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 PRINCIPAL HUGONIOT AND DYNAMIC STRENGTH OF
DOLERITE UNDER SHOCK COMPRESSION
K. Tsembelis, W. G. Proud and JJE. Field
PCS, Cavendish Laboratory, Madingley Road, Cambridge, CBS OHE. UK.
Abstract. A series of plate impact experiments was performed on Dolerite (diabase) igneous rock.
Longitudinal stresses were measured using embedded manganin stress gauges up to ca. 11 GPa. In
addition, lateral stresses were also measured up to ca. 1 GPa. In combination with the longitudinal
stresses, these results have been used to obtain the material shear stress under shock compression.
Results indicate that the longitudinal behaviour is elastic for the stress range involved although shear
stresses indicate deviation from elastic loading for longitudinal stresses higher than ca. 4.3 GPa. The
results are then compared and contrasted to data for other geologic materials.
INTRODUCTION
EXPERIMENTAL PROCEDURE
The shock properties of geological materials
have long been a source of interest. Traditionally,
the main driving forces have been planetary impact
and geological research. Recently, there has been a
growing interest in the shock properties of concrete,
where geological materials are added as aggregates
[1-2]. In addition, most available information
consists of Equation of State (EoS) data. There are
few data on the dynamic strength of such brittle
materials because of the difficulty in obtaining such
results. However, such results are needed to help
develop constitutive models for these materials. In
the last fifteen years a technique has been developed
[3] using manganin gauges to measure the lateral
stresses in materials under shock loading.
Combining both Hugoniot and lateral data, shear
stress information can be obtained. In this paper,
results are presented on Hugoniot and lateral
experiments performed on Dolerite. Dolerite (also
known as Diabase) is a fine-to medium-grained,
dark grey to black intrusive igneous rock [4].
Chemically and mineralogically, it closely
resembles the volcanic rock basalt, but it is
somewhat coarser and contains glass. With increase
in grain size it resembles gabbro.
All the impact experiments were carried out in
the plate impact gun facility at the University of
Cambridge [6], which consists of a single stage 50
mm bore light gas gun. The gun is capable of
achieving velocities up to 1200 m s"1. The impactor
materials consisted of copper and tungsten. Impact
velocities were measured to an accuracy of 0.5%
using a sequential pin-shorting method and tilt was
arranged to be less than 1 mrad by means of an
adjustable specimen mount. To measure the
Hugoniot of Dolerite, manganin stress gauges
Figure 1. Target configuration
1385
(MicroMeasurements type LM-SS-21OFD-050)
were embedded between tiles 8 and 17 mm thick.
One sample was prepared with the stress gauge
supported on the rear surface with a block of
Polymethylmethacrylate
(PMMA).
In
that
configuration the gauge had a faster rise time due to
the near impedance match of the PMMA, epoxy
adhesive and gauge package. Material specimens
for lateral gauge experiments were sectioned in two,
and commercial stress gauges (J2M-SS-580SF-025)
were introduced 3 and 8.2 mm from the impact
surface of each sample. Samples were assembled,
for both configurations, using a low viscosity epoxy
with a curing time of approximately 24 hours.
Lateral gauge data were reduced using the analysis
of Rosenberg and Partom [3]. The shear stress ( )
of the material can thus be calculated through
knowledge of the longitudinal ( x) and lateral
stresses ( y) through the relation,
wave profiles for experiments IHdol/lTdol and
4Hdol/4Tdol, respectively (for impact conditions,
see Tables 1 and 2). The solid trace corresponds to
the longitudinal stress while the dotted traces
correspond to the lateral stresses at two different
positions. It can be seen that the longitudinal
stresses have higher values than the lateral ones and
their difference leads to the shear stress inside the
material according to equation 1.
= a v -a.
(1)
Our method of determining the shear stress has the
49
49.5
50
50.5
51.5
52
52.5
53
Time (MS)
Figure 2. Stress Wave Profiles for experiments
IHdol/lTdol (see Tables 1 and 2 for impact
conditions).
advantage over previous calculations of being direct
since no computation of the hydrostat is required.
MATERIAL DATA
Dolerite tested in this study, was supplied by
Concrete Structures Section (CSS), Department of
Civil & Environmental Engineering, Imperial
College, London, UK as a part of a large block
weighting over 20kg. It was then cut into smaller
specimens with dimensions 8-20 mm thick by 50
mm x 50 mm. Density and ultrasonic measurements
were performed after grinding the samples. Several
samples were used. The density was 2894 ± 27 kg
m"3, while the longitudinal and shear elastic wave
speeds, determined using ultrasonic transducers,
were 5.89 ± 0.07 and 3.34 ± 0.11 mm us"j
respectively.
Time (MS)
Figure 3. Stress Wave Profiles for experiments
4Hdol/4Tdol (see Tables 1 and 2 for impact
conditions).
