Spall Strength of Tungsten Carbide 

by Dattatraya P. Dandekar 

ARL-TR-3335 September 2004 

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ARL-TR-3335 September 2004 

Spall Strength of Tungsten Carbide 

Dattatraya P. Dandekar 

Weapons and Materials Research Directorate, ARL 

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Spall Strength of Tungsten Carbide 

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Dattatraya P. Dandekar 

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14. ABSTRACT 

Spall strength of a hot-pressed tungsten carbide manufactured by Cercom Inc., referred to as CER-WC, is determined by 

performing plane shock wave experiments as a function of shock-induced compressive stress and its duration. Shock-induced 

stress varied between 3.5 and 24 GPa. The duration of shock-induced stress, i.e., pulse width, ranged from 0.35 to 1.13 μs. 

These experiments showed that CER-WC retained substantial spall strength to 24 GPa, i.e., around 3× the value of the Hugoniot 

elastic limit. Spall strength of CER-WC was not significantly influenced by the pulse-width of shock-induced compression. 

Spall strength of CER-WC decreased from a value of 2.06 ± 0.04 to 1.22 ± 0.38 GPa as shock-induced stress increased from 3.4 

to 24 GPa. 

15. SUBJECT TERMS

shock wave, Hugoniot elastic limit, spall strength, tungsten carbide 

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iii 

Contents 

List of Figures iv

List of Tables iv

1. Introduction 1

2. Material 1

3. Experimental Methods 2

4. Results 3

4.1 Compression and release response .....................................................................................3 

4.2 Spall strength....................................................................................................................10 

5. Summary 14

6. References 16

Distribution List 17
iv 

List of Figures 

Figure 1. Configuration of shock wave spall experiments: (a) normal impact and (b) 

compression shear......................................................................................................................2 

Figure 2. Free-surface velocity profile in CER-WC at 3.4 GPa. ....................................................7 

Figure 3. Free-surface velocity profile in CER-WC at 6.5–7.6 GPa. .............................................7 

Figure 4. Free-surface velocity profile in CER-WC at 9.2–10.1 GPa. ...........................................8 

Figure 5. Free-surface velocity profile in CER-WC at 19.8 GPa. ..................................................8 

Figure 6. Free-surface velocity profile in CER-WC at 24 GPa. .....................................................9 

Figure 7. Free-surface velocity profile in CER-WC at 7 GPa under normal and 12° obliquity. ....9 

Figure 8. Shock Hugoniot and hydrodynamic compression of CER-WC....................................10 

Figure 9. Pull-back velocity as a function of stress and pulse width for CER-WC......................12 

Figure 10. X-t diagram of simultaneous compression-shear spall experiments in CER-WC. .....13 

List of Tables 

Table 1. Shock wave compression and release data on CER-WC (according to Dandekar and 

Grady [2])...................................................................................................................................4

Table 2. Shock wave compression and release data on CER-WC (according to present 

work)..........................................................................................................................................5 

Table 3. Spall strength of CER-WC. ..............................................................................................6 
1

1. Introduction 

Tungsten carbide is a high-density ceramic with mechanical properties that make it attractive for 

applications related to high-velocity impacts. Dandekar and Grady (1) report the compressive 

and shear strengths of a hot-pressed tungsten carbide manufactured by Cercom Inc., referred to 

as CER-WC, obtained from the results of plane shock wave experiments. This study reports 

tensile/spall strength of CER-WC obtained from the results of an additional series of plane shock 

wave experiments, and thus supplements the results reported by Dandekar and Grady (1). 

Spall strength of ceramic and other brittle materials is generally thought to be controlled by the 

kinetics of shock-induced defects/damage, i.e., micro- and meso-cracks together with global 

deformation under a given magnitude of shock-induced stress. Experimentally, spall strength of 

a ceramic is found to be generally very low, compared to its Hugoniot elastic limit (HEL), and 

also found to decrease with an increase in shock-induced stress. An exception to this is exhibited 

by silicon carbide (2), in which spall strength is found to increase initially with an increase in the 

shock-induced stress before the decrease in spall strength with a further increase in shockinduced stress. The goal of the present work was to examine whether or not the duration and 

amplitude of shock-wave-induced compression had a significant effect on the spall strength of 

CER-WC, and whether or not the value of spall strength under simultaneous shock-induced 

compression shear above the HEL of CER-WC more closely resembled that observed in a 

titanium alloy, Ti-6Al-4V, reported by Spletzer and Dandekar (3). The results obtained in this 

work and those reported in reference (1) provide information needed to determine material 

parameters used in various material models for computational simulations of high-velocity 

ballistic-impact-induced events. 

