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
ON THE MEASUREMENT OF SHEAR-STRENGTH
IN QUASI-ISENTROPIC LOADING
Z. Rosenberg, N.K. Bourne*, G.T. Gray lll\ and J.C.F. Millett*
RAFAEL, PO Box 2250, Haifa, Israel
*Royal Military College of Science, Cranfield University, Shrivenham, Swindon, SN6 8LA, UK.
f
Los Alamos National Laboratory, MS-G755, Los Alamos, NM87545, USA.
Abstract. It has been a subject of discussion that the rate of loading of a material determines the
strength it appears to exhibit. This observation has implications for understanding and modelling the
deformation mechanisms involved in high-strain rate and shock-loading. Discussion has focussed upon
the response of various metals. The loading has ranged from prompt shock to pillow loads (graded
density impactors) which give uniformly rising pulses over varying times. One variant upon such
loading is to allow the stress to rise in steps to a final Hugoniot level which averages to a lower rate.
Clearly, while the applied strain-rate during the rise in the steps is still of the same order as that in
shocks, the loading is more quasi-isentropic in nature. As a means of observing the strength of a
material, the lateral stress in the sample may be monitored along with the longitudinal stress therefore
allowing a direct measurement (in uniaxial strain) of the difference between these two values. Potential
mechanisms explaining the experimental results and comments on the interpretation of the
experimental diagnostics and design is given.
Other investigation (5) has indicated that the
lower temperature afforded in a material during
loading along the isentrope can cause the difference
in strength between an equivalent shot up the
isentrope. The results of pillow and shock impact
experiments showed that the quasi-isentropic
compression curve lies above the Hugoniot up to
140 GPa in tungsten. The explanation of this
behaviour was attributed to loading rate effects on
temperature. However, the range considered (up to
250 GPa) is an order of magnitude higher stress
values than are applied in the research reported here
(which is to 10 GPa).
In a further recent paper, Al'tshuler (6) has
conducted measurements of the shear strength
under shock. He assesses the strengths and
weaknesses of the various available experimental
methods and emphasises the need to minimise the
thickness of the insulation layers around stress
gauges. However, his analysis of gauge data does
not differentiate between the differences in
calibration of lateral and longitudinal gauges. The
INTRODUCTION
Recent work has shown that an FCC material
loaded at a high strain-rate (but sub-shock) level,
can exhibit higher strength than one loaded by a
prompt shock (1-3). This experimental observation
is puzzling given the state-of-the art in
understanding defect generation and storage during
high strain-rate versus shock loading. The
unexplained loading-rate effect may be followed by
jumping to a shocked state and then ringing up on
an isentrope so that the loading departs from the
Hugoniot after the first bounce. This relies on the
development of an analysis to convert the voltage
recorded in the gauge to lateral stress that must be
checked for the step loading. The materials that are
tested in the current paper are iron and copper that
are representative of BCC and FCC materials to
give an insight as to the mechanism responsible for
the observed phenomena. A mild steel (EN3B) was
also tested since it showed a hardening behaviour
with impact stress in previous work (4).
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foil gauges used must be correctly deconvolved if
correct values are to be obtained (7).
The various loading means applied all have
considerable pedigree. However, standing off an
explosive charge to apply a ramped loading pulse,
may not provide one-dimensional loading with
consequent affects upon the assumed gauge signals.
Post-yield strengths in copper have been
quantified using shock recovery and post-shock
mechanical testing of the targets loaded along
different paths to a peak pressure of 10 GPa and
pulse duration of 1 microsecond using a 'pillowramp', step, and prompt shock loading (8).
Decreasing the strain-rate of loading from a prompt
shock was shown to correlate to an increased level
of post-shock yield strength and defect storage, i.e.
dislocation density (8). The effect of loading rate
on post-shock defect generation and storage and
thereby mechanical response was postulated to be
directly related to changes in the amount of defect
storage in response to the applied plastic strain rate
during the entire shock loading and release cycle
(8).
The current experiments aim to further explore
the influence of strain rate on the evolution of
material strength during high-rate and impact
loading and thereby extend the previously attained
results by obtaining simultaneous direct
measurement longitudinal and transverse stresses to
deduce the shear strength.
and in all cases the experiment was designed to
mimic the effects of a single shock to 10 GPa. A
Lagrangian X-t diagram for the impact is shown in
Fig. 1.
5
.4
- 1 0
-
5
0
5
FIGURE 1. Lagrangian X-t diagram showing shock propagation
in PMMA cover plate ramping the stress pulse arriving in the
target. The vertical dotted lines represent the positions of, at 1
mm a longitudinal gauge, and 3 mm into the target, a lateral
gaugeImpact velocity was measured to an accuracy of
0.5% using a sequential pin-shorting method and tilt
was fixed to be less than 1 mrad by means of an
adjustable specimen mount. Impactor plates were
made from lapped discs and were mounted onto a
polycarbonate sabot with a relieved front surface in
order that the rear of the flyer plate remained
unconfmed. Targets were lapped flat to less than 2
^im across the surface. PMMA sheets of thickness 1
mm were used to encapsulate the manganin stress
gauges (MicroMeasurements type LM-SS-125CH048). Lateral stresses were measured using
manganin stress gauges of type J2M-SS-580SF-025
(resistance 25 Q). These gauges had an active width
of 240 \im and were 2 mm into the metallic target.
