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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
MESOSCALE MECHANICS OF PLASTIC BONDED EXPLOSIVES
Keith M. Roessig
Air Force Research Laboratory/Munitions Directorate
101 W. Eglin Blvd. Ste. 135
EglinAFB,FL 32542
Abstract. The dynamic behavior of participate materials is important to a wide range of problems.
When dealing with energetic particulate materials, mechanical ignition is an added concern for safety
and performance issues. Micrographs from unconfined impact tests show specific crystal damage
paths within the matrix. Under loading conditions consistent with real world applications, these
materials can be subjected to large hydrostatic pressures combined with shear deformation. Subsequent
stress chain formation concentrates the compressive load into small regions, providing ignition sites
within the material. A photoelastic experiment with high speed photography has been constructed to
record stress state formation within PMMA disks set in different binder systems. The propagation of
shear stress across disk/binder interfaces is shown to be important in the overall stress state of the
particle bed. Binders with similar mechanical and acoustic properties as the PMMA disks remove
stress concentrations and allow waves to propagate as if in a continuum. Softer binder with lower
acoustical wave speeds and hard binders that have debonded from the disks do not allow shear stresses
to be transferred. These configurations cause stress concentrations similar to a binderless system of
disks.
approximately 10-20[im in diameter. A plasticized
binder holds all the particles together. At the
mesoscale, there are three distinct components of
INTRODUCTION
The initiation of reaction in energetic materials
through mechanical insult is important from both a
safety and performance viewpoint. Mechanical
loading on the material is at much lower
amplitudes, but for much longer durations, than
investigated for shock initiation (1). The particulate
behavior and the constituent contact mechanics at
the mesoscale become important in the transfer of
stress through the material. Stress concentrations
develop, known as stress chains or stress bridges,
which allow for localized stress and strain
concentrations, and therefore subsequent heating,
within the material (2,3).
A micrograph of a modified PBXN-109, a cure
cast plastic bonded explosive, is shown in Fig. 1.
HMX crystals 150-200j4,m in diameter, substituted
for the RDX crystals in the standard formulation,
are surrounded by small aluminum particles
FIGURE 1. Scanning electron micrograph of the mesoscsale
structure of a modified PBXN-109.
the particulate plastic bonded explosive: the crystal,
the binder, and the crystal/binder interface. The
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transfer of stress through each is governed by the
contact mechanics of the materials.
Unfortunately, it is not possible to observe the
stress state of real materials at the mesoscale during
these high strain rate tests. To understand how the
constituents interact under a dynamic load, the
process must be scaled so that meaningful data can
be obtained. Therefore, photoelasticity is used on
larger particles and binder amounts so that wave
propagation through the material happens at a rate
and length scale that is observable. Photoelasticity
has been used to look at stress states in particles
under dynamic loading (4-7). The purpose of this
work is to use the photoelastic effect to examine the
effects of binder/particle interactions at the
mesoscale on the stress state that develops within
the bulk material. The experimental data generated
here uses only small numbers of particles, not
nearly enough to simulate a real system. But
numerical simulations can be calibrated against this
data and then run for much larger numbers of
particles. Future efforts from there could then work
to homogenize this damage and its effect on bulk
ignition properties.
compared to a binder system consisting of PMMA
disks with no binder.
There are two different geometries used in this
work. This first consists of four disks placed in a
row. Due to symmetry, there is no shear at the
contact point between disks. This geometry will be
referred to as the "ID" or "4 Disk" geometry. The
second setup places the discs at 45° angles to each
other, allowing both compressive and shear stresses
at the contact point between the disks. This
geometry will be labeled "45 degree contact".
The loading cell for the tests consists of a 4340
steel frame with adjustable sides that allowed for
changes in frame width. Dynamic tests were
conducted by placing the load frame into a
compression Hopkinson bar apparatus. High speed
photographs of the fringe patterns were taken with
an Imacon 460 digital camera.
