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
PLASTIC DEFORMATION RATE AND INITIATION OF
CRYSTALLINE EXPLOSIVES
J. Namkung1 and C. S. Coffey2
*Naval Air Warfare Center, Pax River, Maryland 20640
Indian Head Division, Naval Surface Warfare Center, Indian Head, Maryland 20640-5035
2
Abstract Recent theoretical calculations have demonstrated a relationship between the rate of energy
dissipation and the rate of plastic deformation in crystalline solids subjected to plastic flow due to shock or
impact. In the case of explosive crystals the energy dissipated locally within the crystals during plastic
deformation forms the hot spots from which chemical reaction can be initiated. Prompted by this prediction
relating the plastic deformation rate with initiation, a series of experiments were undertaken to measure the
plastic deformation rate at the initiation site at the moment of initiation for a number of polycrystalline
explosives when subjected to impact or mild shock. The experiment and the results will be reviewed here.
INTRODUCTION
The experiment to be discussed here attempts to
measure the plastic deformation rate at the
initiation site at the moment of initiation.
Experimental results will be presented that appear
to substantiate the above mentioned predictions for
HMX, RDX, TNT and TATB. Results will also be
presented for several PBX materials.
Recent calculations have demonstrated a
relationship between the rate of energy dissipation
in a deforming crystal and the rate of plastic
deformation that the crystal experiences.*'2'3 The
energy dissipation required to raise the temperature
of HMX crystals to their initiation temperature
during mild impact has been determined. The
plastic deformation rate associated with this energy
dissipation has also been determined and found to
be about 104 s"1. Similarly, the plastic deformation
rate at the impact initiation threshold of RDX was
determined to be about 104 s"1. The plastic
deformation rates at the impact initiation threshold
of TNT and TATB were estimated to be about 2
x 10s S'1 and > 2 x 105 s"1 respectively. The
uncertainty in these latter calculations is mainly
associated with the value chosen for the shear
modulus.4 At the current time it is not possible to
predict the plastic deformation rate at the moment
of initiation of polymer and explosive crystal
compounds.
THE CONCEPT
It has been observed repeatedly that when
explosive or propellant samples were impacted
between two hardened steel anvils chemical
reactions were always first initiated in the high
shear region near the edge of the expanding
sample.5 Here, advantage is taken of these
observations to estimate the plastic deformation
rate at the moment of initiation. By choosing the
sample geometry to be a right circular cylinder it
is possible to measure the radial velocity at the
edge of the expanding sample disc at the moment
of initiation. The moment of initiation is
determined by fast photo diodes that detect the
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first light due to reaction initiation in the sample
since reaction always occurs at or near the
perimeter of the expanding sample disc. The
photo-diodes were positioned to monitor the entire
circumference of the expanding sample disc.
the anvil and striker surfaces and on these surface
the radial velocity is zero. The maximum velocity
is assumed to occur mid way up the height of the
sample at h/2, so that the plastic deformation rate
can be approximated by
Because the sample is radially symmetric it does
not matter on which radius initiation takes place
since all radii are equivalent. For the mild impacts
typical of a drop weight impact machine the
loading force levels are low and the assumption
can be made that the sample has a constant volume
during the impact. This permits a simple relation
between the velocity of the drop weight and the
radial velocity at the outer edge of the cylindrical
sample. Since the sample volume during impact is
assumed constant, the time derivative of the
volume is zero, d(7ir2h)/dt = 0 and r02h0 = r2h
where r0 and h0 are the initial radius and initial
height of the sample while r and h are the radius
and height of the sample at the moment of
initiation. Combining the above relations gives
following expression for the radial velocity at the
perimeter of the sample disc, dr/dt, in terms of the
vertical velocity of the impactor, dh/dt,
dr
dt
dh
2h'\ h dt
_
dt
h
dh
dt
THE EXPERIMENT
While there are a number of ways that the radial
velocity could be measured among the simplest
and quickest to implement is to measure the
deceleration of the impactor as it encounters and
crushes the sample. The Ballistic Impact Chamber
(BIC) Test apparatus was used as the test vehicle.6
The sample size was typical of that of the BIC
Test and consisted of a right circular cylinder 5
mm in diameter and about 2mm high, with a mass
of approximately 80 to 100 mg. The walls of the
BIC impact chamber were modified to
accommodate four photo diodes as shown in Fig.l.
(1)
Photo-Diode
The negative sign above is canceled by the
negative sign associated with the velocity of the
impactor which is responsible for decreasing the
height of the sample.
Photo-Diode
.177 cal. Barrel
Equation 1. permits the evaluation of the radial
expansion velocity of the edge of the sample disc
at the moment of initiation. To accurately measure
the plastic deformation rate requires an accurate
description of the radial flow throughout the
sample disc. Among other things, this requires
specifying the coefficient of friction between the
disc and the anvil and striker surfaces which is
likely to be an impossible task. Here, the plastic
deformation rate will be approximated by
assuming that the sample completely adheres to
Photo-Diode
Photo-Diode
Sample
Drawing not to scale
Figure 1. Schematic of modified BIC Test
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The moment of initiation was detected by one or
several of these photo-diodes whose outputs were
summed and recorded on a single channel of a
multi-channel digital recorder. An accelerometer
mounted on the impactor provided a measure of
the deceleration of the impactor as it encountered
the sample. This also was recorded on the multichannel recorder as was the pressure-time record
of the reaction gases confined in the BIG Test
chamber. The multi-channel recorder provided a
common time-base for all of the recorded data so
that it was possible to determine the accelerometer
data from initial impact to the moment of
initiation. Integrating the accelerometer record
provided the velocity, v, and the displacement, h,
of the impactor necessary to evaluate the plastic
deformation rate, Equation (2), at the moment of
initiation.
mainly composed of ammonium perchlorate and
aluminum and IH-H7-F was mainly potassium
perchlorate and aluminum.