Figure 4 illustrates the Dolerite Hugoniot curve
together with the Hugoniot data for Gabbro and
Diabase [6-8]. It can be seen that all data are tightly
grouped together. In addition, the Dolerite data have
been fitted with the elastic impedance of
RESULTS AND DISCUSSION
Table 1 summarises the impact conditions and
Hugoniot stresses for the longitudinal experiments,
while Table 2 summarises the impact conditions,
lateral stresses and shear stresses obtained using
equation 1 and the gauge data. Figures 2 and 3
illustrate some typical longitudinal and lateral stress
1386
Table 1. Experimental parameters and results for longitudinal data and Hugoniot points
Shot
no.
Impactor
material
Target Front
Sample
Target Backing
Sample
Impact Velocity
(m s"1)
Hugoniot Stress
(GPa) ± 3%
IHdol
2Hdol
3Hdol
4Hdol
IBdol
lOmmCu
lOmmCu
lOmmCu
6 mm W
lOmmCu
8.26 mm Dol
8.20 mm Dol
7.69 mm Dol
7.35 mm Dol
6.8 mm Dol
17.16 mm Dol
17.22 mm Dol
17.25 mm Dol
8.40 mm Dol
12mmPMMA
519
702
833
815
451
6.08
8.39
10.17
11.34
5.16
Particle Velocity
(mm us"1)
±3%
0.35
0.48
0.57
0.67
0.31
Table 2. Experimental parameters and results for lateral data and shear stresses
Shot no.
ITdol
2Tdol
3Tdol
4Tdol
5Tdol
O
A
S.
Impact Velocity (m s"1)
Impactor
material
lOmmCu
lOmmCu
1 0 mm Cu
6 mm W
lOmmCu
521
703
835
814
265
Lateral Stress (GPa)
±4%
2.90
4.49
5.68
6.86
1.01
Diabase - Meryland
Diabase - Virginia
2*Shear Stress (GPa)
±6%
3.18
3.90
4.49
4.48
2.12
o
I
15
"n
Time (MS)
0.4
0.6
Figure 6. Stress Wave Profile for experiment IBdol
(see Table 1 for impact conditions)
1
Particle Velocity (mm us' )
Figure 4. Dolerite Hugoniot
the material such as G x = p 0 U p C L , where
4
6
0
is the
initial density of the material, Up is the particle
velocity and CL is the longitudinal wave speed. The
agreement with this fit is excellent suggesting elastic
loading. Although no Hugoniot Elastic Limit (HEL)
data are available for Dolerite, HELs for other
igneous geological materials have been quoted; for
instance, basalt [9] has an HEL in the vicinity of 5
GPa, while jadeite has a quoted HEL [10] in the
range 5.8-7.2 GPa. It is possible that the elastic and
shock impedances of Dolerite are similar and thus
make it difficult to resolve the change in slope at the
HEL in the trace.
8
Hugoniot Stress (GPa)
Figure 5. Dolerite Shear Stress
1387
Figure 5 illustrates the Dolerite and Gabbro [7]
shear stress vs. Hugoniot Stress. The Dolerite data
have been fitted to the elastic loading line using
resolve the two-wave structure because of similar
elastic and shock impedances.
ACKNOWLEDGEMENTS
l-2v
„ = ———
2i
1-v
(2)-
The Defence and Evaluation Agency, UK has
sponsored this work, under contract WSS/U3257.
Dr. A. Pullen from Imperial College provided the
cement samples. Dr J. Sheridan, C. O'Carroll, I.G.
Cullis and P.D. Church are thanked for their
interest. Finally, we thank D.L.A. Cross and R.
Flaxman for technical support.
It can be seen that above a Hugoniot stress of ca.
4.3 GPa the material behaviour deviates from the
purely elastic loading suggesting a process such as
fracture or damage in the shock front, which results
in reducing the dynamic strength of Dolerite. Note
that when lateral stress measurements are taken
below 4.3 GPa, the shear stress lies on the elastic
loading line. This result can lead to the conclusion
that a Hugoniot stress of 4.3 GPa is a possible HEL
value.
For that reason, an extra longitudinal shot was
performed where the Dolerite was backed by
PMMA. Because of similar impedance between the
gauge package and PMMA the gauge rise time was
ca. 10ns, compared to 200 ns for a fully embedded
gauge. The measured stress in the PMMA ( p) was
converted to stress in the Dolerite ( D) through the
well-known relation
2Z D
REFERENCES
1.
2.
(3)
6.
where ZD and ZP are the elastic and shock
impedances of the Dolerite and PMMA,
respectively. The trace is illustrated in Figure 6.
The stress induced in the Dolerite was 5.11 GPa,
higher than the presumed HEL. However, no twowave structure was seen, reinforcing the assumption
that the elastic and shock impedances are similar.
Experiments with VISAR are under way to resolve
this discrepancy.
7.
9.
10.
CONCLUSIONS
Plate impact experiments have been presented
to assess the longitudinal and deviatoric behaviour
of the Dolerite. Results indicate that the Hugoniot
curve is elastic up to 11 GPa. However, shear stress
data show a deviation from elastic loading at a stress
of 4.3 GPa. It can thus be concluded that the HEL is
around that value and the gauges were unable to
1388
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