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
MULTI-DIMENSIONAL VALIDATION IMPACT TESTS
ON PZT 95/5 AND ALOX
M. D. Furnish, J. Robbins, W. M. Trott,
L. C. Chhabildas, R. J. Lawrence and S. T. Montgomery
Sandia National Laboratories, PO Box 5800, Albuquerque NM 87185
Abstract. Multi-dimensional impact tests were conducted on the ferroelectric ceramic PZT 95/5 and
alumina-loaded epoxy (ALOX) encapsulants, with the purpose of providing benchmarks for material
models in the ALEGRA wavecode. Diagnostics used included line-imaging VISAR (velocity
interferometry), a key diagnostic for such tests. Results from four tests conducted with ALOX
cylinders impacted by nonplanar copper projectiles were compared with ALEGRA simulations. The
simulation produced approximately correct attenuations and divergence, but somewhat higher wave
velocities. Several sets of tests conducted using PZT rods (length:diameter ratio = 5:1) encapsulated in
ALOX, and diagnosed with line-imaging and point VISAR, were modeled as well. Significant
improvement in wave arrival times and waveforms agreement for the two-material multi-dimensional
experiments was achieved by simultaneous multiple parameter optimization on multiple onedimensional experiments. Additionally, a variable friction interface was studied in these calculations.
We conclude further parameter optimization is required for both material models.
compression curves. Setchell has presented results
from a recent study of the electrical response of
PZT 95/5 to uniaxial shock loading.
However, applications generally impose
diverging waves, shock propagation along rods,
tilted shock fronts, and other two- and threedimensional effects. Recent increasingly stringent
certification requirements demand that computer
models adequately describe such behaviors. The
purpose of the present study is to explore multidimensional validation experiments needed to test
the simulation models.
INTRODUCTION
Knowledge of the electromechanical properties of ferroelectric materials is important for
various pulsed-power applications. Of particular
interest is lead-zirconate-titanate with a Zr:Ti ratio
of 95:5 (PZT 95/5).
In this material, the
ferroelectric/antiferroelectric
(FE/AFE) phase
boundary is quite close to the room
temperature/pressure state. Hence, if this material
is poled, a relatively low amplitude stress wave can
depolarize the material, producing a large pulse of
current or voltage.
Key observations from previous research on
this material in a uniaxial strain environment 1-3
include a gradual pore crush-up between 2.2 and
4.0 GPa (initial porosities range from 3 to 9%,
depending on preparation), the reversible FE/AFE
phase transition at approximately 0.5 GPa, and the
EXPERIMENTAL METHOD
Two types of multi-dimensional gas gun
impact experiments are discussed in the present
paper. For one type, multi-dimensional loading is
generated in a composite material composed of 10-
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SINGLE MATERIAL TESTS
20 micron tabular alumina dispersed in an epoxy
matrix (ALOX). The other type of test was
conduced on specimens composed of a rod of
unpoled PZT 95/5 encapsulated in ALOX.
Geometries for both tests are shown in fig. 1.
A key diagnostic for these experiments is the
line-imaging VISAR5. In this instrument, an
illuminated line on the target is imaged through the
interferometer onto the input to a streak camera.
Hence each lineout on the streak camera record
represents an interference record, and can be used
to derive the velocity history of each point on the
illuminated line (fig. 2).
The first series of experiments, along the lines
of Fig. l(a), was designed to subject a single test
material to a controlled divergent shock wave. Fig.
3 shows the streak camera records obtained and
configurations. Here, the ALOX samples were 48mm diameter and 22.9-mm thick. The copper
projectile impacted at 300 m/s.
For the relatively simple planar impact ((a) in
Fig. 3), the arrival along the line is fairly planar,
and has a rise time of roughly 100-ns. Away from
the centerline, edge effects cause dispersion and
darkening at late times.
Figure 1. Representative gas gun configurations used, (a)
An ALOX cylinder impacted by a projectile with a flat
face, a pedestal face (shown), or curved face, (b) A PZT rod
encapsulated in ALOX impacted by a flat-faced projectile.
(a)
Figure 3. Streak camera records from selected ALOX tests.
Line length was 8.6 mm for these tests. Times are relative to
impact at pins (above and below ALOX). Velocity-per-fringe
was 0.25 km/s. "*" indicates the line monitored by line VISAR.
Figure 2. Line VISAR interpretation.
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The pedestal impact tests show good
reproducibility, with considerable dispersion
following the arrival in the second test (Fig. 3(c)).
The wavefront displays much greater curvature
than for the planar impact. Additionally, the
particle velocity achieved is lower (0.1 km/s vs.
0.38 km/s).
The line VISAR data from these experiments
may be reduced to velocity as a quasi-continuous
function of position and time. We have chosen to
produce discrete lineouts for visualization
purposes, with sample results shown in Fig. 4.
These correspond to the streak image shown in fig.
3(c), for a pedestal impact test (ECF 273).
We modeled the pedestal impact of ECF 275
using a composite model proposed by Drumheller5.
This model includes physics for 3-D contacts and
dilatency, and is implemented in the ALEGRA
wavecode. In fig. 5, computational results are
juxtaposed on the velocity histories deduced from
the line VISAR streak record.
Two issues surface from this comparison.