2. Material 

CER-WC is not strictly monolithic, but is composed of two distinct materials, namely WC 

(97.2% by weight) and W2C (2.8% by weight) (4). WC and W2C both crystallize in hexagonal 

form. The theoretical densities of these carbides are 15.7 and 17.2 Mg/m3

, respectively (4). 

Both melt around 3050 K and have similar thermal expansion coefficients. The values of 

density, elastic longitudinal, and shear wave velocities of this composite are 15.530 ± 0.007 

(Mg/m3), 7.05 ± 0.06 km/s and 4.32 ± 0.04 km/s, respectively. At present, the elastic properties 

of individual phase in this material are not completely measured. Moreover, the reported values 

of theoretical densities of WC and W2C suggest that the composite material must contain some 

lighter impurities and/or voids. The void/volume fraction in this material is reported to be 
2

around 0.01 (4). The grain sizes in CER-WC vary between 0.3 and 1.4 μm, with an average 

grain size of 0.9 μm. 

3. Experimental Methods 

Plane shock wave experiments were conducted at the U.S. Army Research Laboratory (ARL) 

100-mm light gas gun facility. A typical configuration of shock wave experiments performed on 

tungsten carbide is shown in figure 1. In these experiments, an impactor, i.e., a thinner disc of 

CER-WC or c-cut sapphire (S) or x-cut quartz (Q) of appropriate thickness, impacted a relatively 

thicker CER-WC disc (target) with a given velocity to generate a shock compression wave of a 

certain magnitude and of known duration (pulse width). The adopted configuration of the 

experiments assured that the recorded wave profiles in these experiments would yield 

information pertaining to the HEL, the nature of shock-induced deformation, shear strength, 

release impedance, and spall strength of the material. The wave velocity profiles in these 

experiments were monitored at the center of the free-surface of the target by employing the 

velocity interferometer system for any reflective surface (VISAR), developed by Barker and 

Hollenbach (5). Impact velocities were measured by shorting four 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%. 

Uncertainties in the measured values of impact velocities are 0.5%. Seventeen spall experiments 

were performed on CER-WC. 

Figure 1. Configuration of shock wave spall experiments: (a) normal impact and (b) 

compression shear. 
3

4. Results 

Tables 1 and 2 summarizes available shock wave compression data on CER-WC, as reported by 

Dandekar and Grady (1), together with such data collected during the course of the present 

investigation. Table 3 summarizes the spall data obtained from these experiments. Free-surface 

velocity profiles recorded in spall experiments are shown in figures 2–7. 

4.1 Compression and release response 

The first cusp in the recorded wave profiles, identified as the HEL, varies from 6.9 to 9.0 GPa. 

The results of shock wave compression experiments on CER-WC indicated that the HEL varied 

from 6.2 to 7.6 GPa (1). The average value of the HEL, based on all data, was 7.2 ± 0.8 GPa. 

The observed variation in the values of the HEL is larger than the precision of measurements, 

i.e., 1.5%. The large statistical uncertainty associated with the average value of the HEL seems 

to arise from variability of the material itself. For example, in experiments performed at around 

23-24 GPa, the values of HEL in targets of nominal thickness of 6 mm vary from 7.34 to 

8.96 GPa. 

The shock wave following the elastic precursor travels in the elastically-deformed material with 

velocity varying from 5.1 to 6.2 km/s. These values of inelastic/plastic shock wave velocity 

exceed the magnitude of bulk sound wave velocity in CER-WC at the ambient condition, i.e., 

4.96–4.98 km/s. This suggests that deformation of CER-WC is elastic-plastic. However, the 

large values of plastic wave velocities obtained in experiments 507, 302-1, and 302-2 are 

inexplicable. These exceptionally large values are not consistent with the values of plastic 

velocities obtained in the remaining experiments. The least squares fit to shock velocity and 

mass velocity data, omitting those obtained in the previously mentioned three experiments yields 

the following equation: 

 U (P) = 5.088 + 1.419 u (P), (1) 

where U (P) and u (P) are the plastic wave velocity and mass velocity corresponding to inelastic 

deformation in CER-WC. The correlation coefficient for the relation given by equation 1 is 

0.976, and 95% confidence intervals for the intercept and slope are ±0.101 and ±0.237 km/s, 

respectively. Equation 1 is used to calculate plastic wave velocities in experiments 301-1 and 

409. 