RESULTS & DISCUSSION
The following results show wave propagation
through the two geometries mentioned in the
previous
section,
and
three
different
binder/interface conditions. The pictures show
early and late time fringe patterns within the disks
that all are close to the same location. The relative
speeds at which the fringes travel are given by the
time after impact shown with the pictures. All
impact is on the right side of the disks with the
fringe patterns traveling right to left. Reference to
first, second, last disk etc. refers to the order in
which the wave impinges on each disk.
EXPERIMENTAL METHODS
The simulation of explosive crystals in a
plasticized binder took the form of circular PMMA
disks, 6.4mm thick and 50mm in diameter, with
different binder conditions depending on the
material behavior of interest.
Acrylimet, a
commercial acrylic metallographic specimen
mounting material, is used as a hard binder with
acoustic properties similar to that of the PMMA
disks. This material forms a bond to the disks to
allow the transfer of both compressive and shear
stresses across the disk/binder interface.
To
examine the case where only compressive stress
could be transferred across the interface, silicon
grease was placed on the edges of the disks to
prevent bonding of the binder to the disks during
the solidification process and reduce friction at the
interface. The second binder consisted of a
polyalcohol resin used in certain Air Force plastic
bonded explosives. This material is much softer
than PMMA, but bonds to the disks to allow the
transfer of compressive and shear stresses across
the interface. All of these binder systems are
4 Disk problem
The first disk/binder combination of this work
repeats many previous tests conducted by Shukla et
al. (4,5). The fringe patterns generated are shown
in Fig. 2 and are representative of diametrical
compression with Hertzian contact conditions.
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concentrations at the disk contact points reappear in
his case, as shear cannot be transmitted through the
interface. The disks act as wave guides and
concentrate the wave back towards the disk contact
points. The contact zone between disks seems to be
larger than the case with no binder at all, as there is
now material to support the compressive stresses
once the angle of incidence approaches 90 degrees
at the end of the disk. Previous work by Sadd et al.
(6) examined the effect of cementation on the
propagation of stress waves in a particulate
material. The fringe patterns in Fig. 4 resemble the
"soft cement" case of in that work, as both of these
experiments tend to reduce the stress concentration
at the contact. This is in contrast to the "hard
cement" case of Sadd et al. (6), which changes the
position of the stress concentration but does not
eliminate it.
FIGURE 2. Fringe patterns in the 4 Disk geometry without
binder. Pictures are taken 55 and 120 |us after impact.
The next case is the 4 Disk geometry with the
acrylic binder, shown in Fig. 3. With a good
impedance match between the PMMA disks and
binder, an expected result occurs. There is a
concentration at the first disk where impact occurs
and no binder is present, but the wave expands and
only a single diffuse fringe propagates smoothly
down the specimen. A lower stress state develops
within the specimen as the binder can support as
much load as the disks themselves and shear is
transferred at the boundaries. Though not shown
here, this single fringe does travel back up the
specimen upon reflection at the last disk. The
fringes in the first disk distort due to contact with
the side of the load frame.
FIGURE 4. Fringe patterns generated from greased contact
between the PMMA disks and the acrylic binder. Pictures were
taken at 35 \is and 135 (j,s after impact.
The final case for the 4 Disk geometry includes
the polyal binder. The contact regions for this
configuration
show
much
lower
stress
concentrations and wider contact areas than the
binderless case, similar to the greased acrylic
boundaries shown in Fig. 5. Fringe propagation
speeds are also comparable to the binderless and
greased acrylic interface cases.
The most
interesting aspect to this configuration is the ability
to see the stress wave propagate through the binder
itself. The binder exhibits photoelastic properties,
from which a comparison of wave speeds in the two
materials can be made. The wave speed in the
binder is much less than the PMMA disks. This
causes the same kind of stress state as in the greased
interfaces because even though the compressive and
FIGURE 3. Fringe patterns in the 4 Disk geometry with an
acrylic binder 45 (as and 95 ^is after impact.
Stress
concentrations are not present in this configuration.
Figure 4 shows the third experiment, the 4 Disk
problem with acrylic binder but with greased
interfaces to prevent tangential loads being
transferred across the interface.
