CP620, Shock Compression of Condensed Matter - 2001
edited by M. D. Furnish, N. N. Thadhani, and Y. Horie
© 2002 American Institute of Physics 0-7354-0068-7/02/$ 19.00
ON THE FAILURE OF BORON CARBIDE UNDER SHOCK
N.K. Bourne and G.T. Gray III*
Royal Military College of Science, Cranfield University, Shrivenham, Swindon, SN6 8LA, UK.
*Los Alamos National Laboratory, MS-G755, Los Alamos, NM 87545, USA.
Abstract. The failure of brittle materials during uniaxial, compressive shock-loading has been the
subject of extensive recent research. For instance, the physical interpretation of the yield point, the
Hugoniot elastic limit (HEL), remains poorly understood. Stress and particle velocity records show B4C
exhibits a type of behaviour different to that of other brittle materials. A number of features have been
measured to investigate these features. In other ceramics, failure has been seen to occur behind a
travelling boundary that follows a shock front that has been called a failure wave, across which the
strength of the material is dramatically reduced. In order to elucidate whether this failure process
occurs, gauges were embedded to measure the lateral stress behind the shock front in B4C. As in other
materials the stress in B4C was seen to rise across a failure front. However, this phenomenon only
occurred over certain stress ranges. More significantly, the failure penetrated further into the ceramic
than has been seen in other materials. A mechanical interpretation is suggested to explain the observed
behaviour of B4C.
called a fracture, or more lately a failure wave.
Later work (11) confirmed the existence of these
fronts by measuring spall and shear strengths ahead
of and behind them, using manganin stress gauges.
The shear strength of the material may be calculated
from the offset of the Hugoniot from the hydrostat,
and for perfectly elastic-plastic materials this may
be estimated to be 2/3 Y (where Y is yield strength
of the material calculated from the HEL assuming a
Von Mises yield criterion). Evaluating the value for
twice the shear strength in this manner gives 13
GPa using Tresca/Von Mises or 8 GPa if the
Griffith's criterion is adopted (12) given the value
for the HEL. This will be used later to suggest the
brittle nature of the yield in this material.
Recent experiments of this type have used the
measurement of the lateral stress to map the
behaviour of a range of glasses and polycrystalline
materials including aluminas, SiC (13) and titanium
diboride. This range has been extended to include
A1N (14) and, in the work presented here, B4C. As
will be shown, this measurement of the failed
strength may provide a means to assess the ballistic
worth of a material.
INTRODUCTION
Interest in boron carbide stems from its low
density and substantial compressive strength and
there have thus been several studies of its properties
(1-5). Investigations into the dynamic compressive
strengths of brittle materials have been extensive
and various values for the Hugoniot elastic limits
(HELs) have been reported (6). That of boron
carbide has been measured to lie between 15 and 20
GPa according to the differing grain size and
production routes of the materials investigated (7)
but lies at 16.0 GPa for this material (5). The
material displays a spall strength of ca. 0.35 GPa at
stresses below its HEL (5), which indicates its
weakness in tension. Additionally, ballistic
performance data (8, 9) has shown that the material
does not perform as well as may have been
expected. It is know that the shear strength shows a
dramatic loss of strength in post-yield flow, which
may be related to its unusual crystal structure (7).
Rasorenov et al. (10) were the first to observe
the phenomenon of delayed failure behind the
elastic wave in glass, across a front that has been
775
RESULTS AND DISCUSSION
EXPERIMENTAL
12
Impact velocity was measured to an accuracy of
0.5% using a sequential pin-shorting method and tilt
was fixed to be less than 1 mrad by means of an
adjustable specimen mount. Impactor plates were
made from lapped copper and aluminium discs and
were mounted onto a polycarbonate sabot with a
relieved front surface in order that the rear of the
flyer plate remained unconfined. Targets were flat
to less than 2 jam across the surface. Lateral stresses
were measured using manganin stress gauges of
type J2M-SS-580SF-025 (resistance 25 Q). The
gauges had an active width of 240 jam and were
placed at varying distances from the impact face as
shown in Fig. 1.
10
0.5
Figure 2 shows the lateral stress histories
recorded for B4C at longitudinal stresses of 6.2, 9.4,
15.6 and 18.2 GPa. The lowest of these histories
(where the flyer plate was aluminium) show no
failure wave and consist of a rise followed by a flattopped shock pulse. The impacts, in the case of the
higher impact velocities^ were conducted in each
case with 5 mm thick, copper and tungsten alloy
flyer plates onto 25 mm thick B4C targets with
gauges positioned at 2 and 6 mm from the impact
face. The longitudinal stresses for each of these
impacts were calculated from the published
Hugoniot (5).
