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
USE OF HIGH-SPEED PHOTOGRAPHY TO AUGMENT SPLIT
HOPKINSON PRESSURE BAR MEASUREMENTS OF ENERGETIC
MATERIALS
Richard J. Lee and Vasant S. Joshi
Research and Technology Department, NAVSEA Indian Head Division,
101 Strauss Ave, Indian Head MD 20640-5035
The split Hopkinson pressure bar technique has been used successfully to characterize high strain-rate
behavior (103 to 104 S ) of metals and polymeric materials in the past. Similar studies on composite
energetic materials are desired to assist in developing a model that can predict the mechanical response
of energetic materials. The strength of cast-cured and melt-cast explosives are far lower than metallic
materials, requiring a combination of techniques to accurately resolve their deformation characteristics.
High-speed-imaging techniques have been explored here and compared to conventional strain gauge
data for a soft, compliant material as well as a hard, brittle one, which are distinctly different in mechanical behavior. The photographic data coupled with the strain gauge data have proven useful in determining the nature of damage that occurs during the loading cycle.
INTRODUCTION
Striker
Characterizing solid energetic materials response to mechanical stimuli is important to develop
a fundamental understanding of sensitivity and ignition. Cast-cured compositions typically involve solid
energetic crystals, other solids that act as fuel or oxidizers, and a plastic binder. The properties of the
individual constituents and how they bond to the
binder contribute to the overall mechanical-response,
complicating the problem. Understanding the dominant features associated with this response provides
the basis for improved models to determine the vulnerability of munitions.
The split-Hopkinson pressure bar (illustrated in
Figure 1) is one of a number of tools typically used
to establish constitutive relations for materials.
Stress-strain data are obtained for various strain rates
on the order of 103 s"1. Cylindrical test samples are
longitudinally strained in compression between two
cylindrical bars by a stress wave of finite length.
Incident bar
Transmitter bar
Figure 1. Hopkinson Bar Apparatus
This stress wave is induced by launching a short bar
(the striker) into one of the longer bars. Stress,
strain, and strain rate in the sample are determined
by measuring the resulting stress waves in the two
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bridge with a supporting Ectron 2 MHz bandwidth
amplifier. Gains of 100 and 200 (incident and
transmitted bar, respectively) were used to improve
signal amplitude at the oscilloscope.
A Nicolet Integra 40 digital oscilloscope recorded the data with 12 bit resolution. The gauges
were 1.57 mm (0.062"), which provide a time resolution of 3.3 jis (300 kHz response).2 Data was collected at 50 ns/point using a 300 kHz bandwidth filter to reduce signal noise.
Photographed sample deformation was taken
with an Imacon 200 digital camera, which uses a
series of CCD cameras to record 16 images. Individual pixels are 6.7 x 6.7 microns in a pattern of
1280 horizontal x 1024 vertical. Systematic measuring-errors combine to ±0.10 mm when using a field
of view a little larger than the bar diameter. Pictures
were taken every 12 jis for PBXW-128 samples and
8 jis for TNT to span the respective loading cycles.
Faster framing-rates are eventually possible for probing specific periods of interest, e.g., the initial stages
of compression or around an expected failure time.
Data were examined for stress equalization (a
validation requirement) by comparing stress-strain
curves from one and three-wave analyses.1 (The
three-wave analysis uses all three signals to determine stress and strain in the sample: Stress equalization allows reduction of the three-wave data to the
one-wave, where stress is given by the transmitted
signal and strain the reflected signal.) The one-wave
data were also evaluated in light of the photographic
data.
longer bars (incident and transmitted) bounding the
sample. The stress waves are measured with strain
gauges placed on the bars. The distance between
gauges and sample is selected to keep the incident
wave (established by the striker) and the reflected
wave (returning from the sample) from interfering
with one another at the gauge position.
Unfortunately, these types of test have proven
difficult for energetic materials. Cast-cured explosives compositions have relatively low mechanical
impedance (defined by low sound-speed and density)
in comparison to the bars, assuring a very small
transmitted wave. Signal intensities can be improved
by using lower-modulus bars, e.g., aluminum,
thereby reducing the disparity in mechanical impedance.1 Additionally, typical data reduction schemes
assume a linear relationship between radial expansion and axial strain of the sample, which may not
always be true for the materials of interest.
Reported here is the use of high-speed photography as an augmentation to conventional strain
gauge data. Two distinctly different materials were
studied; (1) a cast-cured explosive based on HMX
and a polymeric binder, PBXW-128, and (2) a brittle, melt-cast explosive, TNT. The photographic
technique coupled with comparisons of the typical
strain-gauge data (one and three-wave analysis)1
have proven useful in validating data-integrity for
PBXW-128 as well as providing insight into material
failure for TNT samples.
EXPERIMENTAL
Each test sample was fabricated into rightcircular cylinders with nominal diameters of 9.5-mm.
Sample lengths were 4.75 and 8.55 mm for PBXW128 and TNT, respectively.
The bars were made from 15.8-mm diameter,
hardened 7075 aluminum rods. The incident and
transmitted bars were 1.2 m long. Striker lengths of
508 and 308 mm provided nominal loading cycles of
200 and 120 jis for the PBXW-128 and TNT samples, respectively.