First, calculated peak particle velocities and wave
shapes are in good agreement with experiment.
Second, wave arrival times are very early in the
calculations. Using a simple Mie-Griineisen model
corrects the wave arrival times, but omits the
physics we need for high-fidelity modeling. Any
possible experiment timing errors are being
evaluated.
TWO-MATERIAL TESTS
Another extensive sequence of tests has been
performed with PZT 95/5 rods encapsulated in
ALOX. Two representative tests are discussed
here. The configuration for these tests is shown in
Fig. 6. Impact velocities were 292 and 415 m/s for
tests ECF 298 and 301, respectively. The layered
impactor was constructed to introduce a quasiramp wave loading into the target.
As with the ALOX tests described above, 1-mil
layers of tungsten foil were used to provide a
reflecting surface for the laser. For the PZT rod
experiments, however, it was necessary to segment
this foil to allow for differential motion across the
PZT/ALOX boundary.
Test ECF 301 was modeled using the ALOX
model described above and a PZT model due to
Montgomery and Brannon6.
A frictionless
boundary between the two materials was assumed.
For the initial calculation, parameters in the model
were estimated from data in various sources.
Later, a parameter optimization7 was conducted
using the results of eight uniaxial-strain
experiments described elsewhere8.
The
optimization process resulted in better estimates of
the elastic moduli for the FE and AFE phases as
well as coefficients describing transformation rates.
The calculation was re-run with the new
parameters and results for the PZT motion are
shown in Fig. 7. The simulations with both model
the wave amplitudes fairly well for both
simulations. As with the single-material ALOX
shots, however, the calculated wavespeeds are
Figure 4. Velocity records extracted from streak record
of ECF 273, the first pedestal impact on ALOX.
0.2
Center
Particle
Velocity
(km/s)
0.1
Calculated Measured
. 6 mm from center
0.0
6
8
10
Time after impact (us)
Figure 5. Calculation vs. experiment for velocity records
extracted from streak record ECF 275, pedestal impact on
ALOX.
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greater than the measured wave speeds. The
parameter optimization for the PZT model, is seen
to substantially improve agreement between the
calculations and measurements.
It is worth noting that the experimental results
show an abrupt increase in the PZT material
velocity when the main arrival occurs in the
ALOX.
This suggests a large amount of
mechanical coupling between the two materials
restricting slip of the interface. The calculated
waveforms do not show such a coupling, consistent
with the (apparently erroneous) assumption of a
frictionless boundary.
In view of this strong coupling between the two
materials, the calculation with the optimized PZT
model also included an ad hoc adjustment in the
ALOX moduli to produce a correctly timed ALOX
arrival (not shown in Fig. 7). The predicted slip
between the ALOX and PZT is shown in Fig. 8
(frictionless interface condition) at 5.3 us.
-1
t = 5.3 us
-2
10
Distance Along Interface (mm)
20
Figure 8. Predicted axial motion for PZT rod test ECF
301.
ACKNOWLEDGMENTS
Sandia is a multiprogram laboratory operated by
Sandia Corporation, a Lockheed Martin company, for the
United States Department of Energy under Contract DEAC04-94AL85000.
REFERENCES
til Litii
Chhabildas, L. C., Dynamic shock studies of PZT
95/5 ferroelectric ceramic, Sandia National
Laboratories Report SAND84-1729, 1984.
Chhabildas, L. C., M. J. Carr, S. C. Kunz and B.
Morrison, Shock-recovery experiments on PZT
95/5, pp. 785-790 in Shock Waves in Condensed
Matter, Y. M. Gupta (ed.), Plenum, 1986.
Furnish, M. D., L. C. Chhabildas, R. E. Setchell and
S. T. Montgomery, Dynamic electromechanical
characterization of axially poled PZT 95/5, pp. 975978, in Shock Compression of Condensed Matter1999, edited by M.D. Furnish, L.C. Chhabildas, and
R.S. Hixson (AIP Press, 2000).
R. E. Setchell, Recent progress in understanding the
shock response of ferroelectric ceramics, in this
volume.
D. S. Drumheller, On the dynamical response of
particulate-loaded materials. II. A theory with
application to alumina particles in an epoxy matrix.
J. Appl. Phys., 53, 957-969, 1982
Brannon, R. M,. S. T. Montgomery, J. B. Aidun and
A. C. Robinson, Macro- and mesoscale modeling of
PZT ferroelectric ceramics, in this volume.
M. Wong (Sandia National Laboratories), personal
communication, 2001
Furnish, M. D., R. E. Setchell, L. C. Chhabildas and
S. T., Montgomery, Gas gun impact testing of PZT
95/5 part I: unpoled state, Sandia National
Laboratories Report, SAND99-1930, 2000.
Figure 6. Configuration for PZT rod tests. Projectile
layers are 10 mil thick except TPX (20 mils).
1.0
PZT Rod
0.8
Particle
Velocity
(km/s)
ALOX Potting
Center
Calculated
Optimized
f
PZT Model
A/
Measurec
PZT Rod Center
Calculated . Measured
0.2
0.0 '
3
4
5
6
7
Time after impact (is)
Figure 7. Experiment results compared with calculated wave
histories for ALOX-encapsulated PZT rod experiment ECF 301.
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