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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
ANOMALOUS BEHAVIOR OF ALUMINUM NEAR THE MELTING
TEMPERATURE: TRANSITION IN THE RATE CONTROLLING
MECHANISM OF YIELDING AND REALIZATION OF
SUPERHEATED SOLID STATES UNDER TENSION
G.L Kanel1, S.V. Razorenov2, K. Baumung3, and H. Bluhm3
1
Institute for High Energy Densities, IVTAN, Izhorskaya 13/19, Moscow, 127412 Russia
2
Institute of Problems of Chemical Physics, Chernogolovka, 142432 Russia,
3
Forschungszentrum Karlsruhe, P.O. Box 3640, 76021 Karlsruhe, Germany.
Abstract. Results of measurements of the spall strength and the Hugoniot elastic limit of aluminum,
magnesium, and zinc over a wide temperature range are analyzed. A high resistance to spall fracture
of single crystals is maintained when melting should start. This is treated as evidence of superheated
solid state reached at dynamic tension. This anomaly was not recorded for polycrystalline metals
where melting starts earlier at grain boundaries. The anomalous growth of the dynamic yield strength
is interpreted as evidence of a transition in the rate-controlling mechanism from the dislocation
motion aided by thermal fluctuations to the phonon drag mechanism of over-barrier motion.
It is not quite clear yet what the reasons are for
the observed anomalies in sub-microsecond strength
properties and what these anomalies may mean for
the physics of strength and for other fields of
physics. The main objectives of the analysis
presented here is to contribute in answering these
questions.
INTRODUCTION
It is well known that, under normal conditions,
both the yield strength and the tensile strength are
strong functions of the temperature and decrease
with heating. However, at very high strain rates
unexpected and non-trivial behavior of the strength
properties of polycrystalline metals and metal single
crystals has been revealed when the temperature
was introduced as a varied parameter into the
shock-wave tests [1-3]. It was found the resistance
to spall fracture of metals does not vary much when
increasing the temperature at least up to 85-90% of
absolute melting temperature, Tm. With further
temperature increase different behavior of strength
was observed, depending on the material structure.
Whereas polycrystalline metals exhibit a precipitous
decrease of strength down to practically zero as
soon as temperature approaches Tm, the dynamic
tensile strength of single crystals remains high even
in a close vicinity of Tm. The dynamic yield stress
in some cases increases with heating or is
independent of the temperature.
SPALL STRENGTH AT MELTING.
It is known that the melting temperature grows
with increasing the pressure. Correspondingly, it
should decrease when the pressure turns negative.
The relationships between slopes of the melting
curves Tm(p) and isentropes Ts(p) of solids is such
that, if the initial temperature is sufficiently close to
Tm(p - 0) the state of matter running into tension
may meet the melting conditions.
Figure 1 shows the pressure-temperature
diagram for some of the high-temperature spall
experiments with aluminum single crystals
described in the accompanying paper [3]. The
diagram has been calculated with a complete
equation of state [4] based on semi-empirical free603
energy functions of liquid and solid aluminum. The
p-T state curves of shock compression and
subsequent isentropic rarefaction were calculated
for solid phase aluminum, assuming that no melting
occurs. The lowest points on the curves correspond
to the spall strength values. The adiabatic expansion
shifts the state of solid matter towards the melting
curve and at a certain tension the melting curve is
crossed at the temperature T < TmQ where Tmo is the
melting temperature at zero pressure.
The information about melting should appear in
the free surface velocity histories. It was expected
that, even if the beginning of melting does not result
in a sharp decrease of the spall strength, it should
increase the compressibility of the matter and
decrease the yield stress. Both these effects have to
produce kinks in the wave profiles. However, as it
may be seen in Fig. 2, no kinks are recorded in the
free surface velocity histories.
For analyzing melting under tension it is more
convenient to use a linear estimation of the pressure
at which the isentrope of a solid intersects the
melting curve. It can be shown that the intersection
point is given by the equation
P
—£-
1100
2
4
Pressure, GPa
FIGURE 1. The pressure-temperature diagrams of shock
compression followed by rarefaction of aluminum.