All of the other histories recorded show
evidence of failure waves occurring in the B4C
targets. Additionally, the gauges placed 6 mm from
the impact plane show evidence of this behaviour
indicating that boron carbide does not confine the
failure to a surface region in the same manner as
other
polycrystalline
ceramics
previously
investigated (16). This may be a consequence of the
high sound speed in B4C. The experiments
conducted to date have been at relatively low
stresses mainly in the elastic region so further
results are necessary to define this behaviour.
The traces for the shots at a longitudinal stress
of 9.4 GPa show a ramped rise and then the lateral
stress at 6 mm rises farther, after ca. 1 jus, to its
final value. This trace is similar to that seen in
glasses investigated previously (13).
The lateral stress, <ry was used along with the
longitudinal stress, erx to calculate the shear strength
of the material rthus
This quantity has been shown to be a good indicator
of the ballistic performance of a material (15). This
method of determining the shear strength has the
advantage of being direct since no modelling and
calculation of the hydrostat is required.
The material used in this study was a hotpressed B4C manufactured by Cercom Inc. The
density of this hot-pressed material was
2.52 gm cm'3 or 99.5% theoretical maximum
density. Materials' data are presented in Table 1.
TABLE 1. Properties of Boron Carbide tested
gem'
2.52
mm ps
13.9
mm fts
8.7
0.18
1.5
FIGURE 2. Lateral stress histories measured at 2 and 6 mm from
the impact face of boron carbide targets shot to stresses of 6.2,
9.4, 15.6, and 18.2 GPa.
FIGURE 1. Experimental arrangement for lateral and longitudinal
stress experiments, a) Longitudinal and lateral stress gauge b).
Multiple lateral gauge measurements.
Purity
%
99.5
1
Time (jus)
HEL
GPa
16.0
776
The dark points are measured ahead of the
failure front whilst the open points are those behind.
The lowest impact recorded was below the failure
wave threshold. This behaviour is seen in glasses
but has only been noted for TiB2 previously in
polycrystalline materials (17). The values of
strength for the un-failed B4C increase along the
elastic line until near the HEL. The material above
the HEL then loses strength in what has been
dubbed the un-failed material, which suggests that
this terminology is incorrect and that some yielding
or non-linear dissipative process is occurring. This
phenomenon remains to be fully explained.
However, it is consistent with the findings of other
workers (7).
Above this stress, ca. 8 GPa, there are two
strengths for each longitudinal stress. The failed
values are seen to increase with stress but the value
for 2 T is ca. 1 GPa. It is assumed that by 20 GPa the
material fails in compression as the shock rises.
It may be noted that assuming that the failure of
boron carbide may be ascribed to brittle failure, the
yield strength may be calculated from the failed
strength using the Griffith's criterion. The measured
failed value of 2 r at close to the HEL is 7.2 GPa
which gives a calculated yield stress of 14 GPa.
This is below the quoted HEL for B4C but
nevertheless suggests that brittle fracture is
responsible for the elastic limit in this material.
There was only one gauge, at 2 mm, in the
experiment conducted at a longitudinal stress of
15.6 GPa. The stress is seen to rise, again in a
ramped manner, to a value ofca. 5 GPa and then in
a second rise to a value of ca. 9 GPa. The
corresponding longitudinal stress is calculated to be
very close to that of the HEL in B4C.
The highest stress experiments tested, above the
HEL, exhibited a pair of complex traces. Both
gauges at 2 and 6 mm displayed a ramped rise to
ca.2 GPa and then a more rapid climb. The gauge at
2 mm reaches a plateau and then relaxes back. The
gauge at 6 mm plateaus once and then rises again to
a similar value to that at the first gauge. Just above
the HEL the shock speed will be slow and it is
thought that these later fronts may represented the
shock arrival.
12
10
? 8
& 6
HEL
5
10
15
Longitudinal Stress (GPa)
20
CONCLUSIONS
FIGURE 3. Deviatoric response ahead of and behind the failure
wave for the gauges and shots discussed. The diagonal line is the
calculated elastic assuming v. The HEL is indicated.
The dynamic compressive strength of B4C has
been investigated by mounting piezoresistive
gauges to measure the longitudinal and transverse
stress components behind the shock. A failure front
has been observed to propagate which can penetrate
much further than is seen in other polycrystalline
materials investigated. Like TiB2, but unlike SiC
and A12O3, there is a stress threshold below which
the failure wave does not initiate in B4C. The
measured HEL correlates with the failed strength
seen by the gauges through the Griffith's brittle
yield criterion.
Fig. 3 shows the value of twice the shear
strength plotted against the longitudinal stress and
calculated from the measured values presented in
Fig. 2. The diagonal line is the calculated elastic
response to the induced longitudinal stresses
calculated from the formula
2r =
\-2v
\-v
(2)
where vis Poisson's ratio.
