Combustion, Explosion, and Shock Waves, Vol. 38, No. 5, pp. 598 601, 2002
Shock Compression and Spalling of Cobalt
at Normal and Elevated Temperatures
S. V. Razorenov,1 G. I. Kanel ,2 UDC 539.4
E. N. Kramshonkov,1 and K. Baumung3
Translated from Fizika Goreniya i Vzryva, Vol. 38, No. 5, pp. 119 123, September October, 2002.
Original article submitted August 30, 2001.
Searching for a possibility of registering polymorphic transformations in cobalt un-
der rapid extension, we measured free-surface velocity profiles of high-purity cobalt
samples subjected to shock-wave loading at temperatures of 20 400ć%C. In this temper-
ature range, the spalling strength of cobalt at rates of its extension of 105 106 sec-1
was measured, and the relaxation properties of this material under compression in the
shock-wave front were estimated. In the experiments, we failed to observe expected
wave-profile anomalies due to possible high-temperature polymorphic transformation
of cobalt under extension. Most probably, the volume change due to transformation
is too small to exert notable influence on the wave-profile structure.
Key words: high-purity cobalt, shock compression, phase transformations, spalling
strength, temperature.
The studies of elastoplastic and strength proper- at 20ć%C is 8.79 g/cm3. The high-temperature phase
ties of solids in the submicrosecond range of loading of cobalt has face-centered cubic structure (FCC) [2].
duration imply registration and analysis of plane shock The lowest temperature at which the HCP FCC trans-
waves generated in samples under testing by impinging formation begins is Tf,0 = 423ć%C (or, according to
plates-strikers, explosive-charge detonation, or pulsed other sources, 447ć%C); the transformation temperature
laser or particle radiation. Such measurements have increases with pressure. The derivative dTf /dp in the
been carried out for a broad range of metals and al- low-pressure region amounts to 60 K/GPa, and the pre-
loys and for different amplitudes and durations of the dicted specific-volume increase is 0.026 cm3/mole or
shock-wave action [1]. Nevertheless, the effect of tem- 0.35%.
perature on the mechanical properties of metals at ulti- Since the cobalt transformation temperature in-
mately high deformation velocities still remains poorly creases upon compression, it may be supposed that, un-
studied. der extension, it would be possible to observe transfor-
In the present article, we report experimental data mation below the temperature Tf,0. It is, therefore, of
obtained for 99.9%-pure cobalt. The samples were cut interest to examine the possibility of polymorphic trans-
from a 1-mm thick rolled plate given no additional heat formation under rapid extension caused by a shock-wave
treatment. Under normal pressure, cobalt occurs in action.
two modifications. The low-temperature phase has a Two series of shock-wave experiments were car-
hexagonal close-packed structure (HCP), whose density ried out. In the first series, 0.4- or 0.8-mm alu-
minum plates impinging onto samples with a velocity
1
Institute of Problems of Chemical-Physics,
of (675 ą 25) m/sec were used; the plates-strikers gave
Russian Academy of Sciences, Chernogolovka 142432;
rise to shock waves with a pressure of (8.0 ą 0.3) GPa
[e-mail].
2
behind the shock-wave front. With the help of a VISAR
Institute of Extremal-State Thermal Physics,
Scientific Association for High Temperatures, laser velocimeter [3], we uninterruptedly registered the
Russian Academy of Sciences, Moscow 127412.
motion of the free back surface of the sample. In the
3
Research Center of Technologies and Environment,
second series of experiments, shock-compression pulses
Karlsruhe 76021, Germany.