The inelastic/plastic stresses and densities given in tables 1 and 2 are obtained by using the wellknown momentum and mass conservation relations centered at the HEL (3). 
4

Table 1. Shock wave compression and release data on CER-WC (according to Dandekar and Grady [2]). 

Impactor Target Elastic Compression Plastic Compression 

Experiment Thickness 

(mm) 

Impact

Velocity

(km/s) 

Stress (GPa) 

Mass 

Velocity 

(km/s) 

Density 

(Mg/m3) 

Plastic 

Velocity 

(km/s) 

Stress (GPa) 

Mass 

Velocity 

(km/s) 

Density 

(Mg/m3) 

504 3.148 3.137 0.6130 6.793 0.0620 15.678 5.43 27.61 0.3065 16.417 507 2.023 (S) 3.139 0.2962 7.362 0.0672 15.690 5.79 9.28 0.0883 15.747 

514-1 2.025 (S) 3.147 0.5067 6.354 0.0580 15.669 5.29 15.24 0.1652 15.993 514-2 3.141 6.429 0.5067 7.559 0.0690 15.694 5.56 23.66 0.2534 16.232 

516 0.994 (Q) 6.478 0.5004 6.475 0.0591 15.671 — — — — 517 3.145 6.476 0.1848 6.847 0.0625 15.679 5.10 9.24 0.0924 15.772 102 4.000 6.000 0.0648 3.495 0.0319 15.611 — — — — 103 4.000 6.000 0.0644 3.440 0.0314 15.610 — — — — 

WC-8 6.200 6.178 1.6600 6.201 0.0566 15.666 6.22 81.56 0.8300 17.890 

WC-12 1.507 (Al) 6.192 0.3620 4.295 0.0392 15.627 — — — — WC-13 1.500 (Al) 6.190 0.4540 5.905 0.0539 15.660 — — — — WC-14 6.351 6.342 1.2390 6.201 0.0566 15.666 5.98 58.98 0.6200 17.295 WC-15 6.354 3.000 1.2100 6.201 0.0566 15.666 5.93 57.15 0.6050 17.262 WC-16 6.350 6.341 0.8240 6.201 0.0566 15.666 5.74 38.16 0.4120 16.700 

Notes: Impactor material is identified only when it is different from CER-WC. Impactor material is CER-WC unless identified as c-cut sapphire (S), x

(Al). 
5

Table 2. Shock wave compression and release data on CER-WC (according to present work).

Impactor Target Elastic Compression Plastic Compression 

Experiment Thickness 

(mm) 

Impact

Velocity

(km/s) 

Stress (GPa) 

Mass 

Velocity 

(km/s) 

Density 

(Mg/m3) 

Plastic 

Velocity 

(km/s) 

Stress (GPa) 

Mass 

Velocity 

(km/s) 

Density 

(Mg/m3) 

301-1 2.020 5.950 0.2000 7.450 0.0680 15.691 5.24 10.10 0.1000 15.78 302-1 2.030 6.030 0.4047 7.045 0.0643 15.683 5.81 19.62 0.2023 16.065 302-2 3.990 6.030 0.4047 7.045 0.0643 15.683 5.81 19.62 0.2023 16.065 315-1 2.001 6.030 0.1255 6.880 0.0628 15.680 — — — — 315-2 3.994 6.031 0.1255 6.880 0.0628 15.680 — — — — 

329 2.018 5.965 0.5278 7.340 0.0670 15.689 5.48 24.27 0.2639 16.274 330 3.992 5.971 0.5202 7.340 0.0670 15.689 5.48 23.94 0.2601 16.262 

335/CS12o 3.999 6.045 0.5085 8.765 0.0800 15.718 5.51 23.36 0.2486a 16.214 

401 3.998 6.032 0.5029 8.962 0.0818 15.722 5.52 23.68 0.2514 16.221 407 3.987 6.035 0.1397 7.65 0.0698 15.698 — — — — 409 3.985 6.042 0.2008 8.89 0.0810 15.724 5.24 10.14 0.1004 15.783 

415/CS12° 3.989 6.044 0.1455 7.79 0.0712a 15.702 — — — — 

a Mass velocities are half the normal component of impact velocity consistent with 12° obliquity of impact in these experiments. 
6

Table 3. Spall strength of CER-WC. 

