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
MODELING OF URANIUM ALLOY RESPONSE IN PLANE IMPACT
AND REVERSE BALLISTIC EXPERIMENTS
B. Hen-maim1, A. Landau1, D. Shvarts1'2, V. Favorsky2 E. Zaretsky2
;
2
Nuclear Research Center - Negev, P.O.Box 9001, Beer-Sheva 84106, Israel.
Mechanical Engineering Dept, Ben Gurion University, P.O. Box 653, Beer-Sheva 84105, Israel.
Abstract The dynamic behavior of a solution heat-treated, water-quenched and aged U-0.75wt%Ti
alloy was studied in planar (disk-on-disk) and reverse ballistic (disk-on-rod) impact experiments
performed with a 25 mm light-gas gun. The impact velocity ranged from 100 to 500 m/sec. The
impacted samples were softly recovered for further metallographic examination. The VISAR records of
the sample free surface velocity, obtained in planar impact experiments, were simulated with 1-D
hydrocode for calibrating the parameters of modified Steinberg-Cochran-Guinan (SCO) constitutive
equation of the alloy. The same SCO equation was employed in 2-D AUTODYN simulation of the
alloy response in the reverse ballistic experiments, with VISAR monitoring of the lateral sample surface
velocity. Varying the parameters of the strain-dependent failure model allows relating the features of
the recorded velocity profiles with the results of the examination of the damaged samples.
INTRODUCTION
equivalent plastic strain £ /: : Y = YQ (l -h $€{ Jl. In
the case of the numerical simulation of the reverse
ballistic impacts with the impactors and samples
made of uranium-titanium alloy, by using the same
model with the strain-hardening parameters
determined in planar impact experiments, a
satisfactory description of the experimental results
could not be achieved.
Both the dislocations and the dislocation-related
structures [4], such as stacking faults and twins,
participate in plastic flow of uranium-based alloys.
In contrast to the dislocations-governed plastic flow,
resulting in strengthening the metal with the
increasing of £ f -, the deformation twinning can
effectively either strengthen or weaken the alloy [5].
The purpose of the present work is to find
parameters of the constitutive model, additional to
those determined in the 1-D experiments, enabling
the description of 2-D strain-hardening and failure
events in a uranium-titanium alloy
Uranium alloys are known to be susceptible to
extensive localization of deformation when
subjected to high rate loading. The phenomenon is
usually attributed to local material softening
produced by the strain-induced heat generation.
Lately, special attention was paid to the role of
strain-hardening and strain-rate-hardening in the
localization of the shear strain [1], It has been
shown that intensification of the hardening results
in earlier loss of shear stability and, perhaps, in the
shear localization. The correlation between the
intensification of the strain hardening and material
susceptibility to strain localization due to varying
the strain hardening parameters of the modeled
material was observed by Zaretsky et al, [2] in
numerical simulations of the impact of a tungsten
heavy alloy disk on a rod made of the same material
("reverse ballistic impact"). The simulation was
performed using the Steinberg-Cochran-Guinan
(SCG) [3] constitutive model with a simple
dependence of the material yield strength Y on the
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EXPERIMENTAL
In order to establish parameters of SCO
constitutive equation the solution heat-treated,
water-quenched and aged U-0,75wt%Ti alloy (U-Ti)
was previously characterized in planar impact
experiments utilizing a 25-mm pneumatic gun. Both
the impactors and samples were disks of about 24mm diameter made of U-TL The impactors and
samples thickness was 2 and 6-mm, respectively.
The reverse ballistic (RB) experiments were
performed with the same gun. The U-Ti impactors
were 5-mm thick and the U-Ti samples employed
were cylinders of 20-mm length and 8-mm diameter.
They were impacted at the face of the cylinder. The
impact velocity and the impactor-sample
misalignment (tilt) were controlled by charged pins.
In all impacts, the tilt did not exceed 0.4 mrad. In the
planar experiments, the velocity of the free surface
of the U-Ti samples was monitored by VISAR [6],
In the RB experiments, the VISAR beam was
focused at a point located on the sample cylindrical
surface 3.6 mm from the impacted cylinder face. In
four RB experiments, the impact velocity was 112,
272, 412 and 472-m/sec. The sample recovered after
112-m/sec impact was found plastically deformed.
After the higher impacts the samples were found
damaged along the conical surface based on the
impacted sample face. At 412 and 472-m/sec the
impactors failed by plugging.
The results of the planar impact experiments are
shown in Fig. 1 a. The stress deviators s = a - p ,
Fig. Ib, were obtained from the experimental
velocity profiles by using the known Hugoniot of the
1
2
3
time after impact usec
alloy to estimate the pressure p and calculating the
stress <j and strain e from momentum and mass
conservation laws, considering the compressive part
of the profile as a simple centered wave.
SIMULATIONS
The planar impact experiments with U-Ti alloy were
simulated numerically, using 1-D finite difference
Lagrangian
code
and
material
strength
y = y0(l+/te|.)w suggested in [3]. Since all the
velocity profiles show smooth elastic-plastic
transition, some 20% spatial randomization of the
FO values was added, in order to achieve better
agreement between the modeling and the
experiment. It was found, however, that the
coincidence may be improved by substituting the
above expression by another one, Y = FQ + fief ,
with no need for any randomization.
The
commercial
2-D
Lagrangian
code
AUTODYN-2D was used for numerical simulations
of the RB experiments. Since the point of
intersection of the VISAR beam with the sample
surface moves in Lagrangian coordinate system, the
Lagrangian coordinates of this point was determined
for each calculation cycle and the normal to the
sample axis component of its velocity was saved.
