. 

Army Research Laboratory 

Aberdeen Proving Ground, MD 21005-5066 

ARL-TR-2456 Am-i12001 

Shock Response of Boron Carbide 

Dattatraya I? Dandekar 

Weapons and Materials Research Directorate, ARL 

Approved for public release; distribution is unlimited. 
Abstract 

Boron carbide is of interest because of its potential application in protective 

systems both for personnel and structures. Therefore it is necessary to determine 

its mechanical response when subjected to impact loading. The present work 

was undertaken to determine tensile/spa11 strength of boron carbide under 

plane shock wave loading and to analyze all available shock compression data 

on boron carbide materials obtained from different sources. The principal 

conclusions are: (1) the tensile/spa11 strength of boron carbide when shocked 

between 2 and 15 GPa is 0.35 f 0.07 GPa, (2) the existing shock compression data 

indicates that boron carbide tends to suffer a gradual loss of its shear strength as 

the magnitude of shock stress exceeds its Hugoniot Elastic Limit (HEL), i.e., 15- 

20 GPa, (3) the underlying reason or reasons for the inferred loss of shear 

strength under plane shock wave compression remains to be investigated, and 

(4) a general equation of state for boron carbide in its ambient phase is 

formulated which can adequately represent its hydrodynamic compression up to 

a strain of 0.25, i.e., to a maximum stress around 70 GPa. 

ii 
Acknowledgments 

f 

” 

P 

u 

Mr. P. K. Bartkowski performed spa11 experiments. Author is grateful to 

Dr. D. E. Grady for sharing his re-analyzed boron carbide data. Discussions with 

Drs. G. R. Johnson and T. J. Holmquist and J. M. Boteler were very helpful 

during the preparation of this report. 

..* 

111 
INTENTIONALLYLEWBLANK. 

iv 
Contents 

Acknowledgments 

. . . 

111 

List of Figures vii 

List of Tables ix 

1. Introduction 1 

2. Materials and Their Properties 2 

3. Shock Experiments 5 

4. Results 6 

4.1 Spa11 Experiments . . ..**...................***.~***.......... . . . . . ...*.*...**........**.*.............**.*.* 6 

4.2. Shock Hugoniot and Hydrodynamic Compression .*.......**....****..~....~*,., 11, 

5. Discussion 20 

6. Summary 22 

7, Future Work 23 

8. References 25 

Distribution List 27 

Report Documentation Page 33 

V 
INTENTIONALLYLEFTBLANK. 

vi 
List of Figures 

Figure 1. Configuration of spall experiments. .......................................................... 5 

Figure 2. Free surface velocity profiles recorded in B4C ......................................... 8

Figure 3. Effect of pulse width on spa11 threshold of BsC ....................................... 9

Figure 4. Effect of pulse width on spa11 threshold in B&J.. ................................... 10 

Figure 5, Spa11 strength of boron carbide vs. impact stress. ................................. 10 

Figure 6. Compression of boron carbide (Marsh 1980). ........................................ 12 

Figure 7. Hydrodynamic compression of boron carbide (Marsh 1980). ............ .13 

Figure 8. Compression of boron carbide (Wilkins 1968). ...................................... 14 

Figure 9. Compression of boron carbide (Gust and Royce 1971) ......................... 16 

Figure 10. Compression of boron carbide (Grady 1999) ......................................... 17 

Figure 11. Shock compression of near fully dense boron carbides ....................... .20 

Figure 12, Comparison of compression curves for boron carbide 

(Grady 1999) ................................................................................................ 22 

vii 
. . . 

Vlll 
List of Tables 

Table 1. Density and ultrasonic wave velocites for PAD B4C . . . ..**..*..e**..................* 3 

Table 2. Description of the various boron carbides used in shock wave 

studies . . . . . . . . . . ..***................**.......*.............~*......*. . . . . . ..*..*......~............*~.~..~..~.~..*.. 3 

Table 3. Densities and measured elastic properties’of boron carbides................**. 4 

Table 4. Experimental data for PAD BK . . . . . . ..~...~...**~.....**........~~*.........***...*....~.*...~.... 6 

Table 5. Results of shock wave experiments in PAD BsC .,............... *..** ,.............. **.. 7 

Table 6. Values of shock velocity in boron carbides just above the HELs. ..-.*, 15 

Table 7. Shock Hugoniot data on boron carbide. . . . . ..*...~..........*..~***....**..........*.~..... 18 

Table 8. Calculated values of shock-induced temperature on the solid 

Hugoniot of boron carbide *...**........*.,...**....*.......* . . . . . ..*..........**........*........... 19 

Table 9. Values of KI, K2, and & for boron carbides used in the various 

shock studies . . . . . . . ...*.*..........*.....*.**....*.* . . . ..*...*.~..*.*..........*.~~.......................*~~~ 21 

ix 
INTENTIONALLYLEFTBLANK. 