777
particles flow and rotate so that it represents a
maximum strength of comminuted materials. Others
have shown that initial shear strength is important
in the response of metals to penetration (15). The
ranking of the failed strengths shown to the right of
the figure represents an equivalent material property
for brittle solids.
It is hoped that this work, and other observations
of this type, will stimulate further consideration of
the response of brittle materials to shock loading.
2()——————r^———,———,———
Glass
IB Scatter
Oabbro i Tvtrical error
,
15
Al,03
. - A1N
<
r = B4c
tlOK s^
v»
*N
h
ra
r
51
10
a
15
20
REFERENCES
25
1. Brar, N.S., Rosenberg, Z. and Bless, S.J., in Shock
Compression of Condensed Matter, (ed. S.C. Schmidt,
R.D. Dick, J.W. Forbes, and D.G. Tasker), Amsterdam:
North-Holland, pp. 467-470, (1992).
2. Grady, D.E., J. Phys. IVFrance 4, 385-391 (1994).
3. Mashimo, T. and Uchino, M., in Shock Compression of
Condensed Matter, (ed. S.C. Schmidt and W.C. Tao),
Woodbury, New York: American Institute of Physics,
pp. 531-534, (1996).
4. Johnson, G.R. and Holmquist, T.J., J. Appl Phys. 85,
8060-8073 (1999).
5. Dandekar, D.P., (2001), Army Research Laboratory
Report, ARL-TR-2456.
6. Gust, W.H. and Royce, E.B., J. Appl. Phys. 42, 276-295
(1971).
7. Grady, D.E., in Shock Compression of Condensed
Matter, (ed. S.C. Schmidt, R.D. Dick, J.W. Forbes, and
D.G. Tasker), Amsterdam: Elsevier, pp. 455-458, (1992).
8. Orphal, D.L., Franzen, R.R., Charters, A.C., Menna, T.L.
and Piekutowski, A.J., Int. J. Impact Engng 19, 15-29
(1997).
9. Gooch, W.A., Burkins, M.S., Hauver, G., Netherwood,
P. and Benck, R., J. Phys. IVFrance 10, 583-588 (2000).
10. Rasorenov, S.V., Kanel, G.L, Fortov, V.E. and
Abasehov, M.M., High Press. Res. 6, 225-232 (1991).
11. Brar, N.S. and Bless, S.J., High Press. Res. 10, 773-784
(1992).
12. Rosenberg, Z., in Shock Compression of Condensed
Matter, (ed. S.C. Schmidt and W.C. Tao), Woodbury,
New York: American Institute of Physics, pp. 543-546,
(1996).
13. Bourne, N.K., Millett, J.C.F., Rosenberg, Z. and Murray,
N.H., J. Mech. Phys. Solids 46, 1887-1908 (1998).
14. Pickup, I.M. and Bourne, N.K., inShock Compression of
Condensed Matter, (ed. M.D. Furnish, N. Thadani, and
Y. Horie), Melville, New York: American Institute of
Physics, pp. in press, (2001).
15. Meyer, L.W., Behler, F.J., Frank, K. and Magness, L.S.,
in Proc. 12th Int. Symp. Ballistics, pp. 419-428, (1990).
16. Bourne, N.K., Rosenberg, Z. and Field, I.E., Proc. R.
Soc. Lond. A 455, 1267-1274 (1999).
17. Bourne, N.K. and Gray III, G.T., Proc. R. Soc. Lond. A.
in press (2001).
FIGURE 4. Deviatoric response at 2 mm from impact face of
presented materials. Gray shaded-region of elastic response and
spread of failed strengths.
An assessment of the relative response to shock
loading of many common brittle materials may be
assessed by plotting the shear strength data on a
common plot. In Fig. 4, the known values of the
longitudinal and lateral stresses are used to
calculate the shear strengths of three glasses, the
volcanic gabbro, and the polycrystalline ceramics
SiC and TiB2 ahead and behind the failure fronts.
Now this work and another in these proceedings
(14) has added B4C and A1N to these data (13). No
indication is given in this plot of the time that it
takes to travel from the un-failed to the failed state
which is critical in determining ballistic resistance
(dwell) before penetration begins since the front of
the projectile erodes at the target surface. Values of
the failed state are taken from the 2 mm traces for
the polycrystalline ceramics since the failure wave
does not penetrate to the deeper gauge except for
the B4C presented here. It can be seen that the unfailed state of the material lies on an elastic
trajectory (as constructed using equation 2)
although different materials have differing
Poisson's ratio as indicated by the shaded fan. B4C
shows a failed strength of the same order as A1N in
the stress range looked at. However, above the
latter's phase transition, it shows a declining value
of lateral stress appearing to double its strength
giving values equivalent to TiB2 (14).
The failed states lie on the horizontal lines fitted
through the data and represent the initial strength of
comminuted material. It is thus the starting strength
for material failed under shock that lies ahead of a
penetrator. At later time this will degrade as
778