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
SPALLATION OF HOT PRESSED BORON CARBIDE CERAMIC
Peter T. Bartkowski, Dattatraya P. Dandekar, and David J. Grove
Army Research Laboratory, Weapons Materials Research Directorate,
Aberdeen Proving Ground, Maryland 21005-5069
Abstract This work describes the results of plane shock wave spallation experiments conducted on
Hot Pressed Boron Carbide marketed by Cercom as PAD B4C (>99% pure). Density of the material
was determined to be 2.508 ±0.016 Mg/m3 while the longitudinal and shear wave velocities were
measured at 13.49 ±0.18 km/s and 8.65 ±0.08 km/s, respectively. Spallation thresholds calculated
from the measured "pull-back" velocity were determined up to an impact stress of 15.5 GPa. The
values of spall threshold do not vary significantly with impact pressure but do exhibit a pulse width
dependency indicating a time dependent generation of defects. The value of spall strength of boron
carbide is 0.35 ± 0.07 GPa when shocked between 2 and 15.5 GPa. The values of release impedance
lie between 33 and 37 Gg/m2s and are in good agreement with the longitudinal impedance of 33.8 ±0.5
Gg/m2s at the ambient condition measured ultrasonically. The free-surface velocity profiles obtained
from these experiments were numerically simulated using Rajendran-Grove (R-G) ceramic model.
The paper provides the values of material constants required by the R-G ceramic model for boron
carbide.
INTRODUCTION
respectively. Table 1 lists the elastic constants as
determined from these measurements.
Specimens were cut, ground from ceramic
blocks to form 40 ±1 mm diameter discs. Flyer
discs were either PAD B4C or WC and had a
nominal thickness of 2 or 4 mm while the targets
were nominally 4 or 6 mm thick. The disc faces
were lapped and polished flat to 10 /im while the
disc faces were parallel to within one in 104.
The present investigation is a continuation of
our effort to determine the nature of deformation of
ceramic materials under shock induced tension.
Plane shock wave spallation experiments were
conducted on Cercom Corp.'s PAD B4C Boron
Carbide Ceramic. The particle velocity records
measured during the experiments were then used to
determine the material constants for the RajendranGrove (R-G) ceramic model.
EXPERIMENTS
MATERIAL
The general configuration for the shock
experiments is shown in Fig. 1. Plane shock
experiments were performed using ARL's 100 mm
bore Light Gas Gun. Diagnostics were composed
of projectile impact velocity measurement and free
surface particle velocity measurement of the rear of
the target specimen.
Impact velocity was determined by measuring
the time intervals between the shorting of 4 sets of
electrically charged pins located immediately in
front of the target. Velocity is calculated using premeasured distances between pins and the recorded
PAD B4C is a hot pressed ceramic over 99%
pure. It has a density of 2.508 ±0.016 Mg/m3 while
the single crystal density of B4C is 2.52 Mg/m3 [1]
which results in a pore volume fraction for PAD
B4C of approximately 0.5%. The average grain
size, as reported by the manufacturer, is 15 ptm.
Longitudinal and shear wave velocities were
measured ultrasonically. The longitudinal and
shear wave velocities were measured at 10 and 5
MHz to be 13.49 ±0.18 km/s and 8.65 ±0.08 km/s
779
TABLE 1. PAD B4C Material Properties
Property (units)
PAD B4C
Density (Mg/m3)
2.508 ±0.016
Average Grain Size (jLtm)
15
Void Fraction
0.005
Elastic Wave Velocity (km/s)
Longitudinal
13.49 ±0.18
Shear
8.65 ±0.08
Bulk
9.06 ±0.22
Elastic Modulus (Gg/m2s)
Longitudinal
33.8
Shear
21.7
Bulk
22.7
Poisson's Ratio____________0.151 ±0.014
FIGURE 1. Shot configuration
transit times to an accuracy of 0.5%.
Free surface velocity measurements of the
targets were made using VISAR (Velocity
Interferometer System for Any Reflector) [2]. The
precision of VISAR particle velocity measurements
is better than 1%.
Flyer thicknesses were chosen to produce pulse
widths of approximately 0.3 and 0.6 JLIS. Projectile
velocity and flyer material were varied to produce
impact stresses up to 15.5 GPa.
Aupb [8,9]. The spall strength is calculated using the
following formula:
<V«=i<
Where Zd is the elastic impedance of the
material.