EXPERIMENTAL
A series of different geometries were designed
for impacts using a 50 mm single-stage gas gun to
examine the influence of loading rate on material
shear strength. The means of achieving lower rate
loading was to let the stress ring up in the target by
placing a lower impedance plate onto the impact
face thereby forcing the 'ring-up' of the stress
pulse. This target had a gauge at its centre to
measure the longitudinal stress. The lateral stress
was measured simultaneously 2 mm into a plate of
target material which had been evaluated under
single shock previously (4). The materials used
were XM copper, AQ85 iron, and mild steel EN3B.
The materials' properties are given in Table 1 and
are hereto for referred to as copper, iron and mild
steel. The impactor was a thick tile of the target
material, i.e. simple-centered flow was maintained,
TABLE 1. Materials properties used in this investigation.
XM copper
AQ85 iron EN3B mild
CL /m s"1
cs /m s"1
p/kgnr 3
Vickers hardness
/kg mm"2
Grain size //xm
steel
5913±5
4760±10
2330±5
8924
(±1%)
55±5
5940±15
3260±5
7856
(±1%)
80±5
3248±2
7818
(±1%)
254±3
15±5
30±5
15±5
The lateral stress, cry was used along with the
longitudinal stress, crx to calculate the shear strength
of the material rthus
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The lateral stress traces rise in the same manner and
the first step shows a relaxation with similarly
subsequent steps showing slight rises. A similar
operation was affected in determining the stress and
its error to that described above.
This quantity has been shown to be a good indicator
of the ballistic performance of a material (9). This
method of determining the shear strength has the
advantage of being direct since no modelling and
calculation of the hydrostat is required.
10
RESULTS AND DISCUSSION
-v 8
I
The methodology of the experiment requires the
use of a lateral gauge to measure that component of
stress in the target. As a check it must be ensured
that a cover-plate does not affect the states to be
measured. For this reason a pair of calibration shots,
were executed. In one of the experiments, a glass
target had a 1.6 mm copper cover plate attached to
it which was the same material as the flyer and was
thin enough not to ramp the wave. The shot was
chosen in the elastic range of the DEDF target. It is
known that such materials show a second failure
front behind the shock (10) and that the lateral
stress thus rises in two steps. The two traces, with
and without cover plate were near identical
demonstrating that the gauge is not affected by the
extra interfaces introduced in the sample
configuration.
In the experiments that follow, the impacts
shown schematically in figure 1 were conducted.
The targets chosen were copper (as an example of
an FCC material), iron (a BCC material) and EN3B
mild steel. These materials have previously had
their strengths during single shocks measured (4).
The traces recorded from the two gauges in each
experiment are shown in fig. 2. Traces for the
longitudinal (solid) and lateral stress (dotted) are
shown for each material. The two are separated in
time by the transit time of the shock through 2 mm
of the target.
The longitudinal gauges are seen to rise in a
series of steps as the stress wave reverberates in the
target. The first step represents a shock in the
PMMA due to the impact, but the next, and every
other reflection, are given by the state of
longitudinal stress in the target material.
These steps are rising slightly (after the first)
and so the stress is taken to be at the point where
the next reverberation occurs and the error bar in
fig. 3 reflects the stress increment during the rise.
6
I 4
$
0
a).
0
0.5
1
1.5
Time (/us)
2
2.5
0
0.5
I
2
2.5
0
0.5
1
2
2.5
10
I4
1.5
Time (jus)
10
I4
Ot
c).
1.5
Time (ps)
FIGURE 2. a). Copper, b). iron and c). mild steel targets with
longitudinal gauge in the 2 mm cover plate and a lateral gauge at
2 mm into the target (see fig. 1).
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FIGURE 3. Twice the shear strength (equation 1) plotted against
the stress impacted for the three materials considered, copper
(Cu), iron (Fe) and EN3B mild steel (MS). The open symbols are
single shock experiments at the respective stress values. The
filled symbols represent points measured from fig. 2.
The longitudinal and lateral stress values for
each bounce of the ring-up were measured and
twice the shear strength calculated using equation 1.
The strength for the three sample materials was then
plotted against the longitudinal stress in fig. 3. The
solid symbols represent measured values for the
twice the shear strength determined in single shock
experiments (4). The hollow symbols were
calculated from each of the steps in the loading
curves of fig. 2. The shape of the symbol is used to
identify each material tested. The measurements of
the single shock experiments were done with larger
stress gauges than used presently and the error bars
are consequently larger. The shaded bands indicate
the range of behaviour for copper and iron for the
lighter, and the steel for the darker gray
respectively.
The data plotted in fig. 3 shows that the shock
shear strength remains constant (within error) for
the pure metals, but increases with impact stress for
the steel. On the other hand the dark quasiisentropic points tell the opposite story. Within
error, the successive strengths for the copper
loading remain constant whilst those for iron and
steel increase at a faster rate than the steel did for
the single shock case. Further work is underway to
reduce scatter in the data.
CONCLUSIONS
The influence of strain rate in the impact regime
versus prompt shock loading has been recently
suggested to result in different strength levels in
578
high-symmetry metals such as copper. In the
current paper the results of shear strength
measurements on copper, iron, and a low-carbon
steel as a function of loading rate have been
quantified. The results of varying strain-rate loading
experiments on copper, iron, and steel suggest a
strong positive pressure dependency of the shear
strength of iron and steel (an iron-carbon alloy) on
increasing shock pressure while copper exhibits
essentially a stress independent response. These
results suggest that the overlying importance of
crystal symmetry on the pressure dependency of the
strength of these materials; increased pressure
dependent shear modulus is critical to
understanding loading-rate effects in metals.
Further experiments on model materials are needed
to quantify the role of crystal structure and
microstructure on the shock response of metals and
alloys.
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