CP620, Shock Compression of Condensed Matter - 2001edited 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 TESTSON 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 andalumina-loaded epoxy (ALOX) encapsulants, with the purpose of providing benchmarks for materialmodels in the ALEGRA wavecode. Diagnostics used included line-imaging VISAR (velocityinterferometry), a key diagnostic for such tests. Results from four tests conducted with ALOXcylinders impacted by nonplanar copper projectiles were compared with ALEGRA simulations. Thesimulation produced approximately correct attenuations and divergence, but somewhat higher wavevelocities. Several sets of tests conducted using PZT rods (length:diameter ratio = 5:1) encapsulated inALOX, and diagnosed with line-imaging and point VISAR, were modeled as well. Significantimprovement in wave arrival times and waveforms agreement for the two-material multi-dimensionalexperiments was achieved by simultaneous multiple parameter optimization on multiple one-dimensional experiments. Additionally, a variable friction interface was studied in these calculations.We conclude further parameter optimization is required for both material models.

INTRODUCTION

Knowledge of the electromechanical proper-ties of ferroelectric materials is important forvarious pulsed-power applications. Of particularinterest is lead-zirconate-titanate with a Zr:Ti ratioof 95:5 (PZT 95/5). In this material, theferroelectric/antiferroelectric (FE/AFE) phaseboundary is quite close to the roomtemperature/pressure state. Hence, if this materialis poled, a relatively low amplitude stress wave candepolarize the material, producing a large pulse ofcurrent or voltage.

Key observations from previous research onthis material in a uniaxial strain environment 1-3

include a gradual pore crush-up between 2.2 and4.0 GPa (initial porosities range from 3 to 9%,depending on preparation), the reversible FE/AFEphase transition at approximately 0.5 GPa, and the

compression curves. Setchell has presented resultsfrom a recent study of the electrical response ofPZT 95/5 to uniaxial shock loading.

However, applications generally imposediverging waves, shock propagation along rods,tilted shock fronts, and other two- and three-dimensional effects. Recent increasingly stringentcertification requirements demand that computermodels adequately describe such behaviors. Thepurpose of the present study is to explore multi-dimensional validation experiments needed to testthe simulation models.

EXPERIMENTAL METHOD

Two types of multi-dimensional gas gunimpact experiments are discussed in the presentpaper. For one type, multi-dimensional loading isgenerated in a composite material composed of 10-

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20 micron tabular alumina dispersed in an epoxymatrix (ALOX). The other type of test wasconduced on specimens composed of a rod ofunpoled PZT 95/5 encapsulated in ALOX.Geometries for both tests are shown in fig. 1.

A key diagnostic for these experiments is theline-imaging VISAR5. In this instrument, anilluminated line on the target is imaged through theinterferometer onto the input to a streak camera.Hence each lineout on the streak camera recordrepresents an interference record, and can be usedto derive the velocity history of each point on theilluminated line (fig. 2).

Figure 1. Representative gas gun configurations used, (a)An ALOX cylinder impacted by a projectile with a flatface, a pedestal face (shown), or curved face, (b) A PZT rodencapsulated in ALOX impacted by a flat-faced projectile.

SINGLE MATERIAL TESTS

The first series of experiments, along the linesof Fig. l(a), was designed to subject a single testmaterial to a controlled divergent shock wave. Fig.3 shows the streak camera records obtained andconfigurations. Here, the ALOX samples were 48-mm diameter and 22.9-mm thick. The copperprojectile impacted at 300 m/s.

For the relatively simple planar impact ((a) inFig. 3), the arrival along the line is fairly planar,and has a rise time of roughly 100-ns. Away fromthe centerline, edge effects cause dispersion anddarkening at late times.

(a)Figure 3. Streak camera records from selected ALOX tests.Line length was 8.6 mm for these tests. Times are relative toimpact at pins (above and below ALOX). Velocity-per-fringewas 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 goodreproducibility, with considerable dispersionfollowing the arrival in the second test (Fig. 3(c)).The wavefront displays much greater curvaturethan for the planar impact. Additionally, theparticle velocity achieved is lower (0.1 km/s vs.0.38 km/s).