The stress
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shear forces can be transferred across the boundary,
that information will not reach the next disk before
the transfer of stress near the immediate contact
point. Therefore, the contact region is increased,
but only slightly as the wave speed of the binder
material limits the transfer of information across the
disks.
patterns between the first and second disk,
exhibiting more of a normal load at the contact
point. However, post test examination of the disks
showed that the bond between the first and second
disk fractured. This may be the cause of the fringes
changing character after loading. The second
difference is the speed at which the fringe patterns
propagate. While the bare disks shown in Fig. 6
FIGURE 5. Fringe patterns of the 4 Disk problem with polyal
binder taken 60 and 135 ^s after impact
45 Degree Contact Problem
The 4 Disk geometry by virtue of its symmetry
did not promote shear stresses in the system. The
shear stresses developed from the shapes of the
disks and the reflection of the dilatational waves at
the boundaries. This is the reason for the diffuse
stress state in the bound acrylic case. The second
geometry, the 45 degree contact, promotes shear by
the disk arrangement as well.
As a reference, Fig. 6 shows the 45 degree
contact geometry without any binder. Again, this is
a repetition of work conducted by Rossmanith and
Shukla (3). The friction coefficient between the
disks is very low, exhibited by the fact that the
fringe patterns are symmetric about the contact
zone. With tangential loading, the fringes become
antisymmertic (7). The wave propagates through
the disks and attenuates due to the transfer of load
into the side supports through bending.
Following the cemented particle ideas of Sadd et
al. (6), the disks were bonded together with superglue, but no other binder was added. Two things
are readily apparent in Fig. 7. First, the fringe
patterns exhibit high shear stresses, as they are antisymmetric and tend to travel along the centerline of
the disk formation. Only at later times do the fringe
FIGURE 6. Fringe patterns at 100 and 300 ^is after impact in
the 45 degree contact geometry without a binder.
FIGURE 7. Dynamic fringe pattern for the 45 degree contact
geometry with glued contact points. Pictures are taken at 60 and
135 (as after impact.
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take around 300 |j,s to propagate from the second to
the back edge of the loading frame; the same
distance is traveled in about 80 ^is with the glued
contact. It is not the actual wave speeds of the
material that are increasing. It is the state of
maximum shear stress that increases at a greater
rate along the centerline of the disk assembly. The
fringe patterns generated are lines of constant
maximum shear stress. With the glued contact,
shear is transferred more readily, allowing fringes
to develop at earlier times. As failure many times is
determined by shear, and shearing in the crystals
leads to heat generation, it is important to know
how shear stresses and compressive stresses are
generated in the different geometric and material
conditions.
The next case is the 45 degree contact with the
acrylic binder, shown in Fig. 8. Compared to the
two previous scenarios, a more diffuse fringe
pattern develops as in the 4 Disk problem with
acrylic binder. In this case however, the fringes
seem to concentrate around the centerline similar to
the glued 45 degree contact problem. The ability to
transfer shear along the interface exists in this case
as in the glued contact, but it can now be transferred
over a larger contact area. Further evidence of
shearing along the centerline, there is an interesting
debonding pattern in this test. Debonding occurred
down the centerline, i.e. started at the first disk on
top and continued to the contact point with the
second disk. Debonding then occurred on the
bottom of the second disk until the contact with the
third disk at which point it jumps to the top of the
third. This wavy pattern continues all the way
through the assembly. This is a consequence of the
shear forces being supported at the centerline,
which are exhibited by the fringes. No debonding
occurred in the 4 Disk problem where shear was not
developed by the disk positions.
Figure 9 shows the greased 45 degree contact
configuration with acrylic binder. The same trends
are shown here as in the 4 Disk greased case. The
fringe patterns from greased contact are similar to
the binderless contact, but with larger contact zones
between the disks. Again, as shear cannot be
transferred easily across the interfaces, the stress
state resembles the binderless case without glued
contact.