X 
1. Introduction 

f 

i 

Boron carbide is a potentially attractive material for a lightweight armor system 

due to its low density in comparison with the other monolithic ceramics such as 

AIZ03, Sic, and TiB2. Generally, the ability of ceramics to retain a high 

compressive strength and shear strength under compression make them 

attractive. However, the propensity of ceramics to fail under a small tensile 

stress due to their inherent low ductility presents a challenge to their use as a 

protective element of an armor system. To discover whether ceramics used in 

some combination with other materials can be used effectively in an armor 

system, it is important to determine their tensile strengths under impact loading 

condition. Shock Hugoniot of boron carbide has been investigated by Wilkins 

(1968), Gust and Royce (1971), McQueen et al. (1970), Pavlov&ii (1971), and 

Marsh (1980). Later Kipp and Grady (1989) and Grady (1995) reported shock and 

release response of two different boron carbides manufactured by Eagle Pitcher 

and Dow Chemical, respectively. Recently, Grady (1999) re-analyzed the shock 

compression data on boron carbide manufactured by Eagle Pitcher and Dow 

Chemical. The reanalyzed data is incorporated in this report. The boron carbide 

material used in the investigation of McQueen et al. (1970) was porous with only 

75-78s of the single crystal density, i.e., 2.52 Mg/m3. The densities of boron 

carbide used in the remaining investigations varied between 2.31 and 

2.52 Mg/m3. Hence, the data from the investigation of McQueen et al. (1970) is 

not included in this work, Grady (1995) also performed a limited number of 

experiments to measure spall strength of boron carbide manufactured by Dow 

Chemical. Winkler and Stilp (1992) reported spa11 strength of hot-pressed boron 

carbide. The source of their material was not reported. Brar et al. (1992) 

detenn&ned the Hugoniot Elastic Limits (HEL) of boron carbides with densities 

varying between 2.13 and 2.52 Mg/m 3. The material used by Brar et al. (1992) 

was manufactured by Dow Chemical. The present work was undertaken to 

measure spa11 strength of a hot-pressed BK, marketed as PAD B4C by CERCOM 

INC (hereafter referred to as B4C throughout this report to distinguish it from 

other boron carbide materials) and to analyze the existing shock Hugoniot data 

on the nonporous boron carbides previously mentioned to determine the 

equation of state and to determine the nature of the inelastic deformation above 

its HEL. 

At present, no independent equation of state measurements on boron carbide 

exist to compare with the derived equation of state presented in this work. 

However, the results presented in this report will enable modelers to simulate 

the ballistic data generated to test the impact worthiness of boron carbide. They 

also suggest important avenues for additional experiments on boron carbide for 
uses in applications where the impact-induced stress exceeds 20 GPa or steady 

state pressures at the impactor-target interface exceed that pressure. For 

example, an impact stress of 20 GPa is attained in a tungsten impactor and a 

boron carbide target when the velocity of impact is 1 km/s. 

2. Materials and Their Properties 

CERCOM INC manufactured the boron carbide used in the present study. This 

material is currently used in ballistic investigations at the U. S. Army Research 

Laboratory (ARL). A general description of the procedure used to fabricate PAD 

BJC provided by the manufacturer is as follows. CERCOM INC produces PAD 

B4C by hot pressing, i.e., simultaneous application of heat and pressure, blended 

powders at approximately 2,273 K and 138 MPa pressure, under vacuum. The 

composition of the material is at least 99% boron carbide (boron 76.5% minimum 

and carbon 22.5% maximum), aluminum (1,500 ppm), silicon (2,000 ppm), iron 

(1,500 ppm), and titanium as the major metallic impurities. About l/2% oxygen 

is usually present. The average grain size is 15 ~.un. The boron content is in the 

range of 76.5-77.1 weight-percent. The atomic ratio is slightly less than 41 as free 

boron results in the parts sticking to the graphite die used to fabricate the 

material. The values of measured density and ultrasonic longitudinal and shear 

wave velocities in nine specimens of this material are given in Table 1. The 

density was measured utilizing Archimedes’ Principle. The ultrasonic wave 

velocities were measured following the method developed by Papadakis (1967). 

The longitudinal and shear wave velocities were measured at 10 and 5 MHz, 

respectively. The average values and associated errors (twice the respective 

standard deviation) of density, longitudinal, and shear wave velocities are 

2.508 f 0.016 Mg/m”, 13.49 f 0.18 km/s, and 8.65 f 0.08 km/s, respectively. 

Boron carbide forms rhombohedral crystals and the lattice belongs to the R3m 

space group. The rhombohedral unit contains three molecules of B4C (Wyckoff 

1960). The single crystil density of boron carbide (B4C) is 2.52 Mg/m3 (Thevenot 

1990). Thus, the average porosity of PAD B4C material, in terms of pore volume 

fraction, is estimated to be 0.005. 