The mesh size was 100x100 Jim, The 2-D
simulations were started with both the equation of
state and the SCO-constitutive equation, including
the strength of Y = F0(l + /te(- }n -type, and material
0.02
4
0.04
0.06
true strain
0.08
FIGURE 1. Free surface velocity profiles of U-Ti samples, obtained in the planar impact experiments (a) and the stress deviators
calculated from the corresponding profiles (b). Impact velocities are shown in m/sec.
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parameters suggested for U-Ti alloy by the
AUTODYN library. The increase in the strength was
limited by Fmax whose values for the impact with
velocities 112, 272, 412 and 472-m/sec was found
equal to 1, 1, 1,2 and 2.5-GPa, respectively. The
strength of the Y = YQ + ftef form was also tested.
Surprisingly, the 2-D simulations were found
insensitive to such substitution. With any form of the
strength, the AUTODYN simulations reproduce the
general form of the recorded VISAR signal. The
coincidence was found reasonable only for 112m/sec impact. For stronger impacts, the discrepancy
between the experimental and the simulated profiles
increases with increasing the impact velocity. The
VISAR records obtained after RB shots are shown in
Fig. 2 together with the simulation results.
plastic strain is large, was added to the SCO model.
The plastic stain, unlike in the planar impact
experiments, may be large during such loading.
Simulations, with yield strength of the form
Y = YQ (l + Jfe. Jl exp(l - B s f } were performed (Fig.
la). The exponential form of the factor was chosen
in order to preserve positive value of the strength Y
for any value of the strain EJ . It was found that
varying the softening parameters in a very wide
range has almost no influence on the results of the
simulations. Note, that varying the parameters is
limited by the interruption of the AUTODYNE
calculation due to the mesh distortion.
Failure processes occurring in the internal regions
of the sample may also disturb the complete
momentum transfer. The simplest (bulk) failure
model available in AUTODYN library was
introduced into the calculations. Assuming that the
failure has to occur at the presence of a sufficient
shearing stress and should also be accompanied by
large plastic deformation, the failure criterion
F = A€I\(JI ""^2 was chosen. The indexes 1 and 2
signify the local principal stress values. An example
of failure-included simulations, with the failure
parameter F = 0.875 GPa, are shown in Fig, 2b.
Two conclusions can be drawn: (i) accounting the
failure in the calculations may improve the results
PARAMETRIC STUDY
It is apparent from Fig. 2 that the employed
constitutive equation fits the data well up to the first
maximum of the velocity. The divergence starts
with the velocity decrease after the first maximum
was achieved. The post-maximum velocity values
are supported by the stress signal arriving from the
central part of the impactor-sample interface. We
assumed that some softening of the material hinders
the complete transfer of this signal. A softening
factor, acting presumably when the equivalent
1
2
3
4
5
6
0
time after impact, p,sec
1
2
3
4
time after impact,
FIGURE 2, Free surface velocity profiles and simulations of U-Ti samples, obtained in the reverse ballistic experiments, with hardening
(line) and hardening + softening (dashed line) (a) and with hardening -»• softening + failure (b). Impact velocities are shown in m/sec.
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FIGURE 3. A cross-section metallography (a) and a damage map (b) of a U-Ti sample recovered after RB impact at 412 m/sec.
of the simulations and (ii) the failure criterion in
these runs is too high to have influence in the three
weaker shots. Decreasing the failure criterion
results in interrupting the calculations.
Although the shortcomings of the used failure
description are clear, the simulation reproduces the
main features of the sample damage. The
metallograhic cross-section of the U-Ti sample,
recovered after 412-m/sec impact, is shown in Fig.
3b, together with the corresponding state of the
failure, taking place at the time instant 5.1-usec
after the impact. Several narrow parallel damage
paths, inclined to the sample axis at the angle about
60, are present, both in the real sample crosssection and on the failure map. The simulation
results also show initiation of the plugging observed
in the impactor. Estimation of the velocity of the
propagation of the damage regions, both in the
impactor and in the sample, yields the value of
about 700-750-m/sec.
when rezoning was required due to excessive
deformation.
A finer mesh size, than the 100x100 um that was
employed, should be used in the simulations, in
order to reproduce fine features of the damage as
the width of the widest adiabatic shear band is about
20 um.
Although the failure threshold criterion used in
the present study gives some failure localization, a
more comprehensive constitutive description of the
failure process is required.
REIERENCES
1. Estrin Y., Molinari A. and Mercier S., Journ, Eng.
Mater, and Technology, 119 322-331 (1997).
2. Zaretsky E. et. al,"Lateral Sample Motion in the PlateRod Impact" in SCCM-1999, edited by M. D. Furnish,
et. al., AIP 505-2000, pp. 593-596.
3. Steinberg D.J., Cochran S.J. and Guinan M.W., Journ.
AppL Phys., 51 (1980) 1498.
4. Armstrong P.E., Follansbee P. S. and Zocco T., M A
Constitutive Description of the Deformation of a
Uranium Based on the Use of MTS as a State
Variable" in IPCS No 102, edited by J. Harding, Int.
Conf. PMHRS, Oxford, 1989, pp. 237-244.
5. Yoo M. H., MetalL Trans. 12A, 409-418 (1981).
6. Barker L.M. and Hollenbach R.E., Journ. AppL Phys.,
43,4669(1972).
CONCLUSIONS
Introducing the strength parameters, calibrated on
the base of the planar impact experiments, into the
2-D numerical simulation of the velocity profiles
obtained in reverse ballistic experiments allows one
to reveal the damage processes induced by the
ballistic impact.
More accurate modeling of the damage processes
is impossible at present because the AUTODYN
version that was used exhibited some limitations
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