(D
0.2
Time, us
where a is the thermal expansion coefficient, TQ is
the initial test temperature, KT and Ks are the
isothermal and the isentropic bulk modules,
respectively.
The results of the estimations of the pressures
in the points of intersection between the melting
curve and the isentropes as a function of TQ are
shown in Fig. 3 for single crystals of aluminum and
zinc and in Fig. 4 for polycrystalline aluminum and
magnesium. Whereas the experimental data for
polycrystalline metals are below the estimated
melting lines, part of the high-temperature data for
single crystals are above these lines. In other words,
the strength of polycrystalline metals drops when
the material begins to melt whereas single crystals
maintain a high resistance to spall fracture when
melting should start.
In polycrystalline solids melting may start
along grain boundaries at temperatures below the
melting temperature of the crystal. The effect is
caused by the disordering and by the larger
concentration of impurities in boundary layers of
grains [5, 6]. Very likely, this grain-boundary effect
FIGURE 2. The free surface velocity histories of aluminum
single crystal samples at elevated temperatures (mentioned at
profiles). The arrows show the points where signatures of
melting were expected.
}
310V
)
CL
O
,5-1oV
"ro 1
CL
CO
0
100
200
300
400
500
600
700
Temperature, °C
FIGURE 3. Relationship between spall strength and melting
thresholds for single crystals of aluminum at two different strain
rates and zinc.
604
1.0
v
CL
V
.o
8
0 1.0
jcf
1?8>
4=
52 0.5
Q.
CO
i
i
°o
V
v
V)
° *%\~-
-
I
CO
Thermally activated flow
cpl -
^ "
V- Aluminum AD1
O- Magnesium Mg95
•
nn
0.4
0.6
•
0.8
i rr
1.0
Strain Rate
Homologous Temperature T/Tm
FIGURE 4. Relationship between spall strength and melting
thresholds for polycrystalline aluminum and magnesium.
FIGURE 5. Regions of operating of different mechanisms of
plastic flow depending on the strain rate.
contributed to the precipitous drop in spall strength
near the melting temperature. Besides this, hot spots
may be formed under shock compression of
polycrystalline materials as a result of partial
localization of shock wave energy on imperfections
of their structure. In preheated samples the material
may melt locally in these hot spots, which, in turn,
should reduce the material strength.
If molten spots appear in the volume of a single
crystal, the crystal is no longer homogeneous and
should show a spall strength close to that of
polycrystalline aluminum. However, even at highest
temperatures the single crystals show a higher
strength than polycrystalline materials at room
temperature and at the same strain rate. It seems
more likely that the crystals did not melt and the
spall data in all cases represent the strength of the
solid crystals.
If melting did not occur one has to conclude
that superheated solid states were realized in the
crystals under tension. It is known that, unlike with
liquids, superheating of crystalline solids is
impossible under normal conditions. It is assumed
that the crystal surface plays a crucial role in the
melting process. Melting of an uniformly heated
crystal always begins on its surface. However,
superheated states may be reached inside the crystal
body if its surface is below the melting temperature
[5, 6]. This condition was realized in the discussed
spall experiments. The magnitude of superheating
of aluminum crystals reached 60-65°C at the
shortest load durations.
HIGH-TEMPERATURE YIELDING
For many metals the strain rate sensitivity of
the flow stress increases steeply above a strain rate
of ~103 - 104 s"1. This is interpreted as a transition
in the rate-controlling mechanism of dislocation
motion [7]. At low strain rates the dislocations are
pinned at barriers and a combination of thermal
excitation and applied stress is required to activate
the dislocation over the obstacles. At very high
strain rates the applied stress is high enough to
overcome instantaneously the usual dislocation
barriers without any aid by thermal fluctuations, and
other drag mechanisms (such as the phonon
viscosity, internal stresses generated by other
dislocations and point defects, etc.) become
dominant. Since contributions of some of them are
proportional to the temperature, increase of the flow
stress with rising temperature may be expected at
higher strain rates [8], as shown schematically in
Fig. 5. The strong dependence of the flow stress on
the strain rate should result in a rapid decay of the
elastic precursor wave that was really observed in
the experiments at elevated temperatures (Fig. 6).
