CP620, Shock Compression of Condensed Matter - 2001
edited by M. D. Furnish, N. N. Thadhani, and Y. Hone
© 2002 American Institute of Physics 0-7354-0068-7/02/$ 19.00
A MECHANISTIC STUDY OF DELAYED DETONATION IN IMPACT
DAMAGED SOLID ROCKET PROPELLANT
E. R. Matheson1 and J. T. Rosenberg2
1
Aerothermal Design & Performance, Lockheed Martin Space Systems Company, Sunnyvale, CA 94089
Reliability/Sustainability Engineering, Lockheed Martin Space Systems Company, Sunnyvale, CA 94089
2
Abstract. One method of hazard assessment for mass detonable solid rocket propellants consists of
impacting right circular cylinders of propellant end-on into thick steel witness plates at varying impact
velocities. A detonation that occurs within one shock traversal of the cylinder length is termed a prompt
detonation or a shock-to-detonation transition (SDT). At lower velocities, some propellants detonate at
times later than one shock transit, typically 1-5 shock transits. Because no mechanism for delayed
detonation has been fully confirmed and accepted by the detonation physics community, these lowvelocity detonations are referred to as unknown-to-detonation transitions (XDTs). A leading theory,
however, is that prior to detonation mechanically induced damage sensitizes the material through the
formation of internal porosity which provides new mechanical reaction initiation sites (hot spots) and
enhanced internal burn surface. To study this phenomenology, we have developed the Coupled Damage
and Reaction (CDAR) model, implemented it in the CTH shock physics code, and simulated propellant
impact experiments. The CDAR model fully couples viscoelastic-viscoplastic deformation, tensile
damage, porosity evolution, reaction initiation, and grain burning to model the increased reactivity of
the propellant. In this paper, CDAR simulations of propellant damage in spall and Taylor impact tests
are presented and compared to experiment. An XDT experiment is also simulated, and implications
regarding damage mechanisms and hydrodynamic processes leading to XDT are discussed.
INTRODUCTION
mechanical reaction initiation sites (hot spots) and
enhanced internal burn surface.
To study phenomenology associated with XDT,
we have employed the2 5 Coupled Damage and
Reaction (CDAR) model 6" as implemented in the
CTH shock physics code . The CDAR model fully
couples
viscoelastic-viscoplastic
deformation,
tensile damage, porosity evolution, reaction
initiation, and grain burning to model the increased
reactivity of damaged propellant. In this paper,
CDAR simulations of propellant damage in spall
and Taylor rod impact tests are presented and
compared to experiment. An XDT experiment is
also simulated, and implications regarding damage
mechanisms and hydrodynamic processes leading to
XDT are discussed.
During impact testing of L/D=l cylindrical
samples of certain solid rocket propellants, two
types of detonations are observed. Normal, or
prompt, detonations occur at higher velocities and
during the first transit of the shock wave. For these
detonations, chemical reaction rates dominate over
release waves entering the sample from free
boundaries, and the mechanical behavior of the
solid propellant is readily characterized by its shock
behavior. Abnormal detonations are observed at
lower velocities and typically occur after 1-5 shock
transits along the sample axis. For these delayed
detonations, release waves and ultimately tensile
waves can form in the solid propellant greatly
complicating the sample response during impact.
Because no mechanism for delayed detonation has
been fully confirmed and accepted by the
detonation physics community, these low-velocity
detonations are referred to as unknown-todetonation transitions (XDTs). A leading theory1,
however, is that prior to detonation mechanically
induced damage sensitizes the material through the
formation of internal porosity which provides new
SPALL MODEL CORRELATION
One-dimensional spall tests were performed for
the study material using PMMA flyers at increasing
impact velocities until full damage was achieved.
Fig. 1 shows profiles of damage and solid volume
fraction through the target material simulated with
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limited to a specified level. Here, it was set to
reflect the change in modulus of the propellant
observed in dynamic tensile tests. Decohesion is
modeled as occurring abruptly when tensile strains
exceed the value at which the modulus is observed
to decrease suddenly in the tensile tests.