Free-Surface Velocity 

(km/s) 

Half Pullback Velocity 

(km/s) 

Spa

Experiment Pulse-width 

(μs) 

Impact stress

(GPa) 

Peak Spall Re-Shock Magnitude Error 

(δ) 

Percent

(δ)

Magnitu

(GPa

103 1.13 3.44 0.0628 0.0252 0.0629 0.01880 0.0003 0.018 2.06 516 0.35 6.47 0.1183 0.0941 0.1222 0.01210 0.0008 0.062 1.33 

315-1 0.57 6.87 0.1298 0.0996 0.1282 0.01510 0.0008 0.054 1.65 

407 1.13 7.65 0.1357 0.1143 0.1357 0.01070 0.0009 0.083 1.17 

415/CS12° 1.13 7.79 0.1429 0.1251 0.00890 0.0009 0.107 0.97 

Average 7.20 0.0117 0.0008 0.072 1.28 

507 0.36 9.28 0.1815 0.1492 0.1805 0.01615 0.0012 0.073 1.77 

301-1 0.58 10.10 0.2080 0.1840 0.2070 0.01200 0.0014 0.116 1.31 

517 0.86 9.24 0.1717 0.1444 0.1698 0.01365 0.0011 0.082 1.49 409 1.13 10.14 0.1953 0.1704 0.1953 0.01245 0.0013 0.104 1.36 

Average 9.69 0.01356 0.0012 0.094 1.49 

514-1 0.36 15.24 0.3080 0.2790 0.2959 0.01450 0.0021 0.143 1.59 302-1 0.58 19.82 0.3907 0.3667 0.3858 0.01200 0.0027 0.223 1.31 302-2 1.13 19.82 0.3952 0.3746 0.3935 0.01030 0.0027 0.264 1.13 

Average 19.82 0.01115 0.0027 0.243 1.22 

329 0.50 24.41 0.4912 0.4688 0.4830 0.01120 0.0034 0.303 1.23 (0.330 0.50 24.08 0.4961 0.4725 0.4881 0.01180 0.0034 0.290 1.29 (0.

514-2 0.82 23.66 0.4950 0.4740 0.01050 0.0034 0.326 1.15 (0.

335/CS12° 1.13 23.36 0.4665 0.4465 0.4665 0.01000 0.0032 0.323 1.10 (0.7

401 1.13 23.77 0.4800 0.4580 0.4750 0.01100 0.0033 0.302 1.20 (0.

Average 23.86 0.01113 0.0033 0.309 1.22 (0.8
7 

-10

0.0

10

20

30

40

50

60

70

1.0 2.0 3.0 4.0 5.0 6.0

103

Free surface velocity (m/s)

Time (μs)

Figure 2. Free-surface velocity profile in CER-WC at 3.4 GPa. 

0

50

100

150

0.0 0.50 1.0 1.5 2.0 2.5 3.0 3.5 4.0

516; 0.35 μs

315-1; 0.57 μs

Free surface velocity (m/s)

407; 1.13 μs

Time (μs)

Figure 3. Free-surface velocity profile in CER-WC at 6.5–7.6 GPa. 
8 

0

50

100

150

200

1.20 1.60 2.00 2.40 2.80 3.20 3.60 4.00 4.40

507; 0.36 μs

301-1; 0.58 μs

517; 0.86 μs

Free surface velocity (m/s)

409; 1.13 μs

Time (μs)

Figure 4. Free-surface velocity profile in CER-WC at 9.2–10.1 GPa. 

0

50

100

150

200

250

300

350

400

1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0

302-1; 0.58 μs

302-2; 1.13 μs

Free surface velocity (m/s)

Time (μs)

Figure 5. Free-surface velocity profile in CER-WC at 19.8 GPa. 
9 

0

100

200

300

400

500

1.0 1.5 2.0 2.5 3.0 3.5 4.0

329; pw. 0.50 μs

330; pw. 0.50 μs

514-2; pw. 0.82 μs

401; pw. 1.13 μs

335; pw. 1.13 μs, 12 deg.

