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
HUGONIOT ELASTIC LIMIT AND SPALL STRENGTH OF
ALUMINUM AND COPPER SINGLE CRYSTALS OVER A WIDE
RANGE OF STRAIN RATES AND TEMPERATURES
S.V. Razorenov1, G.L Kanel2, K. Bamming3, and H.J. Bluhm3
1
Institute of Problems of Chemical Physics. Chernogolovka, 14243 2 Russia.
Institute for High Energy Densities. IVTAN, Izhorskaya 13/19, Moscow, 127412 Russia
3
Forschungszentrum Karlsruhe, P.O. Box 3640, 76021 Karlsruhe, Germany.
Abstract. Anomalous rise of the Hugoniot elastic limit (HEL) with increasing temperature was
observed for aluminum and copper single crystals. Within the temperature range from 20°C to 650°C
the HEL of aluminum single crystals increased from 0.12 to 0.96 GPa for 3 mm thick samples and to 3
GPa for -0.25 mm thick samples. The spall strength decreased from 2.3 GPa and 3.2 GPa at room
temperature to 1.3 GPa and 2.2-3 GPa near the melting temperature for thicker and thinner samples,
respectively. For copper single crystals a HEL of 2.6 GPa was recorded at 833°C; whereas the spall
strength decreased from 5.4 GPa at room temperature to 4.8 GPa at 485°C.
practically zero as soon as temperature approaches
Tm [4]. The dynamic tensile strength of zinc single
crystals [3] behaves athermally up to -0,95 Tm, a
further temperature increase also results in a
decrease of the strength.
In this paper we present results of measurements
of strength properties of aluminum and copper single
crystals at normal and elevated temperatures.
INTRODUCTION
Shock wave experiments at elevated
temperatures allow studying strength properties and
governing mechanisms of inelastic deformation and
fracture at extremely high strain rates. In particular,
an anomalous growth of the flow stress with rising
temperature may be expected [1]. However, the
influence of temperature on the yield strength, as
well as on the tensile strength, at very high strain
rates were not enough verified yet by experiments.
There were just a few observations of the
mechanical yielding and strength behavior of metals
under shock wave loading at elevated temperatures.
In contrast to the highly temperature sensitive quasistatic yield stress, the dynamic yield stress was
found to be independent of temperature [2,3] or even
increases [4] near the melting temperature. Shockwave measurements also show a nearly athermal
behavior of the spall strength of solid metals. The
resistance to spall fracture of polycrystalline
aluminum and magnesium does not vary much when
increasing the temperature up to 85-90% of the
melting temperature Tm but precipitously drops to
MATERIALS
Aluminum and copper crystals of 99.999 %
purity were grown from a melt by the directed
crystallization technique. The 11x15 mm samples
were 0.3 to 2.85 mm thick. The sample planes were
parallel to the (100) base crystal plane. The sample
surfaces were ground and then electrochemically
etched to remove surface defects.
EXPERIMENTAL
Two kinds of shock-wave generators were used
in order to cover a wider range of load durations.
Shock load pulses of -200 ns duration were
generated in 2.85 thick samples by 0.4 mm thick
503
aluminum flyer plates launched by explosive
facilities [4] to velocities of 600 to 700 m/s.
For the measurements at shorter times we used
the pulsed high-power proton beam of the Karlsruhe
Light Ion Facility KALIF [5] as a shock wave
generator. The ablative pressure generated by the
proton beam produced a compression wave with
incident load duration of ~40 ns. The sample
thickness in the beam driven experiments varied
from 0.25 mm to 0.85 mm. The free surface velocity
histories of the samples were recorded using VISAR
and ORVIS laser Doppler velocimeters. The ORVIS
was used in the line-imaging mode [6].
The measurements were performed over a
temperature range from 20°C to 650°C for
aluminum and up to 830°C for copper. Note that the
melting temperature is 660. 1°C for aluminum and
1083°C for copper. The power of used resistive
heaters was sufficient to reach the test temperature
after 10 minutes of heating. The temperature was
controlled by a thermocouple placed in contact with
the rear surface of the sample close to the point of
the free surface velocity measurements.
Figure 1 shows an example of the line-imaging
ORVIS streak record. The bell-shaped power density
distribution along the cross-section of the KALIF
beam results in transversely varying amplitude in a
planar ablation pressure wave. The gradient of peak
stresses along the measuring line on the sample
surface results in a varying propagation velocity of
the shock wave that explains the tilt of the shock
wave front relative to the sample plane. The radial
stress gradient should not create problems for the
measurements since the resulting tilt of the shock
wave is small enough to approximately meet the
assumption of planar geometry used in the data
evaluation. Thus, using a line-imaging ORVIS and
the proton beam as a shock-wave generator, we were
able to measure wave profiles over a range of peak
stresses in a single experiment.
The free surface velocity history, Ufs(f), of a
fixed point on the sample surface (that corresponds
to fixed ordinate y in the interferogram) was
determined by the linear approximation
Ufs(t) = n*uQ + u0 xAy(0/4y/(0
FIGURE 1. Line-imaging ORVIS streak record of the KALIF
experiment with a 0.825 mm thick copper single crystal at room
temperature. The total duration of the record is 156 ns, the
velocity-per-fringe constant was MQ = 172.2 m/s,.
50
100
150
Time, ns
FIGURE 2. The free surface velocity histories of copper single
crystal evaluated from the ORVIS interferogram shown in Fig.2.
the fringe closest to the given y in the direction of
the velocity increase; Ay/ is the distance between
two neighboring fringes. Obviously, Eq. (1) may be
used for interpreting the line-imaging interferograms
when the velocity gradients duldy are constant or
almost constant along the.y-axes. We used in Eq. (1)
the values of Ay and Ay/along directions of smallest
local gradients in the interferogram.