The black regions in Fig. 3 are sites where
CDAR has predicted full damage due to binder
scission. Two forms of scission are predicted by
CDAR in Fig. 3:1) strain failure of the binder at the
impact face, and 2) stress failure on-axis near the
back surface. The damage profile at the front face
qualitatively agrees well with the damage shown in
Fig. 2. There is a circumferential macrocrack
predicted at the mid-radius that is penetrating some
distance along the axis. There is also full damage
predicted at the radial periphery of the impact face.
Fig. 2 shows some material missing at the
periphery. If scission damage near the rear of the
sample occurred, it was not reported. In this region,
CDAR predicted that the tensile stress state was
virtually uniform in all directions, and the stress was
greater than that for the 1-D spall threshold.
Considering that it does not conform to the usual
concept of a spall plane and that it occurs over a
small region, it may not have been readily detected.
CDAR. In this case, the impact conditions are at the
threshold for full damage to occur at 6.0 jis. At this
time, the material exhibits a porosity of 2.0% at the
location of 100% damage. At later times, the
damage profile remains unchanged whereas the
voids have fully closed. During the spall process,
the tensile strain rates are very small or nonexistent.
Moreover, the tensile strains remain very small over
the duration of the experiment. Thus, spall damage
is necessarily modeled as a quasistatic stress failure
of the binder system.
1.0
1.000
**\
0.9-
0.995
0.80.7- ——Damage
£ °' 6 ~
—-Solid Volume
Fraction
-0.990
5
I °' "
- 0.985
0.3- 0.980
0.20.1 -
0.975
0.0
0.0
0.1
0.2
03
0.4
0.5
0.6
Position (cm)
FIGURE 1. Simulated damage and volume fraction profiles for
the interrupted spall test.
TAYLOR ROD IMPACT TEST
CORRELATION
Taylor impact experiments were performed on
propellant rods of various L/D ratios. Fig. 2 shows
damage inflicted on a propellant sample with
Z/D=1.27. The upper image in Fig. 2 is of the
impact face revealing an approximately circumferential macrocrack. In the lower image, the
sample was sliced along its axis revealing the same
macrocrack running a short distance up the sample.
In both views, it can be observed that there are large
energetic crystals decohered from the propellant
binder system. For the spall tests, decohesipn
damage was not readily apparent since the tensile
strains were very low relative to the Taylor tests.
The Taylor rod impact experiment was
simulated using CDAR, and Fig. 3 shows contours
of damage in the sample at some time after impact.
At this time, the sample has just begun to rebound
from the aluminum impactor and has experienced
maximum radial strains at the impact face. Gray
regions in Fig. 3 correspond to decohesion damage
levels. In CDAR, decohesion damage may
i)' View of
b)
ini
of
FIGURE 2. Damaged propellant recovered from a Taylor rod
impact experiment.
465
than scission damage. Fig. 4 also shows that there is
a low level of porosity and only decohesion damage
on-axis where the detonation initiates in Fig. 5. This
is quite different from the DDT-like mechanism
postulated in Ref. 1.
FIGURE 3. Simulated damage contours for end-on impact of a
cylindrical sample in a Taylor rod impact experiment.
FIGURE 4. Simulated damage and solid volume fraction
contours for an XDT impact experiment.
XDT IMPACT CORRELATION
Impact-induced XDT was studied previously
using the programmed XDT technique . The XDT
experiment studied in Ref. 7 is simulated here using
the CDAR model. The propellant sample was
25mm in diameter, L/D=1, and fired from a shotgun
onto a steel witness plate. The witness plate was 3.2
mm thick, and there was a PVDF stress gage
embedded on the sample shotline between the
witness plate and a thick steel backing plate.
Fig. 4 shows damage and solid volume fraction
contours immediately prior to the initiation of
detonation. The sample has experienced decohesion
damage throughout, and there is some peripheral
scission damage. The solid volume fraction contour
shows a low level of porosity evolution on-axis near
the front face. Near the rear surface, there is a high
degree of porosity due to decohesion, but the
scission damage is insufficient to form a spall plane.