The values of elastic constants calculated from the measured values of densities 

and ultrasonic wave velocities in PAD B4C are given in Table 2. This table also 

provides properties of various boron carbide materials used in the earlier shock 

wave investigations. The values of the measured elastic wave velocities and 

derived elastic constants of boron carbide materials used by different 

investigators are similar except for the values of bulk moduli (263 GPa) and 

Poisson’s ratios (0.241) reported by Wilkins (1968). Further, the values of sound 
Table 1. Density and ultrasonic wave velocites for PAD BK. 

1 Specimen 1 Density 1 Wave velocities I 

(Mg/m3) uds) 

1 2.512 13.507 8.633 

2 2.489 13.424 8.581 

Table 2. Description of the various boron carbides used in shock wave studies. 

I I Gustand 1 I K&and 1 Win&r 1 1 Present 

Items 

Manufacturer 

Wilkins 

(1968) 

Royce 

(1971) 

Norton 

Grady 

(1995) 

Dow 

&ady 

(1989) 

Eagle 

and Stilp Brar et al. work 

(1992) (1992) 

DOW Cerwm 

Ichemica1l Picher I I Chemical I 

Processing Hot Prwsed Hot Hot 

Pre35ed 

Averagegrainsize 30 - 3 10 - l-3.5 15 

(Pd 

Pensity 2.50 2.503f 2.506 2.516 2.512f 2.1s2.52 2.5o8f 

Mg/ms) 0,017 0.005 0.016 

Void fraction 0.035 0.02 0.01 - - 0.163-0.0 0.005 

Wave vekcitk 1 I I I I I I 

b/S) 

L0ngitudinal (CL) 13;90 13.78 I 14.07 14.07 I 14.04 I 14.074.07 111.85-13.42 11.85-13.42 13.49iO.18 13.49 f 0.18 

Shear (Cs) 8.12 8.53 8.87 8.90 8,81 7.47-8.46 46 8.65f0.08 

Bulk (Cs) 10.26 9.63 9.65 9.57 9.72 8.12-9.20 .20 9.06fO f0.22 " 

ElasticModuli 

(GPa) 

Yol.u&s 03 

Shear(G) 

Bulk (K) 263 232 233 230 237 l&213 206k 11 

?oisson’s Ratio (v) 0.241 0.188 0.17 0.164 0.177 ~~~7-0.18 0.151f0.014 

1EL (GPa) 15.0 15.0 17-19 14.0-14.8 16.7 9.6-19.4 16.0~ 

Yield strewth (YF 10.2 11.5 10.7-15.1 11.3-11.9 13.1 7.6-15A 13.2~ 

(GPa) - 

Shear s&engthb 1 6.8 1 7.7 1 9XklO.l 1 7.5-7.9 1 8.7 1 5.1-10.1 1 8.8 

(GPa) - 

Lateral stwsb 

I I 

I 4.8 I 3.5 ( 3.5-3.9 ) 2.7-2.9 ) 3.6 1 2.0-4.2 1 2.8C 

(GPa) 

$a11 Strength (GPa) o&o.5 0.59477 Stress 

dependent 

Yield strength (Y) is calculated assuming Von Mises yield titerion, i.e., Y= {(1-2$/(1-v)) HEL. 

bShear strength equals (2/3) Y. Lateral stress equals {v/(1-v)} HBL. 

c HEL is assumed to be 16 GPa. It remains to be determined for PAD B4C. The values of Y and shear strength 

correspond to the assumed value of the HEL. 
wave velocities, and consequently, the values of elastic moduli for nearly fully 

dense boron carbide manufactured by Dow Chemical reported by Brar et al. 

(1992) are consistently smaller than the values of respective elastic parameters by 

Grady (1995). Lacking information about the technique used to measure the 

elastic wave velocities and the errors associated with these measurements, the 

reported systematic difference in the values of elastic properties of nearly fully 

dense boron carbide materials is hard to understand and explain The previous 

statement is made under an implicit assumption that the compositions of boron 

carbide manufactured by Dow Chemical used in their investigations were 

identical. Only Gust and Royce (1971) provide detail information about the 

elemental composition and boron to carbon ratio of their material. The 

composition of their material (in weight percentage) was Si (0.08), Ca (O-l), 

Mg (O-02), Ni (0.01-0.05), AhO3 (0.1-0.5), and the remainder was boron and 

carbon The boron to carbon ratio in their material was 3.93:1. 

Table 2 also includes the calculated magnitudes of yield strength, shear strength, 

and the lateral stress developed in boron carbide materials at the plane shock 

wave induced stress equal to their respective HEL values. The magnitude of 

shear strength is the difference between the value of the HEL and hydrodynamic 

pressure required to attain the strain at the HEL. The magnitude of lateral stress 

is the stress under inertial confinement that a material is subjected to during the 

plane wave shock experiments under uniaxial strain condition. Fowles (1961) 

and Jones and Graham (1971) discuss these relationships in detail. 