Figure 2 shows the velocity histories ufs(t)
evaluated from the experimental record shown in
Fig. 1. Each wave profile describes a velocity
history of a separate point on the sample surface. In
this shot the peak stress was close to the spall
threshold, so the free surface velocity histories with
and without a spall signal have been recorded.
(1)
RESULTS
where UQ is the velocity-per-fringe constant of the
interferometer; n is the number of fringes crossing a
horizontal line of a given y\ Ay is the deflection of
Figures 3 and 4 show typical free surface velocity
histories measured for aluminum single crystal
504
800
0.1
0.2
0.3
Time, us
FIGIRE 3. Free surface velocity histories of 2.90±0.05 mm thick
aluminum single crystals impacted by 0.4 mm thick aluminum
flyer plates at different test temperatures.
FIGURE 4. Free surface velocity histories of ion beam driven
experiments at 20°C and 622°C. The sample thickness was 425
JJJTL and 260 jjm, respectively.
samples at normal and elevated temperatures. The
wave profiles demonstrate an anomalous increase in
the precursor wave amplitude as the test temperature
rises. Comparison of the data shown in Figs. 3 and 4
shows a rapid decay of the precursor wave at high
temperature that is an evidence of a strong rate
sensitivity of the yield stress. The velocity pullback,
which is a measure of the spall fracture stress,
remains high up to the maximum temperature of
temperature, the yield strength is less sensitive to
temperature than the Hugoniot elastic limit.
The fracture stress at spalling a* is calculated
from the measured velocity pullback Aufs between
the peak velocity and the value right ahead of the
spall signal front. It was suggested [9] and later
confirmed by a detailed analysis [10] that the tensile
stress just before spall fracture in case of a triangular
load pulse may be calculated using the relationship:
650°C.
The Hugoniot elastic limit GHEL, the dynamic
yield strength 7, and the spall strength were
evaluated from the measured free surface velocity
profiles accounting for temperature dependences of
the elastic constants of aluminum [7] and copper [8].
The longitudinal stress GHEL at the elastic precursor
front relates to the standard yield strength Y by the
well-known relationship
GHEL = P*UeufJ2 = (l-v)7/(l-2 v\
In the stress range realized in the experiments the
nonlinear compressibility of matter has to be
accounted for. This was done by means of
1.0
0.8
(2)
where pQ is the material density, Ue is the
propagation velocity of the elastic precursor wave,
ufse is the free surface velocity at the precursor front,
and v is Poisson's ratio. Within less than 1.5%
uncertainty Ue may be replaced by the longitudinal
sound speed c\.
The results of the measurements of the dynamic
yield strength in the plate impact experiments are
summarized in Fig. 5 where longitudinal stresses at
the elastic precursor spike and in the valley behind
the elastic precursor front are plotted as a function of
temperature. Since Poisson's ratio grows with
S. 0.6
CD
0.4
0.2
0.0
0
100
200
300
400
500
600
700
Temperature, °C
FUGURE 5. Longitudinal stresses in the elastic precursor spike
(curve 1) and in the valley behind it (curve 2). Data labeled as 3
and 4 are the corresponding values of the yield stress. Tm is the
melting temperature.
505
H
600
8
o
KALIF data
3
0
F
b
_£_-
? 2
s>
CO
1
1
CO
_
Q
T>
400
Plate impact
T
,
n
0
200
^^ _
, .
i , i . i , i . i . i J
100 200 300 400 500 600 700
0
20
40
60
80
100
120
140
Time, ns
Temperature, °C
FIGURE 7. The free surface velocity histories of copper single
crystal samples measured on KALIF. The peak stresses were
varied by varying the beam power.
FIGURE 6. Temperature dependence of the spall strength of
aluminum single crystals at two strain rates.
extrapolating the Hugoniot into the negative
pressure region.
Fig. 6 summarizes the spall strength data for
aluminum. Since the measurements were done at
low peak stresses in the shock compression pulses,
the actual temperatures at the beginning of tension
differ from the given temperatures by less than 3°5°C. In order to characterize the spall conditions,
note that in the plate impact experiments with single
crystals the corresponding rate of expansion was
(3^6)xl05 s"1 and the thickness of the spall plates
varied from 0.3 to 0.4 mm. In the beam driven
experiments the expansion rate was (1.5*3)xl06 s"1,
and the spall plate thickness was between 50 jj,m and
100 iLtm.
Figure 7 shows results of a few experiments with
copper single crystals performed on KALIF. The
experiments were done with samples of 0.66 to
0.83 mm thickness at the room temperature, 485°C,
and 830°C. The spall strength is 5.3 GPa at room
temperature and 4.75 GPa at 485°C. Spall fracture
did not occur in the experiment at 830°C that means
the spall strength exceeded 2.8 GPa in this shot. The
Hugoniot elastic limit at 830°C has been determined
as 2.6 GPa, that corresponds to a yield stress
Y= 1.35 GPa.
Thus, anomalous rise of the Hugoniot elastic
limit with increasing temperature and unexpectedly
high spall strength near the melting were observed
for aluminum and copper single crystals. In the
accompanying paper [11] these results are discussed
in terms of transition in dominating mechanisms of
dislocation motion and realization of superheated
solid states in preheated single crystals subjected to
high-rate tension.
ACKNOWLEDGMENT
The work was supported by the Russian-German
Co-operation Program WTZ RUS-545-96, and by
the Russian Foundation for Basic Research, grant
number 00-02-17604.
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