Fig. 5 shows gas pressure contours at four times.
The upper-left quadrant shows that the initial
reaction occurs near the front face about 2/3 of the
way from the axis. In the upper-right quadrant, the
reactive wave has propagated to the axis. The two
lower quadrants reveal that the detonation initiates
on-axis at the impact face and propagates
spherically away from that point. The lower-right
quadrant also indicates that there is a fairly large
region ahead of the detonation front that has
initiated reaction. Examination of gas mass fraction
contours prior to detonation shows that there is a
trivial amount of gas present, and the gas has a
negligible effect on hydrodynamic processes.
There is scission damage shown in Fig. 4 in the
same vicinity as the site where reaction initiates.
Since it occurs later and does not propagate to the
axis as does the reaction, it appears that reaction
initiation is supported by decohesion damage rather
FIGURE 5. Simulated gas pressure contours for an XDT
impact experiment.
Fig. 6 compares simulated and experimental xray records of the expanding detonation products.
The simulation exhibits a radial jet-like structure
similar to that in the experiment. The simulation
also shows the witness plate crater which compares
well with the crater photographic record in Ref. 7.
Fig. 7 compares the axial stress on-axis
computed by CTH at the PVDF gage location with
the experimental gage record. The simulation shows
a precursor to the detonation similar to the data but
occurring somewhat early. The precursor pulse
causes the pores to close generating a significant
466
DDT-like behavior was postulated as a possible
cause for XDT, but it appears that the
microstructure in conjunction with the binder
toughness is the cause. For the Taylor test
simulation, CDAR underpredicted the increase in
sample volume observed in shadowgraphs. It is
thought that adding pressure-dependent shear and
shear-induced dilatation into the CDAR constitutive
models might solve this problem8. Inclusion of
these processes in CDAR may be important for
predicting XDT under all impact conditions.
gas pressure. However, the mass fraction of gas is
so low the hydrodynamics are unaffected. It is the
solid pressure in response to the compressive pulse
that is generating hot spots leading to the
detonation. CTH also computed a peak stress due to
the detonation that is in very good agreement with
the data. The simulated pulse is probably wider
because the interface between the witness and
backing plates which provides a path for transverse
release waves to unload the gage was not modeled.
REFERENCES
1.
2.
Green, L. G., James, E., Lee, E. L., Chambers, E. S.,
Tarver, C. M., Westmoreland, C, Western, A. M.,
Brown, B., "Delayed Detonation in Propellants from
Low Velocity Impact," Seventh Symposium
(International) on Detonation, Annapolis, MD, 1619 June 1981, pp. 256-264.
Olsen, E. M., Rosenberg, J. T., Kawamoto, J. D.,
Lin, C. F., and Seaman, L., "XDT Investigation by
Computational Simulation of Mechanical Response
Using a New Viscous Internal Damage Model,"
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Snowmass, CO, 30 August - 4 September, 1998, pp.
170-178.
FIGURE 6. Experimental versus simulated flash x-ray record
for an XDT impact experiment.
3.
CTH Axial Stress
PVDF Gage Record
4.
fi
oo
5.
Time
FIGURE 7. Experimental versus simulated flash x-ray record
for an XDT impact experiment.
Matheson, E. R., Drumheller, D. S., and Baer, M.
R, "An Internal Damage Model for ViscoelasticViscoplastic Energetic Materials," in Shock
Compression of Condensed Matter - 7999, edited by
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6.
DISCUSSION AND CONCLUSIONS
7.
This study demonstrates that material damage
enhances material reactivity in CDAR to produce
XDT-like responses in solid rocket propellants. In
the XDT simulation, CDAR predicted that
decohesion damage rather than macrocracks due to
binder scission is responsible for XDT. In Ref. 1,
8.
467
Hertel, E. S., et al, "CTH: A Software Family for
Multi-Dimensional Shock Physics Analysis," in
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Butcher, G., "Programmed XDT: A New Technique
to Investigate Impact-Induced Delayed Detonation,"
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