stress sustained by Cercom WC increases
with an increase in shock-induced stress. For
example, at shock stress of 82 GPa, the value of
sustained shear stress is 6 GPa.
0.85
0.90
0.95
1.00
V/VO
FIGURE 3. Shock compression of Cercom WC
magnitude of shear stress sustained above the HEL
needs to be determined by conducting appropriate
shock-reshock experiments of the type reported by
Asay et al. [5] and Dandekar and Gaeta [6].
REFERENCES
1
2
3
4
5
CONCLUDING REMARKS
6
The results of the present investigation indicate that
Cercom WC deforms like an elastic-plastic solid
under shock wave compression.
The
786
Gooch, W. J. (Private communication).
Gauthier, M. M., Engineered Materials
Handbook, ASM International, Cleveland,
1995, pp. 961-963.
Barker, L. M., and Hollenbach, R. E., J. Appl.
Phys., 43, 4669-4675 (1972).
McQueen, R. G., Marsh, S. P., Taylor, J. W.,
Fritz, J. N., and Carter, W. J., "The Equation of
State of Solids from Shock Wave Studies", in
High-Velocity Impact Phenomena, edited by R.
Kinslow, Academic Press, New York, 1970, pp.
293-417 and 521-568.
Asay, J., Chhabildas, L. C, and Dandekar, D.
P., J. Appl Phys. 51, 4774-4783 (1980).
Dandekar, D. P., and Gaeta, P. J., "Double
Shock and Release Experiments in PMMA and
Z-cut Sapphire", in Shock Wave in Condensed
Matter-1987, edited by S. C. Schimdt and N. C.
Holms, North - Holland, New York, 1988, pp.
281-284.