DISCUSSION
The predicted plastic deformation rates required
for initiation of pure crystalline materials and the
measured plastic deformation rates for these same
materials are in reasonable agreement. This is true
generally, but particularly so for the case of hard
crystals of sensitive materials. For the softer
materials, TNT and TATB, the agreement between
prediction and experiment is still good. But to
obtain the predicted plastic deformation rates
required much smaller sample thickness at
initiation and for TATB a higher impact velocity,
20 m/s. The sample thickness needed to achieve a
plastic deformation rate of a few times 105 s"1
required for initiation is less than 100 JLI so that the
spatial resolution of the twice integrated
accelerometer data must approach 10 ji. This
represented an instrumentation challenge as does
the survival and calibration of the accelerometer at
20 m/s impacts. It is possible to calibrate the
accelerometer on every experiment by integrating
the acceleration to determine the velocity change
at the moment the impactor stops and comparing
that velocity with the independently measured
velocity of the impactor at the moment of impact.
RESULTS
The plastic deformation rates at the moment of
initiation for several different materials are listed
in the following table.
TABLE. Plastic Deformation Rate at Initiation, s"1
HMX(125 ji)
HMX(5 in)
HMX(5 JLI, calculated)
RDX(calculated)
IH-H7-D
IH-H7-D2
IH-H7-F
Comp B
TNT
TNT(calculated)
PBXN-109(heated)
PBXN-109
PBXW-128
TATB(calculated)
PBX-9502
.7 x 104
.8 x 104
1 x 104
1 x 104
2 x 104
2 x 104
7 x 104
7 x 104
> 2 x 105
2 x 105
1.4 x 105
1.7 x 105
2 x 105
> 2 x 105
> 3 x 105
Detonation (All Materials,
calculated)
a few times 106
The measured plastic deformation rates required
to initiate the plastic bonded explosives fall in the
expected order. To exploit and explore this
ordering represents both experimental and
fundamental physics challenges. Experimentally, it
was very difficult to prepare and measure
cylindrical samples of extremely soft materials
such as PBXW-128. It maybe that a non-intrusive
means can be used to obtain the initial sample
thickness. However, to quickly prepare a sample
pellet of a soft material like PBXW-128 will be a
much more difficult task.
Recall that this experimental effort was prompted
by theoretical calculations relating the plastic
deformation rate with the energy dissipation rate in
shocked or impacted solids and the numerical
The compositions IH-H7-D and IH-H7-D2 are
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prediction of the plastic deformation rate of several
crystalline explosives at the moment of initiation.
The agreement between the predicted and the
measured plastic deformation rates for crystalline
materials is gratifying. The plastic deformation rate
data obtained for the PBX materials is encouraging
and suggests an underlying regular behavior. In
recent work one of us (CSC) has shown that all
crystalline solids and liquids approach a maximum
plastic deformation rate of a few times 105 s'1 to
about 5 x 106 s"1 for shock wave amplitudes
ranging from about 5 GPa to in excess of 200
GPa.7'8 The viscosity of all liquids and solids are
shown to approach a few time 104 poise over this
shock wave pressure range. These predictions are
in good agreement with experiment. Similar
calculations are the basis of the final entry in the
above Table.2
ACKNOWLEDGEMENTS
The authors want to thank Dr. C. W. Anderson
and the Office of Naval Research for their
encouragement and support. They also want to
thank their colleagues both for their insights and
for supplying many of the materials used in the
test series. In particular they want to thank P. A.
Thomas, F. J. Zerilli, R. H. Guirguis, N. Jones and
J. M. Kelley.
REFERENCES
1. Coffey, C. S., Phys. Rev. B 24, 6984 (1981).
2. Coffey, C. S. and Sharma, J., Phys. Rev. B 60, 9365 (1999).
3. Coffey, C. S. and Sharma, J., J. Appl. Phys. 89, 4794 (2001).
4. The following values were used for the shear modulus, GIJMX
= 4.3 GPa., GRDX = 4.0 GPa., GTATB « G^ « 1 GPa. The
shear modulus for TATB was suggested by H. Cady, private
communication.
5. Coffey, C. S., Frankel, M. J., Liddiard, T. P., and Jacobs, S,
J, in Seventh Detonation Symposium, p. 970, (1981).
6. Coffey, C. S., DeVost, V. F. and Woody, D. L., in Ninth
Detonation Symposium, p. 1234, (1989).
7. Coffey, C. S., Phys. Rev. B 49, 208 (1994).
8. Coffey, C. S., Submitted to Phys. Rev. B June 2001
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