FIGURE 8. The fringe patterns generated with the acrylic
binder at 75 and 150 (is after impact. The 45 degree contact with
acrylic binder shows a much more diffuse pattern, but still has
some shear concentratioon down the centerline.
FIGURE 9. Fringe patterns developed in the 45 degree contact
geometry with acrylic binder and greased interfaces. Pictures
were taken 100 and 200 |us after impact.
The final configuration is polyal binder in the 45
degree contact geometry, shown in Fig. 10. The
fringe patterns in the disks again are closer to the
binderless case as the polyal binder has a low shear
modulus. There is definitely some shear transfer
though, as seen from the slight anti-symmetry in the
initial fringes generated at each contact point. This
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effect decreases at later times once the full wave
establishes itself in the disk. There is no debonding
in this case, so that is not the cause of the slight
change in character of the fringes. The disparate
values of wave speeds are exhibited by the fringe
propagation in the two materials. The average
estimate of fringe propagation speed in the polyal
binder is 50 m/s, compared to 1000 m/s in the
PMMA disks.
Similar binders but with low friction interfaces
prevent the transfer of shear and return the stress
state to one similar to a no binder system. Stresses
at the contact point are less concentrated than pure
Hertzian contact conditions. Soft binders also
generate a stress state similar to that of a binderless
system, but low shear stresses can be supported,
which allow for the diffusion of stress at the contact
point.
ACKNOWLEDGEMENTS
I would like to thank Dr. Joe Foster and Dr. Scott
Bardenhagen for their help and willingness to
discuss technical issues at any time. I would also
like to thank ILt Daniel Warrensford and Thomas
Sprague of the Air Force Research Laboratory's
High Explosive Research and Development Facility
(HERD) for their help by mixing and curing the
polyalcohol resin.
REFERENCES
1. Foster, Jr., J. C., Christopher, F. R., Wilson, L. L.,
Osborn, J., "Mechanical Ignition Of Combustion In
Condensed Phase High Explosives,"
Shock
Compression of Condensed Matter 1997, edited by
S.C. Schmidt et al, AIP Conference proceeding 429,
pp. 389-392.
2. Roessig, K.M., and Foster, J.C., Jr., "Dynamic Stress
Chain Fracture in Particle Beds," in Plastic and
Viscoplastic Response of Materials and Metal
Forming, edited by A.S. Khan et al., proceedings of
Eighth International Symposium on Plasticity and Its
Current Applications, July, 2000, pp. 437-439.
3. Foster, J.C., Jr., Glenn, J.G., and Gunger, M., "MesoScale Origins of the Low Pressure Equation of State
and High Rate Mechanical Properties of Plastic
Bonded Explosives", in Shock Compression in
Condensed Matter - 1999, edited by M.D. Furnish et
al., AIP Conference Proceeding 505,1999, pp. 703-706
4. Rossmanith, H.P. and Shukla, A., Acta Mechanica 4J
211-225(1982).
5. Shukla, A. and Damania, C., Experimental Mechanics
44,268-281(1987).
6. Sadd, M.H., Shukla, A., Sienkiewicz, F., and Gautam,
A., Wave Propagation and Emerging Technologies
188,11-28(1994).
7. Shukla, A. and Higam, H., Journal of Strain Analysis
20,241-245(1985).
FIGURE 10. The 45 degree contact with the polyal binder
produces a fringe pattern similar to the binderless case. Pictures
are taken 75 and 250 us after impact.
CONCLUSIONS
The effect of disk geometry, disk/binder
materials, and disk/binder interface condition all
have a large effect on the stress states developed in
a particulate material under dynamic loading. This
work examines the ability to transfer compressive
and shear stresses through a particle and binder
materials and across the interface between them.
Geometries with no binder were used as test cases
and also to provide repeatable results from past
research. Glued contact point in the 45 degree
geometry showed that the ability to transfer
tangential loads at the contact point resulted in a
much greater shear stress within the particles at
much earlier times. Hard binders with similar
mechanical properties as the particles will allow for
a more diffuse stress state, but still may have shear
concentrations depending upon the disk geometry.
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