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
For special copyright notice, see page 306.
TRANSMISSION OF SHOCKS ALONG THIN-WALLED TUBES
D.A. Salisbury, A.R. Giles and R.E. Winter
AWE, Aldermaston, Reading, Berkshire, RG7 4PR, UK
Experiments have been fired in which stainless steel tubes of internal diameter 50 mm, ranging in
thickness from 2.5 mm to 7.5 mm and of two lengths, 40 mm and 80 mm, are shocked at one end by an
explosive charge. The other end of the tube is positioned in contact with a steel anvil. Before it reaches
the anvil, the transmitted stress pulse attenuates to an elastic-plastic wave. The transmission of the
stress pulse along the tube and into the anvil is monitored (a) by strain gauges on the surface of the tube
and (b) by pressure gauges positioned at the input and output ends of the cylinder and embedded in the
steel anvil. The experimental data is compared with the ALE code CORVUS. The timing and shape of
features observed within the calculated wave profiles match those in the gauge data.
INTRODUCTION
The use of hydro-codes to model the response of
complex systems to extreme environments requires
reliable treatments of material properties over a
wide range of strain rates and stress regimes.
Applications to real problems generally involve
multiple materials in complicated geometries.
Underwriting such code methodologies involves the
identification of specific aspects of the overall
problem and designing simpler focussed
experiments to provide data against which to
benchmark. A programme is underway at AWE to
underwrite the application of hydro-codes to the
response of complex assemblies to explosively
generated shocks. The transmission of shocks along
thin walled tubes has been identified as an area for
focussed study. Thin walled structures in the form
of external packaging or internal fixtures may
provide the fastest route through which shocks
generated externally can reach any particular
internal component. During propagation through
these thin structures, attenuation and dispersion will
degrade the shock wave to an elasto-plastic pulse.
The form of the pulse reaching the location of
interest will depend on the path length and
geometry of the transmitting material as well as its
mechanical properties. Konrad et al (1,2) required
data against which to benchmark the ALEGRA
code over a wide range of strain-rates. Gas gun
experiments were reported in which spherical
projectiles impacted the end of a closed tube
instrumented with VISAR, strain and Carbon
gauges.
The experiments described here use an explosive
charge to shock one end of a stainless steel tube in
an axi-symmetric geometry. Strain gauges and
PVDF stress gauges diagnose the shock entering the
end of the tube, its propagation along the tube wall
and its transmission into a stainless steel anvil in
contact with the lower face of the tube. Data from
experiments on tubes of 3 different wall thicknesses
and 2 different lengths are compared with results
from calculations performed with the AWE finite
element Arbitrary Lagrangian-Eulerian (ALE)
hydrocode CORVUS. A purely Lagrangian
calculation could never be applied satisfactorily to
geometries such as this, as the escaping detonation
products would cause the mesh to tangle and stop
the calculation prematurely and a uniform Eulerian
calculation would either lack sufficient mesh
resolution, particularly in areas of interest, or
become computationally expensive. The ALE route
attempts to keep as much of the flow Lagrangian in
nature as possible in important areas, whilst dealing
with thin and contorted layers of material with a
more robust Eulerian-type treatment. The
calculations presented here are performed with
Winslow's equipotential mesh movement algorithm
(3) and the material in the thin wall is weighted to
effectively double the resolution of the elasticplastic wave.
CORVUS uses Van Leer's well-established
second order monotonic scheme in volume coordinates to rezone the single material cells (4) and
a Volume of Fluid (VOF) description to represent
the material interfaces that have been allowed to
ALE. The resulting multi-material cells are then
advected using an improved SLIC interface
reconstruction scheme (5).