Table 3 gives the measured values of densities, longitudinal wave velocities (CL), 

and Poisson’s ratios (Y) for boron carbides (Brar et al. 1992). The magnitudes of 

Young’s, bulk, and shear moduli, and shear and bulk wave velocities given in 

this table are calculated from the measured quantities. It should be noted that 

the values of shear wave velocities given by Brar et al. (1992) are not consistent 

with the corresponding values of longitudinal wave velocities and Poisson’s 

ratios. 

Table 3. Densities and measured elastic properties of boron carbides (Brar et al. 1992). 

4 

1 Resent work 0.151 1 0.121 1 0.110 1 0.092 1 0.107 1 

B4C specimens used in the shock wave experiments were 40 f 1 mm in diameter. 

The thicknesses of the B4C targets, and B4C or WC are given in Table 4. 

Specimens used in these experiments were lapped until they were flat and 

parallel within 10 p. Precise thickness measurements were then taken to the 

nearest micron. Target specimens were then prepared to produce a diffuse 

reflective surface, for use with the laser and VISAR diagnostics. Using a diffuse 

reflective surface minimizes the chances of a data signal being lost due to slight 

misalignments that may occur during the shock wave experiments. Boron 

carbide specimens were hand polished using a diamond paste to produce the 

desired reflectivity. 

Table 4. Experimental data for PAD BK. 

Impact Pulse 

Experiment Thickness velocity width Free surface velocity 

bus-t) w-ds) Q.l.9) (km/s) 

Impactor ( Target Shock 1 Spa11 1 Reshock 

4. Results 

4.1 Spa11 Experiments 

Tables 4 and 5 summarize the results of spa11 experiments conducted on PAD 

B4C. Table 4 gives the measured values of target and impactor thicknesses, 

impact velocity, pulse width (i.e., duration of the shock compression), and free 

surface velocities corresponding to impact-induced shock, tension, and reshock 

(i.e., recompression of the spalled material). In this table, whenever a WC 

impactor was used in an experiment, the thickness of the impactor follows its 

identification. The remaining experiments employed boron carbide as the 

impactor. A tungsten carbide impactor was used to induce higher stresses in 

boron carbide. Table 5 gives the values of shock-induced stress, mass velocity, 

density change, release impedance, and spall-related parameters, namely, half 

the pull-back velocity (l/2 A upb ) and spa11 strength. 

6 

t 
f 

Table 5. Results of shock wave experiments in PAD BK. 

a Pulse widths in these experiments were 0.3 p. The pulse widths in the other experiments were 

0.6 p.s. 

The free surface velocity profiles recorded in experiments with a shock-induced 

compression duration of 0.6 p are shown in Figure 2. The profiles of these 

experiments are arbitrarily shifted in time to preserve the clarity of the figure. 

Thus relative time duration of each profile represents a chronology of events 

occurring due to propagation of shock waves. These profiles show a shockinduced jump in the free surface velocity of a given magnitude persisting for 

about 0.6 p followed by a sudden small decline in the free surface velocity 

(identified as spa11 signal in Figure 2) and finally attaining a velocity nearly 

identical in magnitude to the first jump in the free surface velocity, The column 

l/2 A upb in Table 5 is half the magnitude of difference in the free surface 

velocities under shock and spa11 given in Table 4. The errors associated with 

various entities in Table 5 are as follows: impact stress (l-6%), mass velocity 

(0.5%), density (1.5%), and release impedance (4.5%). The errors in the values of 

l/2 A upb range between 0.001 km/s and 0.006 km/s corresponding to free 

surface velocities 0.120 km/s in experiment 840 and 0.904 km/s in experiment 

826, respectively. Thus the values of spa11 threshold stress are subject to larger 

uncertainties. 

7 



4.2. Shock Hugoniot and Hydrodynamic Compression 

It is well known that the shock Hugoniot for nontransforming material with a 

low compressibility is adequately represented by a linear relationship between 

its shock velocity (U,) and particle velocity (u,). The slope (s) of this linear 

relationship is used in the calculations of the hydrodynamic compression of the 

material and the pressure derivative of its bulk modulus. The generated 

hydrodynamic compression of a material used in conjunction with its shock 

Hugoniot data permits a first order estimate of magnitude of shear strength 

sustained by the material under plane shock wave loading. This estimate 

represents a maximum limit of the shear strength a material can sustain under 

inertial confinement. Since, the shock velocity-particle velocity data reported by 

Marsh (1980) were presumed to be hydrodynamic in nature, it is examined first. 

