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
THE STUDY OF INTERNAL DEFORMATION FIELDS IN
GRANULAR MATERIALS USING 3D DIGITAL SPECKLE X-RAY
FLASH PHOTOGRAPHY
H,T. Goldrein, S.G. Grantham, W,G. Proud, J.E. Field
Cavendish Laboratory, Madingley Road, Cambridge, CBS OHE. UK
Abstract. Digital Speckle X~ray Flash Photography is a technique which combines Digital Speckle
Photography with Flash X-Ray Photography to measure 2- and 3-D displacement fields within
dynamically deforming specimens. Measurements are made throughout a plane within the specimen
seeded with X-ray opaque particles. This technique has already been successfully applied to the study
of polyester, cement1 and sand2, and is used here to study the influence of water on a sand bed under
impact from a hemispherical-tipped copper rod travelling at 100 m s"1. Significant differences in the
response of dry and wet sand beds were detected, and examples of the deformation fields measured are
illustrated here. These results may be applicable in many spheres, for example, in the design of
mechanisms to destroy buried ordnance.
the "gauge" (the lead filings) is of the same
dimension as the sand grains, introduces an
insignificant perturbation in the sample, and no
leads or power supply are required. The method
provides very data rich results with x and y
components of displacement obtained at every point
on the plane to a resolution defined by the fourier
sampling size chosen in the analysis. Here sand in
both dry and saturated states has been subjected to
an impact from a copper rod and the effect of the
moisture in the sand studied.
INTRODUCTION
Being able to measure the internal response of
sand to shock and ballistic impacts is of great use in
many fields. One possible application is in the
destruction of ordnance which are often buried in
sand. There have been investigations into the
penetration behaviour of shaped charges travelling
through sand3, but it is very difficult to obtain
dynamic measurements of the sand's response. The
technique described here is known as digital speckle
X-ray flash photography which uses digital speckle
photography (DSP) combined with flash X-rays,
Standard DSP algorithms are used4, but instead of
producing the speckle pattern by white light or laser
methods we instead seed a specimen with a
sprinkled layer of X-ray opaque filings. A
specimen such as sand lends itself naturally to this
technique because of the granular nature of the
material, and the relative ease of producing a
specimen that incorporates a layer of lead filings at
a chosen depth in the sample. The difficulty
associated with mounting conventional gauges in a
granular
material
also
demonstrates
the
advantageous nature of this technique. In this case
EXPERIMENTAL
The sand used for this study was fraction C
(David Ball Group pic, Huntingdon Road, Bar Hill,
Cambridge, CBS 8HN, England), which has a grain
size ranging from 300 to 600 |im. The projectile
was a round ended copper (XM) rod with a
diameter of 5.0 ± 0.1 mm, a length of 50.0 ± 0.5
mm and a mass of 8.6 ± O.lg. To find how much
water was needed to achieve 100 % saturation of
the sand, a volume of sand was placed in a
measuring cylinder and a known volume of water
1105
Figure, la. 120 us delay, dry (displacement vectors x3).
Figure.lb. 120 us delay, saturated (displacement vectors x3).
Figure. 2a. 240 us delay, dry (displacement vectors x3).
Figure. 2b. 240 us delay, saturated (displacement vectors x3).
Figure. 3a. 360 us delay, dry (displacement vectors x3).
Figure. 3b. 360 us delay, saturated (displacement vectors x3).
1106
added and left to soak through the sand. The
volume of supernatant water could then be
subtracted away from the total added, and the
water/sand ratio and its density could then be
calculated.
The samples were prepared in PMMA
(poly methyl methacry late)
containers,
with
dimensions of 60 x 70 x 30 mm3, (the 60 x 30 mm2
face being the impact face) filled to a depth of 10
mm with sand. The lead layer was introduced at a
depth of 5 mm. A sand depth of 10 mm was chosen
to give the optimal exposure of the film using our
ISOkeV X-ray heads. The X-ray flashes had a
duration of 30 ns. The projectile was fired at 100 ±
3 m s"1, and X-ray photographs were taken at delays
of 120 JLLS, 240 jus, and 360 jus after impact, for both
the dry and saturated samples.
To investigate more quantitatively the
displacement ahead of the projectile, graphs have
been plotted of the y-component of displacement
0.15
i
. . . . . . . . . .
X
-a— Saturate i
1 '7
;
':
^l>
:
N
f
ja
** -0.05
lw>"^^
-0.1
:
y«
:
x*i^
Nfc
j/
-n 1*5
5
10
15
• 20
25
Distance Ahead of Project:
Fig. 4a. Displacements ahead of projectile, 120 ps.