A summary of the experiments conducted is
given in Table 2. All experiments were symmetric
impact in nature except for 826 and 846 where a
WC flyer was used, instead of boron carbide, to
reach a higher impact stress. Table 2 also lists the
determined impact shock state, release impedance
and calculated spall strength of PAD B4C as
determined from the steady free surface velocity
and pull back particle velocity change measured
from the VISAR waveforms. The values of release
EXPERIMENTAL RESULTS
The reported HEL of nearly fully dense boron
carbide is 15-19 GPa [3,4,5,6,7]. All experiments
conducted in this work were at 15.5 GPa or below
and are considered elastic. As such, the spall
strength of the material can be determined by the
magnitude of the pull back particle velocity change
TABLE 2. Summary of PAD B4C shock experiments
Flyer
Thickness
Pulse
Shot
Impact
#
Matl. Flyer Target Width Velocity
(mm)
(mm)
(km/s)
(MS)
B4C
4.052
5.956
0.60
0.6129
825t
WC
2.033
5.957
0.59
826
0.6106
B4C
4.053
5.958
0.60
0.4086
828f
B
C
4.051
5.956
0.60
0.2327
829t
4
B4C
4.063
5.960
0.60
833-1
0.4120
B4C
5.954
833-2
2.043
0.30
0.4120
B4C
4.053
5.956
840
0.60
0.1228
WC
5.954
846
2.028
0.59
0.5070
B4C
2.043
4.058
0.30
0.1229
910t
(1)
Stress
(GPa)
10.37
15.54
6.91
3.94
6.97
6.97
2.08
12.91
2.08
780
Shock State
Velocity
(km/s)
0.3065
0.4595
Density
(Gg/m5)
2.566
2.596
0.2043
0.1164
2.530
0.2060
0.2060
0.0614
0.3815
0.0615
2.547
2.547
2.547
2.519
2.581
2.519
Release
Imp.
(Gg/m2s)
32.8
35.0
33.4
34.6
36.3
35.7
35.4
33.0
36.8
Spall Strength
ViAUpb
Stress
(km/s)
(GPa)
0.0095 0.32±0.14
0.0070 0.24±0.20
0.0120 0.4110.10
0.0105 0.36±0.07
0.0090
0.0135
0.0095
0.0100
0.0125
0.30±0.10
0.46±0.10
0.3210.03
0.3410.17
0.4210.03
0.7
i1
ik
0.6 JL/S Spall
•
0.3 A/S Spall "
",
i>
0.11-
o.o
•
•
!"
, , . i ., , i , . , 1 , , . i , , , 1 . , ,
oD
2
4
6
8
10
i,, ,
12
14
11
-0.5
Impact Stress (QPa)
FIGURE 2. Spall stress vs. Impact stress
FIGURE 3. Particle Velocity Waveforms
2
impedance vary between 33 and 37 Gg/m s and
agree favorably with the ultrasonically measured
longitudinal impedance of 33.8 Gg/m2s. Plotted as
a function of impact stress in Fig. 2, the spall
strength can be seen to decline with increasing
impact stress. Two of the experiments (833-2 &
910) were conducted with a pulse width of 0.30 JLIS
instead of 0.6 /is to investigate the effects of pulse
width on the spallation process. These two
experiments at first seem to indicate a time
dependent generation and propagation of defects;
however if one considers the calculated
uncertainties given in Table 2, the difference
between the two pulse widths become insignificant.
Nonetheless, these values of spall strength are
consistent with Grady's values for Dow Chemical's
Boron Carbide Ceramic [5].
the crack growth, measured by the crack size
parameter a. Crack orientation is not considered
and assumed to be random throughout the material.
Permanent strain is a function of plastic flow only
and the strains from microcracking are elastic.
Plastic flow occurs in the model only under
compressive loading when the pressure exceeds the
HEL. The strains due to pore collapse are assumed
to be visco-plastic and are modeled using a pressure
dependent yield function.
Microcracks are allowed to grow when the
stress state satisfies a generalized Griffith criterion.
This criterion uses the material fracture toughness
and dynamic friction coefficient.
As damage
accumulates in the material from crack growth,
stress relaxation occurs. The pressure in the
material is a direct function of the degraded bulk
modulus.
R-G MODEL
Simulations
Four of the experiments listed in Table 2
(denoted by t) were simulated using the RG
ceramic model [10,11,12] running in EPIC finite
element code. The model is based on an elasticplastic cracking deformation process. The scalar
damage is measured by the crack density parameter
Y. The number of flaws remains constant while a
strain energy release based evolution law governs
The lowest velocity experiment (#910) was used
to determine the model constants.