The Steinberg-Guinan elastic-plastic model (6)
was used to model the material strength of the steel
with a Gruneisen EoS (7). A standard mesh size of
0.5 mm was used. Comparisons were made with a
finer mesh of 0.25 mm. As one would expect the
coarser meshed calculations give lower resolution
and smoother output than the fine mesh. Although
rise times are increased and peak pressures slightly
degraded, it was decided to use the standard
meshing scheme for the main study. These were
found to be more robust, enabling longer coverage
in significantly less CPU time (approximately 4
hours to run 25 jus).
detonate on axis
40mm & 80mm
PVD!
gauges
FIGURE 1. Test Geometry
close to the anvil. These gauges were orientated to
record strain in the axial direction only. PVDF
gauges of 1 mm by 1 mm size were positioned on
both end faces of the tube, centred on the wall midthickness. Larger (3.18 mm by 3.18 mm) PVDF
gauges were located at the anvil interfaces directly
in line with the wall mid-thickness.
RESULTS AND DISCUSSION
EXPERIMENTAL GEOMETRY
The small element PVDF gauge located at the
input face of the tube is identified as PL In all four
experiments it records a strong, fast rising shock
entering the tube wall. Although above the
breakdown threshold for the gauge insulation, the
data and the calculations suggest that a shock of
magnitude over 160 kb and duration of the order of
1 jus is transmitted into the tubes. All four signals
provide a time of arrival for the shock and all time
scales for the data presented here have been
adjusted so that the time origin is the shock arrival
at this first gauge.
Figure 2 shows data obtained in the 2.5 mm tube
experiment from PVDF gauges positioned on the
end face of the tube and embedded in the anvil.
Also shown are calculated stress profiles. Data from
gauges located at the same interface but at different
rotations imply good symmetry. It can be seen that
the shock wave transmitted into the top of the tube
has undergone dispersion and attenuation during its
propagation along the tube length. The resulting
The experimental arrangement for the tests is
shown in Fig. 1. Stainless Steel tubes (304S11) with
internal diameter 50 mm, length 40 mm and wall
thicknesses of 2.5 mm, 5.0 mm and 7.5 mm were
studied. A test was also conducted on an 80 mm
long 5.0 mm thick tube. One end face of the tube is
covered by a thin steel plate upon which is located
the explosive charge. The 100 g donor charge
consists of a cylinder of PE4 (88% RDX, 12%
lithium stearate grease) of diameter 60 mm and
depth 48 mm. It is confined within a 5 mm PMMA
cylinder and is initiated by an EBW detonator
inserted into a hole in the top plate of the confining
PMMA. The other face of the tube is in contact with
a 22 mm thick steel "anvil". The anvil is made up of
one 2 mm and two 10 mm plates, providing
interfaces at 0, 2 and 12 mm from the end of the
tube into which gauges were embedded. All steel
plates and tubes were manufactured from 304S11
steel. Two strain gauges were located on the outside
wall of the tubes, one near the "donor", the other
304
P r e s s u r e (Mb)
0.IOOOOOOE-02
0.2000000E-02
0.3000000E-02
Q.4000QOOE-02
O.SOQQOOOE-02
0.6000000E-D2
0.7000000E-02
0.8000000E-02
0.9000QOOE-Q2
0. IOOOQQOE-01
FIGURE 4. Calculated pressure contours (7.5 mm tube at 7 us)
FIGURE 2. PVDF gauge data and calculation at anvil for
2.5 mm tube
6
8
10
time relative to P1, MS
12
have similar rise times and magnitudes. The
attenuation and wave speed decrease in these two
thicker tubes is significantly less than measured and
calculated for the 2.5 mm tube. A noticeable feature
of the calculated profiles is the oscillations that
appear to increase in wavelength and amplitude
with increasing wall thickness. The recorded stress
profiles for the 5.0 and 7.5 mm tubes show steps
with similar wavelengths. Contour plots from the
calculations, an example of which is shown in Fig.
4, show the origin of these features to be reflections
and releases from the tube walls creating a
succession of propagating pulses. Both the
experiment and the calculation show that these
oscillations are rapidly damped in the 2.5 mm thick
tube.