Free surface velocity (m/s)

Time (μs)

Figure 6. Free-surface velocity profile in CER-WC at 24 GPa. 

80

90

100

110

120

130

140

150

0.00 0.500 1.00 1.50 2.00 2.50 3.00

407 415

Free surface velocity (m/s)

Time (μs)

Figure 7. Free-surface velocity profile in CER-WC at 7 GPa under normal and 12° obliquity. 
10 

Hydrodynamic compression of CER-WC, reported in reference (1), and shock compression data, 

given in tables 1 and 2, are shown in figure 8. The shock compression data of the present work 

does not change the general conclusion regarding retention of shear strength in CER-WC under 

plane shock wave compression reported by Dandekar and Grady (1). The values of shear 

strength tend to increase with an increase in the shock-induced stress in CER-WC. For example, 

whereas the value of shear strength at the HEL is 2.7 ± 0.3 GPa, its value at 24 and 82 GPa are 

3.4 ± 0.3 and 6 ± 0.3 GPa, respectively. However, the work hardening of CER-WC remains to 

be confirmed through shock-release-re-shock experiments similar to those performed in titanium 

diboride (6). 

The effective overall release impedance of CER-WC calculated from the plastic stress, plastic 

mass velocity, and recorded free-surface velocity range from 96 to 116 Gg/m2

s. These values 

are very close to the elastic impedance of CER-WC, i.e., 109.5 Gg/m2

s. This result appears 

consistent with the work-hardening nature of CER-WC, but needs to be substantiated through the 

type of experiments suggested in the previous paragraph. 

0

20

40

60

80

0.0560 0.0580 0.0600 0.0620 0.0640

Hydrodynamic Ref.[1]

HEL

Plastic

Stress/Pressure (GPa)

Specific density (m3/Mg)

HEL

Figure 8. Shock Hugoniot and hydrodynamic compression of CER-WC. 

4.2 Spall strength 

Table 3 summarizes the spall data and the values of spall strength of CER-WC obtained for 

various pulse widths at a specific value of impact-induced stress. These experiments were done 

over a period of years. Thus, the values of spall strengths given in this table provide a measure 

of variability due to variation in different batches of the CER-WC material. Further, the 

observations of the variation in the values of spall strength due to pulse width are discussed in 
11 

terms of the average impact stresses. It should be noted that in a spall experiment, the freesurface velocities measured from the arrival of a shock compression wave lasts for the duration 

of the pulse width. Measurements show a precipitous decline in free-surface velocity, indicative 

of spall, and a recompression wave following the generation of spall in the material. These freesurface velocities are identified as peak, spall, and reshock in table 3. The values of half pullback velocity given by one-half the product of difference between the peak and spall free-surface 

is a measure of the spall strength of a material. Based on the assumption that the observed 

release impedance is elastic, the values of spall strengths are calculated from the product of half 

pull-back velocity and longitudinal elastic impedance of CER-WC. However, if future 

experiments show that tensile impedance of CER-WC is plastic, then the more realistic value of 

spall strength would be less than the values based on elastic impedance. For example, if the 

tension from an impact stress of 24 GPa is generated following a plastic path, then a lower bound 

on the spall strength at 24 GPa for CER-WC may be estimated by multiplying the observed half 

pull-back velocity with the ambient plastic impedance of CER-WC. The ambient plastic 

impedance is given by the product of the ambient density and bulk sound wave velocity. The 

value of the ambient plastic impedance of CER-WC is thus 77.2 Gg/ m2s. These lower values of 

spall strengths at 24 GPa for CER-WC are given in parenthesis in table 3. 