However, the initial densities of boron carbide specimens used in the 

investigation varied between 2.312 to 2.452 Mg/m3. This presents a problem 

related to applicability of the magnitude of slope (s) obtained from their data for 

use in generating hydrodynamic compression for near fully dense boron carbide 

investigated by Wilkins (1968), Gust and Royce (1971), and Grady (1999). In the 

present work, the following procedure is adopted to solve the above-mentioned 

problem. Two linear relations between Us-up are computed using the least 

squares technique, The first linear relation is obtained using all the applicable 

shock velocity-particle velocity data, The second relation is obtained using shock 

velocity-particle velocity data corresponding to initial densities of boron carbide 

varying between 2.407 Mg/m3 and 2.452 Mg/m3. If these two relations do not 

differ significantly from one another, then the variability in the initial densities 

(i.e., porosities of boron carbide) does not affect the slope and, thereby, the 

magnitude of the pressure derivative of the adiabatic bulk modulus. This is a 

very unlikely case. If these two relations differ significantly, then the slope (s) of 

the second relation is more likely to be representative of the near fully dense 

boron carbide material. 

Figure 6 shows a plot of pressure (P) versus volume ratio (V/Vo) (i.e., ratio of 

initial density [p(O)1 and density [p(P)] at pressure (I’) for boron carbide). The 

initial densities varied between 2.31-2.39 Mg/m3 and 2.41-2.45 Mg/m3. This 

figure shows that Pressure-volume ratio coordinates of boron carbide with 

densities in the above two ranges do not appear to lie on a single locus. Further, 

this figure shows a cusp around 15 GPa due to the elastic precursor. In other 

words, the Hugoniot data reported by Marsh (1980) is not totally hydrodynamic 

in nature. Hence, the hydrodynamic compression of boron carbide must be 

generated from a linear relationship between shock and particle velocities 

measured at and above the pressure when a single shock wave carries the 

material in its final compressed state. This pressure is determined by the 

intersection of the elastic Rayleigh line extending from zero pressure with the 

11 



Table 6. Values of shock velocity in boron carbides just above the HELs. 

I Wilkins (1968) 1 Gust and Rovce (1971) 1 Grady (1999) 

Stress 

GPa) 

21.1 

21.5 

Shock 

Velocitya 

k-ds) 

9.58 

9.75 

Stress 

(GPa) 

20.4 

21.2 

Shock 

Velocity 

&ds) 

8.03 

9.40 

Stress 

(GPa)b 

23.8/24.6 

29.0/31.2 

Shock 

Velocityb 

b-ds) 

8.13/9.04 

8.48/9.95 

22.4 10.39 20.4 9.20 40.2/40.5 9.10/9.20 

24.0 9.57 26.6 9.34 25.8/26.5 8,68/9,33 

24.3 9.78 27.0 9.14 55.9/56.0 10.18/10.22 

27.1 9.93 29.4 10.77 

27.5 10.33 28.4 9.79 

28.4 10.09 26.8 9.79 

38.6 11.51 26.2 9.51 

39.7 11.44 23.1 9.16 

I 43.8 I 11.34 1 23.7 1 9.62 1 I I 

26,l 10.26 

28.6 9.19 

37.0 10.05 

37.6 10.02 

42.5 11.07 

41.3 10.25 

59.3 11.34 

78.4 12.14 

91.7 12.4 

87.0 1227 

a Shock velocities were calculated from the stress and densities given in Holmquist et al. (1999). 

b The set of numbers preceding the slash sign are obtained using Transmitted technique and 

those following the slash are obtained by using Pulse-echo technique. 

Figure 9 shows the calculated hydrodynamic compression for the boron carbide 

materials investigated by Gust and Royce (1971). This figure shows the boron 

carbide material used by Gust and Royce does not appear to suffer a total loss of 

its shear strength like the material used in the earlier investigation by Wilkins 

(1968). However, the values of shock velocity just above the HEL vary between 

8.03 km/s and 9.19 km/s, less than the value of the initial local bulk sound 

velocity 9.63 f 0.43 km/s (Table 6). To understand this contradictory behavior of 

boron carbide used in the investigation of Gust and Royce (1971), Figure 9 

includes the bounds of hydrodynamic compression of their material (shown by 

the dashed loci) generated from the precision of the bulk modulus 232 + 21 GPa 

(Table 2). It shows that from the experimental data of Gust and Royce (1971), the 

material must be undergoing some loss of shear strength, but the loss is not total. 

15 


26 GPa seemed to be influenced by the propagation of the elastic precursor. The 

values of initial shock velocity and s calculated from the linear relation between 

the remaining three shock wave velocity and particle velocity measurements are 

10.63 km/s and 0.688. The value of the initial bulk modulus of this material 

calculated from the initial shock velocity and density is 283 GPa. In order to 

understand the implication of the difference in the values of s obtained from the 

investigations of Marsh (1980) and Pavlovskii (1971), the values of pressures 

corresponding to the magnitudes of compression of boron carbide in the 

experiments of Pavlovskii (1971) were calculated assuming the value of s = 0.914 

and values of bulk moduli 232 and 283 GPa, respectively. The results of these 

calculations are given in Table 7. These results show that the pressures obtained 

from his experiments and those calculated are reasonably close to one another 

except at 220 GPa. The calculated pressures required to attain a density of 

4.22 Mg/m3 in boron carbide in solid state are 237-289 GPa not the observed 

220 GPa. This leads one to wonder whether such a density in boron carbide may 

be attained through the melting of boron carbide. Thus the data generated by 

Pavlovskii (1971) on boron carbide was partly in solid state and partly in liquid 

state. The reasonableness of this idea may be discerned from the calculated 

values of shock-induced temperature associated with these pressures and 

volume changes in solid boron carbide (Table 8). Temperature along the 

Hugoniot (TH) at a given compression (c=Vo/V) is calculated from the following 

relation (Carter 1973): 

