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
MOIRE INTERFEROMETRY STUDIES OF PBX 9501
Philip J. Rae*, H. Timothy Goldrein*, Stewart J. P. Palmer* and William Proud*
""University of Cambridge, Cavendish Laboratory, Madingley Road, Cambridge, UK. CB3 OHE
Abstract The microstructure of polymer bonded explosives influences significantly the mechanical response to quasi-static and dynamic loading. The microstructure of PBX 9501 is examined using moire interferometry, a sensitive optical technique useful for measuring in-plane displacement. Quasi-static deformation
and fracture has been followed and the influence of the crystal microstructure is found to be significant. If
moire interferometry is to be useful at high strain rates, changes in the experimental setup are required. These
alterations are outlined.
INTRODUCTION
The US composition PBX 9501 is a much studied explosive [1, 2, 3, 4]. It is manufactured from 95% by
weight crystalline explosive and 5% rubbery binder
[5]. An image of the microstructure, taken with polarised light, is shown in figure 1. The explosive crystals in this composition are typically angular in shape
and can be extensively flawed, with growth inclusions, voids and deformation twins. Post failure optical and electron micrographs can be taken showing the failure route and nature of cracking but this
method reveals no quantitative information about the
material deformation. Past studies have revealed that
the quality of the explosive crystals and the toughness of the binder play a key role in the mechanism
of fracture [6, 7, 8, 9]. These experiments followed
deformation and failure under quasi-static loading.
An obvious extension of this research is into the dynamic regime.
As in many other areas of scientific investigation,
researchers are seeking to create analytical and computer models of the response of PBXs to a variety
of impact situations [10]. The strain-rate regimes of
interest vary between creep and high intensity shock
waves and such models require experimental verification. In order to understand in a quantitative manner the microscopic deformation of these materials
under load, a high-resolution measurement technique
is required. A number of possible techniques could
be employed [11] but moire interferometry offers a
non-contact, sensitive and whole-field solution.
FIGURE 1. Optical micrograph of PBX 9501 showing
the angular nature of the filler, growth inclusions, voidage
and deformation twins.
QUASI-STATIC MOIRE
INTERFEROMETRY
High Resolution moire interferometry is a sensitive
coherent optical technique which allows the measurement of in-plane displacements [12, 13, 14]. By
taking white-light images of the microstructure in
exact registration with laser interferograms, a direct
correlation of the measured displacement field with
features in the composite microstructure is made.
The technique works by using collimated laser
beams falling onto a thin phase diffraction grating
bonded to the test specimen surface. A single beam
falling onto a phase grating surface produces a number of diffracted beams. The number and angle at
which they are formed depends on the frequency of
825
the laser light, the angle of incidence and the pitch
or spatial frequency of the grating. If two collimated
beams are set up so that their +1 and — 1 diffraction
orders respectivly leave normal to the grating surface, as in figure 2(left), then any change in the grating pitch produced by mechanical strain will cause
a change in the angle at which the diffraction orders
leave the grating, figure 2(right).
In quasi-static experiments the interference pattern created by the overlapping diffracted beams
may be recorded as a two-dimensional fringe pattern on a CCD camera. It can be shown [12] that
each fringe represents a local displacement of half
a grating pitch, in a direction perpendicular to the
grating rulings. In these experiments a He-Ne laser
(wavelength 632.8 nm) is shone onto a phase grating of 1200 lines mm"1 cast onto the PBX surface.
This produces an extra interference fringe for each
0.4167 /urn of local in-plane displacement. Only local strains are measured by this system since rigid
body motion of the specimen does not change the
grating pitch. Out of plane motion is not measured
since the path length of each beam is equally affected
leading to an unchanged interference pattern. Using
computer analysis and phase stepping [15, 16, 17], a
sensitivity of around one hundredth of a fringe may
be achieved, leading to a displacement uncertainty of
approximately 10 nm. A schematic of the optical arrangement is presented in figure 3.
Phase gratings are replicated on the specimen using a low modulus epoxy resin which does not reinforce the specimen surface significantly. Thin gratings (<5 ^um) are required to prevent the 'smearing'
of high local strains over a larger surface area. The
grating is coated with a thin layer of gold (^5 nm)
to enhance the diffraction efficiency, whilst allowing white light pictures to be obtained with the video
camera through the grating.
Figure 4 shows a contour map of a fractured sample of PBX 9501. The specimen has been loaded at a
strain rate of approximately 10~4 s"1 in the Brazilian test [18, 19]. In this biaxial test compression occurs vertically while the measurement is taken in
the horizontal, tensile, direction. It can be seen that
a significant vertical crack has occurred in a large
filler particle (marked A). It can also be seen that
the material on the left of the image has deformed
uniformly and with little correlation to the underlying microstructure. Figures 5 and 6 show only the
white-light micrographs obtained before and after
FIGURE 2. Principal of moire interferometry. Left: undeformed phase grating with symmetric input beams.
Right: deformed phase grating resulting in altered angles
of diffraction.
Optical fibre 2 —— \J———————————————————^Mirror 2
FIGURE 3.
A schematic of a moire interferometer.
failure. The cracked crystals are more obvious in
these images. Only the post failure contour map is
presented here. Eleven others were recorded during
loading; they show incremental increases in displacement prior to total sample failure.
DYNAMIC MOIRE
INTERFEROMETRY
In principal moire interferometry is applicable to dynamic events, however some simplifications are required. Is is not possible to perform phase-stepping
at more than a few hundred frames per second.
For fast events the fringes patterns need to be photographed and analyzed using the 'fourier transform
technique'[20]. This necessity reduces the fringe interpolation accuracy to about 1 /10th of a fringe, corresponding to about 100 nm. A typical set of interference fringes showing the sinusoidal nature of the
pattern produced is shown in figure 7.
In addition, powerful lasers are required. If one
826
1200
FIGURE 4.
0.5 //m.
Post failure contour map in PBX 9501. The applied tensile stress is horizontal and the contour displacement is
FIGURE 5. Microstructure of the sample shown in figure 4 prior to sample loading.
FIGURE 6. Microstructure of the sample shown in figure4.
wishes to capture the deformation due to a shock
front moving at between 2-1 km s"1, exposures of
less than 100 ns are required. Even with image intensified cameras a great deal of light needs to be
delivered to the specimen. This high-power-density
precludes the use of single-mode optical fibres in the
system and forces the researcher to use bulk optics
despite a considerable increase in experimental dif827
4.
5.
6.
7.
8.
FIGURE 7.
9.
A typical set of interference fringes.
10.
ficulty. One final limitation is that whilst white-light
images may still be taken through the grating before
loading it is not possible to do this during the dynamic event in addition to capturing interferograms.
11.
ACKNOWLEDGMENTS
The authors wish to thank the Los Alamos National
Laboratory (USA) for suppling samples of PBX
9501 and the Atomic Weapons Establishment, Aldermaston UK for funding the research.
12.
13.
14.
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