598 0010-5082/02/3805-0598 $27.00 � 2002 Plenum Publishing Corporation
Shock Compression and Spalling of Cobalt at Normal and Elevated Temperatures 599
Fig. 1. Free-surface velocity profiles of cobalt sam- Fig. 2. Experimental data obtained using a pulsed pro-
ples, measured in experiments with 0.4-mm thick ton beam for generating shock waves in cobalt samples
strikers at temperatures of 20 and 365ć%C (the arrow at temperatures of 20 and 400ć%C.
shows a wave-profile region in which the polymorphic
transformation under extension was expected).
its maximum to the value ahead of the front of the
spalling pulse is proportional to the failure stress, or
of much shorter duration (H" 50 nsec) were used, which the spalling strength of the material under given load-
were generated by pulsed proton beams acting upon ing conditions. Subsequent oscillations of the surface
the samples; this series was performed on the KALIF velocity are caused by multiple reflections of waves in-
facility [4] of the Research Center in Karlsruhe (Ger- side the spalling part of the sample between its back
many). In these tests, to register the free-surface veloc- surface and the failure surface. The period of velocity
ity profiles, another modification of the laser velocime- oscillations depends on the speed of sound and on the
ter, namely ORVIS [5], was used. The maximum shock- spalling thickness. The amplitude of the oscillations is
compression pressure in the tests on the KALIF facility likely related to the shape of the incident loading pulse.
was 20 21 GPa. In both cases, to vary the tempera- The constant mean surface velocity during the wave re-
ture, ohmic heaters [6] were used; the temperature was verberation points to a rapid loss of linkage between the
controlled by thermocouples provided in an immediate spalling plate and the remaining part of the sample.
vicinity of the point at which the surface velocity was The experimentally registered shape of the free-
measured. surface velocity profile points to elastoviscous rather
Figure 1 shows the free-surface velocity profiles of than elastoplastic behavior of cobalt under the adopted
cobalt samples, which were measured in the experiments loading conditions. The initial amplitude of the elastic
with 0.4-mm thick strikers at temperatures of 20 and precursor, which depends on the yield stress of the ma-
365ć%C, and Fig. 2 depicts typical wave profiles extracted terial under high-velocity deforming, does not exceeds
from the experimental data obtained on the KALIF fa- 2 3 m/sec. In the tests with strikers, the rise time of
cility. The wave profiles at normal and elevated tem- the stress in the plastic compression wave from 0.1 to
peratures are seen to be not only generally similar but 0.9 of its amplitude amounts to 18 20 nsec, and the
also close to one another in value. The egress of the maximum acceleration reaches 2 1010 m/sec2, which
elastoplastic compression wave and that of some part corresponds to a deformation velocity of 4 � 106 sec-1.
of the rarefaction wave propagating behind were reg- With increasing shock-compression pressure, the rise
istered. After the reflection of the compression pulse time of the plastic shock wave has decreased to 3 4 nsec,
from the free surface, tensile stress arises in the sample, which corresponds to a compression rate increased to
giving rise to mechanical failure of the sample. In this (2 2.5) � 108 sec-1. The relation between the compres-
situation, the tensile stress relaxes, and a compression sion rate in the shock wave and the pressure behind
wave forms (spalling pulse), whose subsequent egress its front is in agreement with the data of [7], which
onto the surface causes a second rise in the surface veloc- show that the compression rate is proportional to the
ity. The fracture that occurs as the compression pulse fourth power of the final shock-compression pressure.
reflects from the body surface is termed spalling. The Although the rarefaction front in cobalt propagates with
decrement of the surface velocity at its decrease from the velocity of a longitudinal elastic wave, it is hardly
600 Razorenov, Kanel , Kramshonkov, and Baumung
TABLE 1
Measured Spalling Strength of Cobalt Samples
Ł
Test conditions "ufs, m/sec �", GPa hs, mm V /V0, sec-1
Striker 0.4 mm, 20ć%C 197 ą 3 4.0 0.32 ą 0.005 4.2 � 105
Striker 0.4 mm, 20ć%C 176 ą 3 3.6 0.31 ą 0.005 4.2 ą 105
Striker 0.4 mm, 255ć%C 172 ą 3 3.5 0.31 ą 0.005 4.2 � 105
Striker 0.4 mm, 280ć%C 175 ą 3 3.55 0.33 ą 0.005 4.2 � 105
Striker 0.4 mm, 365ć%C 174 ą 3 3.5 0.31 ą 0.005 4.2 � 105
Striker 0.8 mm, 360ć%C 159 ą 3 3.2 0.65 ą 0.005 2.6 � 105