TH= TO exp. [y&l>&"] 

+(s K&oCv) exp.hd5-1)/52]~ b-5 (s-U -3 (S-1)” exp.[-y&-M2] dc}, (5) 

where yois the ambient Gruneisen gamma, Cv is the specific heat at constant 

volume, and the remaining symbols have already been identified earlier in the 

report. 

Table 7. Shock Hugoniot data on boron carbide. 

Data from experiments 

(Pavlov&ii 1971) 

Shock Particle Volume 

velocity velocity Pressure Density ratio 

(kdsj b.dsj Wd Wg/i3) 

11.39 0.91 26.0 2.72 0.9228 

11.50 1.25 36.1 2.82 0.8901 

12.28 2.43 75.0 3.13 0.8019 

14.73 5.96 220.0 4.22 0.5948 

Calculated pressures 

GW 

s = 0.914 

Ko=232GPa 1 &=283GPa / 

68 84 

237 289 

F 

, 

18 
l 

Table 8. Calculated values of shock-induced temperature on the solid Hugoniot of 

boron carbide. 

s = 0.914 8 = 0.688 

Volume ratio Ko = 232 GPa 

0.9228 345 

0.8901 396 

0.8019 804 

0.5948 8853 

KJ = 283 GPa 

343 

387 

761 

6124 

These calculations were done assuming the ratio of Gruneisen Gamma ($ and 

volume is constant. The values of Gruneisen Gamma (‘yo) and specific heat at 

constant volume for boron carbide at the ambient condition are 1.282 and 

0.9616 J/gm/K. The calculated temperatures on the Hugoniot due to volumetric 

compression of 0.595 in boron carbide in solid state with s = 0.688 and 

Ko = 283 GPa and s = 0.914 and Ko = 232 GPa are 6124 K and 8853 K, respectively. 

The melting temperature of boron carbide at the ambient pressure is 2703 K. 

Thus the requirement of around 237-289 GPa to obtain a density of 4.22 in solid 

boron carbide and attainment of temperature in the range of 6124-8853 K 

strengthens the suggestion that the boron carbide Hugoniot determined by 

Pavlov&ii (1971) could easily traverse solid and liquid states. The author is not 

aware of any experimental data pertaining to the change in melting temperature 

of boron carbide with pressure to substantiate the above suggestion. It is further 

complicated by the well-known fact in the shock literature that solid to liquid 

transition cannot be solely detected from the shock velocity and particle velocity 

data (McQueen et al. 1970). 

In view of the above and a similarity in the deformation locus of boron carbide 

and that found in AlN that undergoes a phase transition around 20 GPa 

(Dandekar et al. 1994) there is a need to conduct careful shock experiments on 

boron carbide at comparable stresses to investigate whether the indicated loss of 

shear strength is mechanical in nature or due to a phase transition. The results of 

such an investigation will have an important impact on the use of boron carbide 

in an armor system. Briefly, all the currently existing shock Hugoniot data on 

boron carbides, irrespective of their sources, indicate that boron carbide suffers a 

partial or a total loss of its shear strength when shocked to and beyond 

304 GPa. Consistent with the suggested loss of boron carbide and possible 

melting of it accompanied with a small volume change at the highest 

compression data, almost all the shock Hugoniot data on boron carbide with 

initial density equal to and greater than 2.50 Mg/m3 very nearly lie on a single 

locus (Figure ll), 

19 

coefficients for the materials used in the previous shock experiments are set out 

in Table 9. These coefficients are all positive except the value of K2 in the work 

of Johnson and Holmquist (1999). Further, Johnson and Holmquist determined a 

value of K3 that is 4 to 4.5 times larger than the other three values found for I&. 

The reason for the observed discrepancies in the values of K2 and I& is due to the 

fact that JH2 material model applied to simulate penetration requires a material 

to have non-vanishing shear strength, and so the constants K2 and K3 are 

determined through an iterative procedure which will simulate reasonably well 

the shock wave profiles and match the ballistic experiment data. In brief, their 

coefficients other than K1 do not reflect observed loss of shear strength of boron 

carbide when shocked above 30-40 GPa as described in the last section. Hence, 

the compression of boron carbide based on their coefficients is not consistent 

with experimental evidence for a loss of shear strength in boron carbide 

presented in the last section, but it is only an artifact of the JH2 model. Since, 

Johnson and Holmquist (1999) chose the shock wave profiles in boron carbide 

obtained by Grady to calibrate their penetration model, it is of interest to plot 

Hugoniot data from Grady (1999) and hydrodynamic compressions of boron 

carbide obtained from equation (6), and equation (8) using the coefficients from 

the present work and those given by Johnson and Holmquist (1999). Such a plot 

is shown in Figure 12. 