0.5
a— 33ry
0.4
RESULTS
-fl— Saturate 1
The results of these experiments can be seen in
figures la to 3b. In each of these pictures, the bolts
used to stop the sample container from moving
backwards during the impact can be clearly seen, as
can the fiducial marker region at the bottom of each
picture below the bolts. This region enables the
rigid body motions introduced by the scanning
process to be calculated and subtracted. The
displacement vectors in these images have been
scaled up by a factor of three to make them more
visible. A comparison of the 120 jis impacts shows
that there is some movement away from the tip of
the projectile in the dry case, but very little obvious
movement in the saturated case with the
displacements appearing quite noisy. This noisy
displacement map is probably due to out-of-plane
motions being comparable in magnitude to the inplane motion. By 240 jus after impact larger
displacements occur ahead of the projectile in the
saturated case than in the dry case. After 360 (is it
is clear that there is more bulk motion occurring
ahead of the projectile in the saturated case than in
the dry case. In all of these images, the response of
the sand to the impact is to flow away from the rod,
both forward and to the sides, in a manner that is
more hydrodynamic in behaviour than the response
a solid would exhibit. It is also possible to see the
effect of cavitation to the sides of the rod in all
these results (indicated by "C" in Fig. 3a). It causes
a change in density in the sand which is apparent as
a lighter shade in the X-ray image.
5
10
15
20
25
Distance Ahead of ftrolect;
Fig. 4b. Displacements ahead of projectile, 240 jis.
Fig 4c. Displacements ahead of projectile, 360 |js.
ahead of the projectile. In figure 4a to 4c, the result
of averaging the 4 columns of the displacement
vectors in the centre of the image, 21 mm in front of
the projectile can be seen. The dry sample is
represented by the solid line, and the saturated
sample by the dashed line. From these graphs it is
clear that in the 120 jis case there is very little
1107
difference between the two graphs, with the
displacement reducing quite gradually further from
the projectile tip. At 240 jus, the displacements in
the dry sand have changed little, whereas in
saturated sand the displacements are larger directly
ahead of the projectile, and remain relatively
constant at approximately 0.2 mm further into the
target. By 360 jus the disparity between the two
cases is quite pronounced. The dry sand has
remained very similar to the 240 jus case with very
little change, whereas the saturated sand has moved
significantly further, the graph being relatively flat
throughout. The behaviour seen in these plots can
be explained by considering the effect that
saturation has on the sand. The more open structure
of the dry sand enables it to compact and move
away from the projectile to the sides and even
slightly backwards, this reduces the overall effect of
bulk forward motion.
In the saturated case,
however, the sand cannot compact in the same way
since the cavities are already filled with water,
effectively an incompressible fluid at these
pressures. Consequently the sand appears to move
more like a rigid body ahead of the projectile.
ACKNOWLEDGEMENTS
The authors would like to thank Dr. I. G. Cullis
(Defence Evaluation and Research Agency
(DERA), UK, for his advice and encouragement.
The research is supported, in part, by the
Engineering and Physical Sciences Research
Council.
REFERENCES
1.
Synnergren, P., Goldrein, H.T., Proud, W.G., Appl.
Opt, 38,4030-4036 (1999).
2. Grantham, S.G., Proud, W.G., Goldrein, H.T., Field,
J.E., "The Study of Internal Deformation Fields in
Granular Materials Using 3-D Digital Speckle X-Ray
Flash Photography," in Laser Interferometry X:
Applications-2000, edited by G.M. Brown, W.P.O.
Juptner, and RJ. Pryputniewicz, Proceedings of
SPIE 4101, San Diego, USA, 2000, pp. 321-328.
3. Resnyansky, A.D., Wildegger-Gaissmaier, A.E.,
"Hydrocode Modelling of High-Velocity Jet
Penetration Into Sand," in Proceedings 19lh
International Symposium of Ballistics-200, edited by
I.R. Crewther IBS Conference Proceedings,
Interlaken, Switzerland, 2001, pp. 1561-1567.
4. Sjodahl, M., Benckert, L.R., AppL Opt. 32, 22782284(1993).
5. Goldrein, H.T., Synnergren, P., Proud, W.G.,
'Three-Dimensional Displacement Measurements
Ahead of a Projectile," in Shock Compression of
Condensed Matter-1999, edited by M.D. Furnish,
L.C. Chhabildas, and R.S. Hixson, AIP Conference
Proceedings 505, Snowbird, Utah, 1999, pp. 10951098.
CONCLUSION
A series of experiments have been carried out
on sand utilising the technique of digital speckle Xray flash photography. The measurements which
have been made of the internal displacements of dry
and moist sand would not have been possible using
any other existing technique. It was shown that
there was a measurable difference between the
response of the dry and saturated sand when
subjected to identical impacts. The purpose of this
research was to validate the use of this technique
when applied to granular materials, and its ability to
make useful comparative studies. With this proven,
the technique can now be used for more interesting
and realistic situations, and we are currently in the
process of scaling up the experiment to study
impacts from shaped charge jets on sand beds and
using a stereoscopic geometry with two X-ray
heads5. This will allow out of plane motion to be
measured as well, reducing the errors in the in-plane
measurements.
1108