For the following discussing let us consider the
relationship between the resolved shear stress T, the
plastic shear strain rate ^, and the mobile
dislocation density Nm:
T-
B
-r
(2)
where b is the Burgers vector, and B is the drag
coefficient. The results of experiments with
605
deformation and has allowed studying melting
under tension. An exotic behavior of single crystals,
such as growth of the yield stress with increasing
temperature and generation of super-heated solid
states were observed and explained.
The measurements show that the spall strength
slightly decreases with increasing temperature
whereas the yield stress rises. One may speculate
that the growth of voids does not much contribute to
the stress relaxation at fracture and that mainly
nucleation processes control the measured fracture
stresses. Probably, coalescence of vacancies at
elevated temperatures produces microvoids, which
are the damage nucleation sites that results in
decreasing the total resistance to spall fracture.
Thus, new prospects in studying mechanisms of
high-rate plastic deformations and fractures are
opened. The results stimulate also an interest to
studying phase transitions and polymorphous
transformations in the negative pressure region.
600 -
>
400 -
C/5
o
o
20
40
60
80
Time, ns
FIGURE 6. Variations of the elastic precursor wave as a
function of propagation distance and peak stress in aluminum
single crystals at 622°C
aluminum single crystals [3] show that the dynamic
yield strength increases with temperature. Since the
initial density of mobile dislocations in single
crystal samples obviously does not depend on
temperature the observed increase in the yield stress
Y and, correspondingly, in the resolved shear stress
T is determined by an increase in the drag
coefficient B.
The over-barrier motion of dislocations at high
temperatures is decelerated by different obstacles
and by friction forces due to phonons. The
interaction of moving dislocations with electrons is
essential only at low temperatures. The phonon drag
coefficient Bp grows linearly with temperature [9]
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.
REFERENCES.
Bogach, A.A., Kanel, G.I., Razorenov, S.V., et al.
Physics of the Solid State, 40(10), 1676-1680 (1998).
Kanel, G.I., Razorenov, S.V., Bogatch, A.A., et al.
J.Appl.Phys., 79(11), 8310-8317 (1996).
Razorenov, S.V., Kanel, G.I., Baumung, K., and
Bluhm, H. Hugoniot elastic limit and spall strength of
aluminum and copper single crystals over a wide
range of strain rates and temperatures. In this issue.
4. Asay, J.R and Hayes, D.B. J. Appl Phys., 46(11),
4789-4800(1975)
5. A.R. Ubbelohde. Melting and Crystal Structure.
Clarendon Press, Oxford (1965).
6. Dash, J.D. Review of Modern Physics, 71(5), 17371743(1999).
Kumar, A. and Kumble, R.G. J. Appl Phys., 40(9),
3475 (1969).
8 Sakino, K. J. Phys. IVFrance, 10, Pr9-57 - 62
(2000).
9. Ninomura T., J. Phys. Soc. Jpn, 36, 399 (1974)
10. P. G. Cheremskoy, V.V. Slezov, and V.I. Betehtin.
Pores in Solids. Energoatomizdat, Moscow, 1990,
376 p. (In Russian).
(3)
71 C
where kB is the Boltzmann constant, COD is the
Debye frequency, and c is the sound speed. The
drag forces created by obstacles are obviously
proportional to their concentration in the crystal
structure that increases exponentially with
temperature [10]. Since the observed linear growth
of the dynamic yield stress with temperature agrees
with the behavior of the phonon drag coefficient, it
looks very probable that the dislocation drag at high
strain rates is connected mainly with thermal
oscillations of atoms in the crystal lattice.
DISCUSSIONS AND CONCLUSIONS
Introducing temperature as a variable parameter
in shock-wave experiments has revealed a transition
in the rate controlling mechanisms of plastic
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