Table 9. Values of K, Kz, and J& for boron carbides used in the various shock studies. 

I I Kl I K2 I K3 I 

riiizls (1968) 1 263 1 480 1 659 1 

Gust and Royce (1971) 232 424 581 

Grady (1999) 233 426 584 

Tohnson and Holmauist (19991 233 -593 2800 

The effect of truncation to the third degree of r~ is insignificant to 70 GPa. For 

example, when 11 is 0.25, the pressure calculated from the third degree 

polynomial is underestimated by 5%. However, the use of coefficients based on 

the model of Johnson and Holmquist leads to a much larger error in the value of 

pressure. Moreover, estimated pressures require that boron carbide retain shear 

strength contrary to the inference that it has no shear strength left above 30 GPa. 

Thus, the hydrodynamic compression of boron carbide based on the coefficients 

determined by Johnson and Holmquist could lead to erroneous results if used in 

conjunction with some other model for simulations of ballistic events. 

21 

compression of boron carbide in the investigation of Marsh was attained in 

its solid state, the compression in the investigation of Pavlov&ii was 

attained through solid and melt states of the material. 

(6) The equation of state obtained from the hydrodynamic compression of 

boron carbide differ significantly from the equation of state used by 

Johnson and Holmquist (1999). The difference in the representation of the 

hydrodynamic compression arises from the fact that the material model 

proposed by these authors to simulate accurately the ballistic data require a 

material to retain shear strength under shock compression. This is contrary 

to the response of boron carbide under plane shock wave compression 

when the compressive stress exceeds 30 GPa. 

7. Future Work 

. 

Since the stresses where the loss of strength in boron carbide is inferred can be 

easily reached at ordinance velocities, it will be necessary to confirm inferred loss 

of shear strength in boron carbide under shock induced compression 

independently. This can be achieved by conducting appropriate shock wave 

experiments above the HEL and by an independent determination of the 

equation of state of boron carbide. It will be most useful to generate shock data 

on PAD BK at stresses larger than those presented in this report to determine its 

HEL and the nature of its inelastic deformation beyond the HEL. It is equally 

important to determine the mechanism responsible for the loss of shear strength 

of boron carbide under shock loading. One of the possible mechanism may be 

due to its inability to deform plastically above its HEL like single crystal sapphire 

(Graham and Brooks 1971). Recently, Mashimo and Uchino (1997) reported that 

boron carbide exhibited a jagged wave profile at the free surface irrespective of 

whether its deformation was totally elastic or elastic-inelastic. The jaggedness of 

the observed wave profiles was attributed to heterogeneous shock front motion 

(i.e., heterogeneous deformation of boron carbide). Based on the observed 

spatial .extent of the jaggedness in their profiles, they suggested that the 

macroscopic heterogeneous deformation behavior displayed by the boron 

carbide was not likely to be due to a dislocation process but may be due to 

propagation of cracks, cleavages, and melting zones. A second possibility is that 

boron carbide may be undergoing a phase transition where its Hugoniot points 

lie below the hydrodynamic compression curve like the case of aluminum nitride 

(Dandekar et al. 1994). At present, there exists no data that permits inference 

about the actual physical state of a nontransforming solid when it suffers a total 

loss of shear strength under plane shock wave compression. This leaves the 

physical meaning of the inferred loss of shear strength unanswered. 

23 
INTENTIONALLYLEFTBLANK. 

24 
8. References 

. 

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Fowles, G. R. “Shock Wave Compression of Hardened and Annealed 2024 

Aluminum.” JournaI of Applied Physics, vol. 32, pp. 1475-1487,1961. 

Grady, D. E. “Dynamic Properties of Ceramic Materials.” SAND 94-3266, 

Sandia National Laboratories, 1995. 

Grady, D. E. ‘Technical Presentation and Minutes, 24th Semiannual Meeting, 

DOD/DOE MOU, TCG-I.” Los Alamos National Laboratories, Los Alamos, 

NM, 15-16 December 1999. 

Graham, R. A., and W. P. Brooks. “Shock-Wave Compression of Sapphire From 

15 to 420 Kbar the Effects of Large Anisotropic Compressions.” Journal of 

Physics Chemistry of Solids, vol. 32, pp. 2311X330,1971. 

Gust, W. H., and E. B. Royce. ‘Dynamic Yield Strengths of BK, BeO, and Al203 

Ceramics.” Journal of Applied Physics, vol. 42, pp. 276-295,1971. 