Strain gauges were placed at the mid point of the
incident and transmitted bars. At each measuring
location, two 350 Q gauges were placed 180° from
one another on the bar to compensate for any bending. Gauge-pairs were configured in a two-arm
RESULTS
Figure 2 shows a comparison of true-stress vs.
true-strain from one and three-wave analyses at a
nominal strain rate of 2300 s"1 for the PBXW-128
sample. The strain rate actually increases over the
loading cycle from 1900 to 2700 s"1. It is desirable
to achieve a constant true strain-rate, however,
gradually increasing rates are expected for high
strains in the sample. The difference between the
one and three-wave plots shown here would normally
indicate a loss of stress equalization in the sample
resulting from some internal damage, e.g., de-wetting
of solids from the binder. However the photographic
data suggest otherwise. As shown in Figure 3, the
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sample diameter and radius obtained from the photographs as well as that calculated from the true-strain
vs. time data (assuming constant volume) are comparable. (Figure 4 shows three of the sixteen photographs taken.) Moreover, volume vs. time, calculated from the photographic data, indicate that the
sample volume remains constant over the loading
cycle. These data argue that stress equalization was
maintained during the loading cycle.
Figure 5 shows stress versus strain at a nominal
strain rate of 750 s"1 for a TNT sample. Strain rate
varied from 650 to 870 s"1. Here, the one and threewave data are fairly comparable. These data might
have been mistaken for reasonable results if the photographs had not indicated fracturing along the sample's outer surfaces as shown in lower portion of
Figure 5. This fracturing begins early in the loading
cycle and corresponds with the slope change from
positive to negative in the stress-strain plot.
Strain rate - 2300 1 s
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
True-Strain
Figure 2. One and three-wave data for PBXW-128.
56 [is
120 |is
Figure 5. One and three-wave data for TNT, and selected photographs.
DISCUSSION
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Photographic data indicate that PBXW-128 deforms at constant volume under compression at strain
rates comparable to 2300 s"1. This indicates that
stress equalization occurs, on average, through the
loading cycle despite observed differences between
one and three-wave data reduction schemes. It must
be noted that the framing rate for the photographs
were relatively course with respect to oscillations
observed on the stress-strain plot. A close inspection
of the true-stress vs time (as indicated by the transmitted wave) suggests that there is a cyclic increase
and decline of stress during the first portion of the
loading pulse. Chung has observed this phenomenon
in copper and attributed it to radial relaxation follow-
40 60 80100120140160180200220
Time (us)
Figure 3. Photographic vs. strain gauge data for PBXW-128.
Plots with error bars are measured values from photographs.
Lines without error bars, are corresponding dimensions calculated
from true-strain vs. time data.
Oias
84,118
Figure 4. Selected Photographs for PBXW-128 showing smooth
lateral expansion during the loading cycle.
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ing a gradient buildup from the central axis to the
periphery.3
The initial disagreement of one and three-wave
data may be attributed to this phenomenon. However it is equally possible that the difference may be
attributed to an inability to accurately compare the
difference of incident and reflected signals to the
transmitted signal, in the way that is typically done
with harder material, e.g., metals. This difficulty
arises from the disparity between the reflected and
transmitted signal magnitudes observed in softer
materials. Despite efforts to improve diagnostic precision, errors are introduced from an inability to accurately correct for dispersion introduced as the
stress waves propagate down the bars. This was
brought to light during recent efforts to confirm our
dispersion correction routines. They are adequate
for correcting data for hard materials but fall short
when the material is soft.
These problems are greatly reduced for TNT
because of its firmness. The one and three-wave
data for TNT are similar, suggesting that stress
equalization occurs in the sample despite its fracturing. The supposition here is that fracturing occurs
only along the outer periphery of the sample, leaving
an inner core intact. Stress equalization is maintained in this inner core allowing an opportunity to
glean stress-strain data from these types of experiments. The negative slope may be attributed to a
decreasing ample diameter, which may eventually be
monitored and compensated for by back lit photography (not employed in this study).
ACKNOWLEDGEMENTS
The sponsors for this effort were the Office of
Naval Research (ONR) under the Air and Surface
program and the Navy Explosives Ordnance Disposal (EOD) Technology Center. We wish to also
thank Chak-Pan Wong and Dennis Budd for their
assistance in performing these experiments.
REFERENCES
1. Gray, G.T., and Blumenthal, W.R., Metals Handbook., Vol 8, 10th Ed, ASM Publications, 2000,
pp 462-476 and pp 488-496.
2. Ueda, K. and Umeda, A., Experimental Mechanics, 38(2), 93-98 (1998).
3. Chung, D.T., Shock Compression in Condensed
Matter - 1995, edited by Schmidt et. al, AIP
Conference Proceedings, New York 1996, pp
483-486.
CONCLUSIONS
Two very different materials have been observed
in Hopkinson bar experiments using high-speed photography. Studies on PBXW-128, a very soft material, demonstrated constant volume deformation.
Also, it may not be possible to use comparisons of
one and three-wave data to validate for stress equalization due to the disparity in reflected and transmitted signal magnitudes typical to testing soft materials. TNT proved to be a brittle material easily fractured early in the loading cycle. However, data may
be obtained if the diameter of un-fractured inner-core
can be monitored.
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