Data and calculations from the 80 mm length, 5
mm thick tube show that the stress pulse has
undergone further dispersion as it has transited the
additional 40 mm of tube giving an increase in the
observed rise time. The gauge has recorded a
distinct two-wave structure that is in close
agreement with the calculated stress profile.
The data from the strain gauges near the lower
face of the tube all show very similar features over
an extended time-scale as can be seen in Fig. 5.
Periods of both constant and zero strain rate can be
identified. Figure 6 shows that calculated strain
histories agree very well with this data at early time.
The wave reverberations observed in the stress data
and calculations are very clear in this strain data
and, as suggested by the stress profiles, damping of
these reverberations is seen to increase as wall
thickness decreases.
14
FIGURE 3. Measured and calculated shock profile 2 mm into
anvil for 5.0 and 7.5 mm tubes
stress wave measured in the anvil is elasto-plastic in
nature with significantly reduced magnitude and
increased rise time relative to the input pulse.
Figure 3 compares data from the PVDF gauge
located 2 mm into the anvil and the calculated
stresses for the 5.0 and 7.5 mm thick tubes. The
PVDF traces shown have not been corrected for
lateral strain. However, data from a bi-directional
strain gauge at this position indicate that the gauges
do not encounter any lateral strain for at least 5 us
after stress wave arrival. Differences between
calculated and measured arrival times imply that the
calculated wave speeds are 5 to 10% higher than
those measured. Fine mesh calculations were found
to achieve a much closer agreement in wave arrival
times. Experiment and calculation show that the
initial waves transmitted in the 5 and 7.5 mm tubes
305
0.005
-0.005
-0.01 -0.015
-0.06
— 2.5mm X 40mm
—2.5mm calc
— 5.0mm X 40mm
—5.0mm calc
-0.02
10
20
30
40
50
60
70
10
time relative to P1, ps
15
20
25
time relative to P1, [is
FIGURE 5. Strain data from gauge located near anvil
FIGURE 6. Comparison of calculation and early time strain
records
CONCLUSIONS
An investigation into the transmission of
explosive shocks along tubes has been described.
Examples of data obtained from PVDF stress
gauges and strain gauges have been presented,
PVDF gauges embedded in the anvil provide
information on the transmitted wave arrival time,
rise time and structure at early time. Strain gauges
positioned near the end of the tube survive to record
a longer deformation history. Experimental results
have been compared with preliminary calculations
performed on the ALE code CORVUS. Results
from a standard mesh resolution and material model
show qualitative agreement. Calculations with finer
mesh appear to improve the agreement to time-ofarrival data but currently do not run sufficiently
long to merit inclusion in this paper. Evidence of
wave reverberations predicted in the calculations
can be seen in the experimental data. Both
calculation and experiment suggest that damping of
these modes increase with decreasing wall
thickness. Data of the form presented here will be
used to optimise the CORVUS methodology for
assessing the response of complex assemblies to
explosively generated shocks.
2.
3.
4.
5.
6.
7.
Bench Mark Data for ALEGRA Code Validation", in
Shock Compression of Condensed Matter edited by
Furnish, Chhabildas, Hixon, AIP Conference
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Winslow, A. M., "Equipotential zoning of twodimensional meshes" Technical Report UCRL-7312,
Lawrence Livermore National Laboratory, (1963).
Barlow, A. J., "ALE in CORVUS", in Proceeding of
New Models and Numerical Codes for Shock Wave
Processes in Condensed Media, Oxford, pp 581-596,
(1997).
Barlow, A. J., "Mesh Adaptivity and Material
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Cochran, S. G., Steinberg, D. J. and Guinan, M. W.
"A Constitutive Model for Metals Applicable at High
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© British Crown Copyright 2001/MOD
Published with the permission of the Controller of Her
Britannic Majesty's Stationery Office.
REFERENCES
I. Konrad, C. H., Reinhart, W. D., Chhabildas., L. C,
Mann, G. A., Mosher, D. A., Kipp, M. E., Trucano, T.
G., Summers, R. M., Peery, J. S., "Experimental
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