Holmquist, T. J., A. M. Rajendran, D. W. Templeton, and K. D. Bishnoi. “A 

Ceramic Armor Material Database.” TARDEC Technical Report No. 13754, 

U.S. Army Tank-automotive Research, Development, and I Engineering 

Center, 1999. 

25 
Jones, 0. E., and R. A. Graham. “Shear Strength Effects on Phase Transition 

Pressures Determined From Shock-Compression Experiments.” Accurate 

Characterization of the High-Pressure Environment, National Bureau of 

Standards Special Publication 326, ed. E. C. Lloyd, pp. 229-237,1971. 

Johnson, G. R., and T. J. Holmquist. “Response of Boron Carbide Subjected to 

Large Strains, High Strain Rates, and High Pressures.” Journal of Applied 

Physics, vol. 85, pp. 8060-8073,1999. 

Kipp, M. E., and D. E. Grady. “Shock Compression and Release in High-Strength 

Ceramics.” SAND 89-1461, Sandia National Laboratories, 1989. 

Manghnani, M. H., Y. Wang, F. Li, P. Zinin, and W. Rafaniello. “Elastic and 

Vibrational Properties of B4C to 21 GPa.” Science and Technology of High 

Pressure, eds. M. H. Manghnani, W. J. Nellis, and M. F. Nicol, Hyderabad, 

India: Universities Press, pp* 945-948,200O. 

Marsh, S. I?. LASL Shock Hugoniot Data. Ed. S. P. Marsh, Berkley, CA: University 

of California Press, pp. 245-246,198O. 

Mashimo, T., and M. Uchino. “Heterogeneous Free-Surface Profile of B4C Under 

Shock Compression” Journal of Applied Physics, vol. 81, pp. 7064-7066,1997. 

McQueen, R. G., S. P. Marsh, J. W. Taylor, J. N. Fritz, and W. J* Carter. ‘The 

Equation of State of Solids From Shock Wave Studies.” In High-Velocity Wave 

Phenomenu, ed. R. Kinslow, New York, NY: Academic Press, pp. 29M17, 

521-568,197O. 

Papadakis, E. P. ‘2lltrasonic Phase Velocity by the Pulse-Echo-Overlap Method 

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Pavlov&ii, M. N. “Shock Compressibility of Six Very Hard Substances.” Soviet 

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Ruoff, A. L. “Linear Shock-Velocity-Particle-Velocity Relationship.” Journal of 

Applied Physics, vol. 38, pp. 497w980,1967. 

Thevenot, F. “Boron Carbide-A Comprehensive Review.” Journal of European 

Ceramic Society, vol. 6, pp. 205-225,199O. 

Wilkins, M. L. ‘Third Progress Report of Light Armor Program.” UCRL50460, 

Lawrence Livermore National Laboratory, University of California, CA, 1968. 

Winkler, W., and A. J. Stilp. “Spallation Behavior of Ti&, Sic, and B4C Under 

Planar Impact Tensile Stress.” Shock Waves in Condensed Matter-1992, 

eds. S. C. Schmidt, R. D. Dick, J. W. Forbes, and D. G. Tasker, Elsevier 

Science, pp. 47H78,1992. 

Wyckoff, R. W. G. Crystal Structures. Vol. 2, New York, NY: 

John Wiley, pp. 13&139,1960. 

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REPORT DOCUMENTATION PAGE Form Approved 

OMB No. 07044188 

Shock Response of Boron Carbide 

ATTN: AMSRL-WM-TD 

Aberdeen Proving Ground, MD 2 1005-5066 

AGENCY REPORT NUMBER 

11. SUPPLEMENTARY NOTES 

12a. DlSTRlBUTlON/AVAllABlLlTY STATEMENT 

Approved for public release; distribution is unlimited. 

12b. DISTRIBUTION CODE 

13. ABSTFtACT(Max~mum 200 words) 

Boron carbide is of interest because of its potential application in protective systems both for personnel and 

stTllchlres. Therefore it is necessary to determine its mechanical response when subjected to impact loading. The 

present work was undertaken to determine tensile/spa11 strength of boron carbide under plane shock wave loading and to 

analyze all available shock compression data on boron carbide materials obtained from different sources. The principal 

conclusions are: (1) the tensile/spa11 strength of boron carbide when shocked between 2 and 15 GPa is 0.35 f 0.07 GPa! 

(2) the existing shock compression data indicates that boron carbide tends to suffer a gradual loss of its shear strength z 

the magnitude of shock stress exceeds its Hugoniot Elastic Limit (HEL), i.e., 15-20 GPa, (3) the underlying reason or 

reasons for the inferred loss of shear strength under plane shock wave compression remains to be investigated, and (4) a 

general equation of state for boron carbide in its ambient phase is formulated which can adequately represent its 

hydrodynamic compression up to a strain of 0.25, i.e., to a maximum stress around 70 GPa. 

14. SUWECT TERMS 

boron carbide, spall, shear strength, equation of state 

15. NUMBER OF PAGES 

38 

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