Results of these experiments show that when shocked to 24 GPa, i.e., around 3× the value of the 

HEL, CER-WC retains substantial spall strength. The observed scatter in the values of pull-back 

velocity declines with an increase in the impact stress, even though the errors in the 

measurements increase substantially (table 3). The upper and lower extreme, shown in figure 9, 

are the maximum and minimum pull-back velocities recorded at given average impact stresses 

(table 3). The reasons for the observed large scatter at low stresses and reduction in the scatter at 

high stresses for the pull-back velocity in CER-WC are difficult to state with any confidence due 

to the paucity of material properties data for WC and W2C phases in CER-WC, the two phases 

constituting CER-WC. The measured values of spall strength show an initial large decline of 

impact stresses from 3.4 to 7 GPa, compared to those from 7 to 24 GPa. Further, the dependence 

of spall strength of CER-WC on pulse width, i.e., duration of shock-induced compression, is at 

best moderate and the values of spall strength as indicated by the magnitude of half pull-back 

velocity are not significantly different above 7 GPa. A relatively large decrease in the spall 

strength of CER-WC when shocked from 3.4 to 7 GPA and a much smaller gradual decrease in 

the spall strength of CER-WC from 7 to 24 GPa suggests that weakening due to shock-induced 

compressive fracture damage is apparently compensated/mitigated through blunting of cracks 

and propagation due to shock-induced plastic deformation of CER-WC, a dissipative process, 

initiated at and above stresses around magnitude of the HEL. 

Two spall experiments, 335/CS12° and 415/CS12°, were performed under simultaneous 

compression-shear at 12° obliquity on CER-WC at 23.4 and 7.8 GPa, respectively, to determine 

the role of induced shear stress under simultaneous compression-shear on the spall strength of 

CER-WC. The configuration of the experiments assured that the shock-induced shear wave 
12 

would traverse the spall plane located at around 2 mm from the impact surface of CER-WC 

target prior to generation of tension in the target at the spall plane. A space-time diagram for 

these compression-shear experiments is shown in figure 10. It was expected that, to the extent 

that the deformation was controlled through shock-induced plasticity, the spall strength of 

CER-WC would not degrade significantly. The measured value of half pull-back velocity is 

0.0100 ± 0.0032 km/s in experiment 335/CS12° and is not significantly different from the 

measured values of half pull-back velocity 0.0110-0.0118 km/s under normal shock-induced 

compression, i.e., at 0° obliquity. A similar result is obtained from experiment 415/CS12° at 

7.8 GPa. The results of these two experiments appear to be consistent with the idea that plastic 

deformation of CER-WC mitigates the effect of weakening due to compressive fracture damage 

through blunting of cracks and their propagation. 

0.008

0.01

0.012

0.014

0.016

0.018

0.02

0.00 5.00 10.0 15.0 20.0 25.0

0.5 μs pulse-width

1.13 μs pulse-width

Average

Upper extreme

Lower extreme

1⁄2 pull-back velocity (km/s)

Stress (GPa)

Figure 9. Pull-back velocity as a function of stress and pulse width for CER-WC. 

Frutschy et al. (7) report the results of pressure-shear experiments on pure WC obtained from 

Cercom, Inc. at around 6.5 and 19.5 GPa at 18° and 16° obliquities, respectively. The values of 

density, longitudinal, and shear wave velocities for the pure WC are 15.4 Mg/m3

, 6.86, and 

4.3 km/s, respectively. Based on theoretical density of WC, pure WC was reported to have 1.5% 

porosity. Pure WC was taken to be a single phase material with no metallic additive. But pure 

WC material provided to them for their investigation by ARL was CER-WC. Thus, the values of 

density, elastic wave velocities, and porosity should be those given in section 2. They found that 

the normal velocity component wave profiles show features similar to those observed in freesurface velocity profiles under normal plane shock wave loading to 8 and 20 GPa. The values of 

8 and 20 GPa are based on the results of shock wave experiments given in tables 1 and 2. But 
13 

the free-surface velocity profiles corresponding/related to shear wave velocity component in 

these two experiments displayed different patterns. Whereas the free-surface velocity profiles 

corresponding/related to shear wave velocity component at lower peak stress, i.e., 8 GPa, rose to 

stable value within a duration of around 0.2 μs, the profile at 20 GPa showed a ramp-like 

structure and rose slowly to a stable magnitude over a duration of 0.7 μs. The peak magnitudes 

of shear stress-induced free-surface velocity in these two experiments were 0.04 and 0.138 km/s, 

respectively. They attributed the recorded ramp-like shear wave front at 20 GPa to dissipative 

frictional processes associated with the damage resulting from collapse of pores initially present 

in the pure WC. Since the porosity in CER-WC is estimated to be around 1%, the relative role of 

dissipative effects of plasticity and pore collapse on the observed spall strength of CER-WC 

under simultaneous compression-shear and under pure compression under shock wave loading 

remains to be determined. However, based on almost exact matching of normal velocity wave 

profiles under compression alone and under compression-shear at 7 and 23 GPa, respectively 