KALIF, 20ć%C 250 ą 10 5.05 0.078 ą 0.004 106
KALIF, 400ć%C 235 ą 10 4.85 0.085 ą 0.004 106
KALIF, 450ć%C 250 ą 15 5.05 0.078 ą 0.004 106
possible to single out a definite elastic-unloading region The measured values of the cobalt spalling strength
in the measured wave profiles, especially at elevated test at normal and elevated temperatures are summarized
temperatures. in Table 1, which also gives the spalling thickness hs
The period of the surface-velocity oscillations after and the expansion rate of the substance in the inci-
Ł
spalling is almost identical to the duration of the ini- dent rarefaction wave V /V0, which characterizes the
tial loading pulse. It follows from here that, first, the rate of crystal failure at the initial spalling stage [1]
high-velocity failure is initiated without a notable in- (V and V0 are the current and initial specific volumes,
duction period and, second, the elastoviscoplastic prop- respectively). The indicated measurement errors are
erties of the material exert no appreciable influence on predominantly induced by the small-scale oscillations
the wave-interaction dynamics during spalling. Hence, (electronic noise) in measured wave profiles. As the
to determine the spalling strength in the case under temperature increases, the resistance to spalling some-
consideration, we may use the acoustic approximation what decreases; however, as the deformation velocity
[8], which implies that the tensile stress at the onset of increases, the spalling strength becomes almost inde-
spalling is given by the formula pendent of temperature.
In the present study, we assumed that an increase
1
�" = �cb"ufs, (1)
in volume during the polymorphic transformation under
2
extension should be accompanied by the formation of a
where cb = Ks/� is the  bulk speed of sound, Ks is
rarefaction shock wave, in close analogy with unload-
the isentropic volume-compression modulus, � is the
ing of shock-compressed iron and other materials un-
density, and "ufs is the velocity decrement ahead of the
dergoing a reversible transformation under compressing
spalling-pulse front. In the above relation, the nonlinear
[1]. The corresponding tensile-stress values at which the
behavior of the compressibility of the material should be
appearance of anomalies in wave profiles was expected,
taken into account; to this end, we used extrapolation
were estimated as follows.
of shock adiabates in the coordinates  pressure mass
In a linear approximation, the relations between
velocity to the region of negative pressures. According
the pressure p and the temperature along the equilib-
to [9], the cobalt shock adiabate in the form of a rela-
rium line of the two phases and along the expansion
tion between the shock-wave front velocity Us and the
isentrope, respectively, have the form
mass velocity of the substance behind the front up is
given by the formula Us = 4.73 + 1.306 up. In treating
dTf "T
high-temperature measurement data, the change in the Tf = Tf,0 + p, Ts = T0 + p, (2)
s
dp "p
bulk modulus Ks was estimated using the relation
"Ks "Ks MPa
where Tf is the temperature at the phase-equilibrium
H" -Ksą - � H" -16 ,
"T "p K
line, Tf,0 is the zero-pressure transformation tempera-
where "Ks/"p = 4.26, � is the Gr�neisen coefficient ture, Ts is the temperature at the expansion isentrope,
(� = 2.0 2.2), and ą = (4.0 ą 0.5) � 10-5 1/K [10, 11] is T0 is the initial temperature in the tension test; the
the coefficient of thermal volumetric expansion. subscript s denotes differentiation along the isentrope.
Shock Compression and Spalling of Cobalt at Normal and Elevated Temperatures 601
polymorphic transformation of cobalt. On the other
hand, in the tests at temperatures of 255 and 280ć%C, in
which the expected transformation pressure was close
to the fracture stress, a time delay for the onset of crys-
tal failure and a noticeable reduction in the amplitude
of velocity oscillations after spalling were observed.
Thus, although no direct evidence for the high-
temperature transformation in cobalt under extension
was observed, the change in the spall fracture proper-
ties of the material in the high-temperature and high-
tension regions corresponding to the expected transfor-
mation may be indirect evidence for the transformation
under the adopted experimental conditions.
This work was supported by the Russian Foun-
dation for Fundamental Research (Grant No. 00 02
Fig. 3. Free-surface velocity profiles of cobalt sam-
17604).
ples measured in the experiments with 0.4 and 0.8-
mm thick strikers (solid and dashed curves, respec-
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