These
determined constants for PAD B4C are given below
in Table 3. Three other experiments (#829, 828,
825) were then simulated using these constants.
The results of all four simulations can be compared
to the experimentally recorded particle velocity data
781
Table 3. RG Model Constants for PAD B4C
Description
Symbol
A
Static compressive strength (GPa)
C
Coefficient for strain rate dependence
Static fracture toughness (MPa Vm)
KIC
Initial void volume fraction
fo
Initial microcrack size (pirn)
a0
Initial microcrack density (m~3)
No'
Dynamic friction coefficient for mode II crack growth
H
Coefficient for mode II crack growth
n{
Spall criterion for damage evolution under high triaxial tensile loading (GPa)
& spall
Critical crack density parameter for pulverization
rP
Slope of linear strength-pressure relationship for pulverized material
A
Strength "cap" for pulverized material (GPa)
*Vmax
Constants
12.5
0.01
2.0
0.03
1.0
5xlOn
0.45
0.10
0.5
0.75
1.5
3.0
3. Wilkins, M. L. "Third Progress Report of Light
Armor Program." UCRL50460, Lawrence Livermore
National Laboratory, University of California, (1968).
4. Gust, W. H., and E. B. Royce, "Dynamic Yield
Strengths of B4C, BeO, and A12O3 Ceramics." J.
Appl. Phys. 42,276-295 (1971).
5. Grady, D. E., "Dynamic Properties of Ceramic
Materials," Sandia National Laboratory Report,
SAND 94-3266 (1995).
6. Kipp, M. E., and D. E. Grady, "Shock Compression
and Release in High-Strength Ceramics," Sandia
National Laboratory Report, SAND 89-1461 (1989).
7. Winkler, W., and A. J. Stilp, " Spallation Behavior of
TiB2, SiC, and B4C under Planar Impact Tensile
Stress," in Shock Waves in Condensed Matter-1991,
Ed. S. C. Schmidt et al., Elsevier Science, 1992, pp.
475-478.
8. Dandekar, D.P. and D.C. Benfanti, Journal of
Applied Physics 73, 673-679 (1993).
9. Dandekar, D.P. and P. Bartkowski, "Shock Response
of AD995 Alumina," in Proceedings of the AlP
Conference 309 Part /, 1994, pp. 733-736.
10. Rajendran, A.M., and D.J. Grove, International
Journal of Impact Engineering, Vol. 18, No. 6, 1996,
pp. 611-631.
11. Grove, D.J. & A.M. Rajendran, in Shock
Compression of Condensed Matter - 7997, Ed. S.C.
Schmidt et al., AIP, New York, 1998, pp. 255-258.
12. Grove, D.J. & A.M. Rajendran, in Shock
Compression of Condensed Matter - 7999, Ed. M.D.
Furnish et al., AIP, New York, 2000, pp 619-622.
in Fig. 3; the simulations are offset 30 m/s vertically
above the experimental data for clarity. Clearly, the
RG model does an excellent job of predicting
spallation behavior of PAD B4C.
CONCLUSION
Plane shock wave spallation experiments were
conducted on Cercom Corp.'s PAD B4C Boron
Carbide Ceramic.
Spallation thresholds were
determined vs. impact stress for two pulse widths of
0.3 & 0.6 /is. For 0.6 jits pulse width, a spall
strength of 0.35 ±0.07 GPa was determined. A
pulse width of 0.3 /is resulted in a higher spall
strength of approximately 0.47 GPa. Although
higher spall strengths were measured with the
shorter pulse width, a consideration of the errors in
measurement indicates that the differences may be
insignificant.
The values of release impedance were
determined to be between 33 and 37 Gg/m2s which
is in good agreement with the ultrasonically
measured value of 33.8 Gg/m2s.
The particle velocity records measured during
one of the experiments was then used to determine
the material constants for the Rajendran-Grove (RG) ceramic model. These constants were then used
to accurately predict spallation behavior at higher
impact stresses.
REFERENCES
1. Thevenot, F. "Boron Carbide-A Comprehensive
Review," J. Europ. Ceramic Soc. 6, 205-225 (1990).
2. L. M. Barker and R. E. Hollenbach, J. Appl Phys. 41,
4208-4226 (1970).
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