(see figure 6 profiles for experiments 401 and 335 and figure 7 profiles for experiments 407 and 

415), suggests that spall strength itself may not be influenced significantly due to the dissipative 

frictional processes associated with collapse of pores as manifested in the shear wave velocity 

profiles. It would be fruitful to conduct pressure-shear experiments on CER-WC to higher 

magnitudes of compressive stress. 

0

0.5

1

1.5

2

-4 -2 0 2 4 6

Time (

μs)

 CER-WC impactor and target (mm)

Spall location

CER-WC impactor CER-WC target

Longitudinal

Shear

Impact plane

Figure 10. X-t diagram of simultaneous compression-shear spall experiments in CER-WC. 

The results of spall experiments under normal impact and under simultaneous compression-shear 

show that the measured values of half pull-back velocity are not significantly different from one 

another. It remains necessary to perform additional spall experiments under simultaneous 
14 

compression-shear both below and above the HEL of CER-WC to strengthen the previously 

mentioned suggestion of a mitigating effect of plastic deformation on cracks/damage. Finally, 

the magnitudes of spall strength expressed in terms of stress to 20 GPa would show a sudden 

decline in its value at 24 GPa if the effective tensile impedance at 24 GPa is plastic. For 

example, the spall strength of CER-WC would decrease from a value of 2.06–1.22 GPa as shockinduced stress increased from 3.44 to 19.82 GPa. The value of spall strength of CER-WC at 

24 GPa is 1.22 GPa if the effective tensile impedance is elastic. On the other hand, if the 

effective tensile impedance of CER-WC is plastic, then the magnitude of spall strength becomes 

0.84 GPa for the same value of the observed half pull-back velocity at 24 GPa. This is an 

expected response, since at 24 GPa tension may be generated through interaction of release 

waves in CER-WC following plastic loci, as was indeed the case for a heavy tungsten alloy 93W. 

Dandekar and Weisgerber (8) measured values of tensile impedance for 93W, deforming like an 

elastic-plastic material under shock wave propagation, in spall experiments where tensile stresses 

were generated through interaction of release waves following plastic loci. The values of tensile 

impedance were indeed close to the value of the plastic impedance of 93W. Grady (9) reported 

spall strength of CER-WC at impact stresses of 4.3 and 5.9 GPa to be 1.65 ± 0.05 and 

1.4 ± 0.1 GPa, respectively. These values are consistent with the measured values of spall 

strength of CER-WC obtained at 3.4 and 7 GPa. 

Finally, the quasi-static tensile strength of CER-WC is reported to be 0.59 ± 0.06 GPa (4). This 

large difference in the spall strength of CER-WC, measured quasi-statically and under plane 

shock wave loading, can be due to differences in the stress and strain states, and strain rates 

under uniaxial stress state attained under quasi-static loading condition and uniaxial strain state 

achieved under plane shock wave propagation. Strain rates control kinetics and the time 

available determines the generation and propagation of defects. Bridgman (10) measured tensile 

strengths of brittle and ductile materials under hydrostatic pressure. In general, he found that 

tensile strengths of materials increased significantly under high hydrostatic pressures. For 

example, the tensile strength of carboloy, a tungsten carbide cermet containing metallic cobalt 

binder, increased by two to three times under hydrostatic pressure of 2.6 GPa compared to under 

the ambient pressure. Thus, the measured lower magnitude of quasi-static spall strength 

0.59 ± 0.06 GPa of CER-WC is at least in part due to the unconfined loading condition. Since 

spall strength measurements of a material under plane shock wave loading is done under the 

uniaxial strain condition, i.e., a confined condition, the smaller magnitude of quasi-static tensile 

strength of CER-WC compared to its spall strength is consistent. 

5. Summary 

1. Shock-induced compression and release response of CER-WC may be modeled as an elasticplastic solid material to 82 GPa. The HEL of CER-WC is 7.2 ± 0.8 GPa. 
15 

2. Shear strength of CER-WC increases with an increase in the shock-induced stress to 82 GPa. 

The values of shear strength at the HEL and at 82 GPa are 2.7 ± 0.3 and 6.0 ± 0.3 GPa, 

respectively. 

3. The effective release impedance of CER-WC to 24 GPa is elastic. 

4. Spall strength of CER-WC decreases with an increase in the shock-induced compressive 

stress. It does not show a strong dependence on duration/pulse-width of shock-induced 

compressive stress between 0.5 and 1.1 μs. The initial decline in spall strength is very rapid, 

decreasing from a value of 2.06 ± 0.08 to 1.38 ± 0.12 GPa when shocked to 3.4 and 7.2 GPa, 

respectively. An increase in the shock stress to 24 GPa leads to only a moderate decrease in 

the value of spall strength at 24 GPa, i.e., 1.22 ± 0.45 GPa. A lower bound of the magnitude 

of spall strength, based on plastic impedance of CER-WC at 24 GPa, is 0.84 ± 0.31 GPa. 

5. The mitigation of the initial precipitous decline in the spall strength of CER-WC appears to be 

due to the mitigating influence of plasticity-dominated deformation on compressive stressinduced damage in CER-WC, i.e., blunting of cracks or microcracks above the HEL. 

However, the role and contributions of pore collapse suggested by Frutschy et al. (7), and the 

deformation of WC and W2C phases under shock wave compression and simultaneous 

compression-shear on the spall strength of CER-WC, although unknown, cannot be 

discounted to understand the spallation of CER-WC. 

6. Finally, quasi-static tensile strength of CER-WC is reported to be 0.59 ± 0.06 GPa, 

significantly less than the spall strength of the material determined in this study showing the 

combined influences of kinetics of defect generation and confined stress state of CER-WC on 

the value of its spall strength. 
16 

6. References 

1. Dandekar, D. P.; Grady, D. E. Shock Equation of State and Dynamic Strength of Tungsten 

Carbide. Shock Compression of Condensed Matter—2001; Furnish, M. D., Thadhani, N. N., 

Horie, Y., Eds.; American Institute of Physics: NY, 2002; pp 783–786. 

2. Dandekar, D. P.; Bartkowski, P. T. Spall Strengths of Silicon Carbides Under Shock 

Loading. Shock Wave and High-Strain Rate Phenomena; Staudhammer, K. P., Murr, L. E., 

Meyers, M. A., Eds.; Elsevier: NY, 2001; pp 71–77. 

3. Spletzer, S. V.; Dandekar, D. P. Deformation of a Low-Cost Ti-6Al-4V Armor Alloy Under 

Shock Loading; ARL-TR-2386, U.S. Army Research Laboratory: Aberdeen Proving 

Ground, MD, 2001. 

4. Gooch, W. A.; Burkins, M. S.; Palicka, R. Ballistic Development of U. S. High Density 

Tungsten Carbide Ceramics. J. de Physique IV 2000, 10, 735–741. 

5. Barker, L. M.; Hollenbach, R. E. Laser Interferometer for Measuring High Velocities of any 

Reflecting Surface. J. Appl. Phys. 1972, 43, 4669–4675. 

6. Dandekar, D. P. Response of Protective Ceramics Under Single and Multiple Impacts. Wave 

Propagation and Emerging Technologies, AMD-Vol. 188; Kinra, V. K., Clifton, R. J., 

Johnson, G. C., Eds.; ASME Press: NY, 1994; pp 133–141. 

7. Frutschy, K. J.; Clifton, R. J.; Mello, M. High Temperature Pressure Shear Plate Impact 

Studies on OFHC Copper and Pure WC. Shock Compression of Condensed Matter-1997; 

 Schmidt, S. C., Dandekar, D. P., Forbes, J. W., Eds.; American Institute of Physics: NY, 

1998, pp 463–466. 

8. Dandekar, D. P.; Weisgerber, W. J. Shock Response of a Heavy Tungsten Alloy. Int. J. of 

Plasticity 1999, 15, 1291–1309. 

9. Grady, D. E. Private communication, 1996. 

10. Bridgman, P. W. Studies in Large Plastic Flow and Fracture; Harvard: Cambridge, 1964; 

pp. 106–11. 
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