The line VISAR data from these experimentsmay be reduced to velocity as a quasi-continuousfunction of position and time. We have chosen toproduce discrete lineouts for visualizationpurposes, 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 275using a composite model proposed by Drumheller5.

This model includes physics for 3-D contacts anddilatency, and is implemented in the ALEGRAwavecode. In fig. 5, computational results arejuxtaposed on the velocity histories deduced fromthe line VISAR streak record.

Two issues surface from this comparison.First, calculated peak particle velocities and waveshapes are in good agreement with experiment.Second, wave arrival times are very early in thecalculations. Using a simple Mie-Griineisen modelcorrects the wave arrival times, but omits thephysics we need for high-fidelity modeling. Anypossible experiment timing errors are beingevaluated.

TWO-MATERIAL TESTS

Figure 4. Velocity records extracted from streak recordof ECF 273, the first pedestal impact on ALOX.

0.2

0.1

0.0

Center

ParticleVelocity(km/s)

Calculated Measured. 6 mm from center

6 8Time after impact (us)

10

Figure 5. Calculation vs. experiment for velocity recordsextracted from streak record ECF 275, pedestal impact onALOX.

Another extensive sequence of tests has beenperformed with PZT 95/5 rods encapsulated inALOX. Two representative tests are discussedhere. The configuration for these tests is shown inFig. 6. Impact velocities were 292 and 415 m/s fortests ECF 298 and 301, respectively. The layeredimpactor was constructed to introduce a quasi-ramp wave loading into the target.

As with the ALOX tests described above, 1-millayers of tungsten foil were used to provide areflecting surface for the laser. For the PZT rodexperiments, however, it was necessary to segmentthis foil to allow for differential motion across thePZT/ALOX boundary.

Test ECF 301 was modeled using the ALOXmodel described above and a PZT model due toMontgomery and Brannon6. A frictionlessboundary between the two materials was assumed.For the initial calculation, parameters in the modelwere estimated from data in various sources.Later, a parameter optimization7 was conductedusing the results of eight uniaxial-strainexperiments described elsewhere8. Theoptimization process resulted in better estimates ofthe elastic moduli for the FE and AFE phases aswell as coefficients describing transformation rates.The calculation was re-run with the newparameters and results for the PZT motion areshown in Fig. 7. The simulations with both modelthe wave amplitudes fairly well for bothsimulations. As with the single-material ALOXshots, however, the calculated wavespeeds are

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greater than the measured wave speeds. Theparameter optimization for the PZT model, is seento substantially improve agreement between thecalculations and measurements.

It is worth noting that the experimental resultsshow an abrupt increase in the PZT materialvelocity when the main arrival occurs in theALOX. This suggests a large amount ofmechanical coupling between the two materialsrestricting slip of the interface. The calculatedwaveforms do not show such a coupling, consistentwith the (apparently erroneous) assumption of africtionless boundary.

In view of this strong coupling between the twomaterials, the calculation with the optimized PZTmodel also included an ad hoc adjustment in theALOX moduli to produce a correctly timed ALOXarrival (not shown in Fig. 7). The predicted slipbetween the ALOX and PZT is shown in Fig. 8(frictionless interface condition) at 5.3 us.

-1

-2t = 5.3 us

10Distance Along Interface (mm)

20

Figure 8. Predicted axial motion for PZT rod test ECF301.

ACKNOWLEDGMENTS

Sandia is a multiprogram laboratory operated bySandia Corporation, a Lockheed Martin company, for theUnited States Department of Energy under Contract DE-AC04-94AL85000.

til Litii

Figure 6. Configuration for PZT rod tests. Projectilelayers are 10 mil thick except TPX (20 mils).

1.0

0.8

ParticleVelocity

(km/s)

0.2

0.0 '

PZT Rod ALOX PottingCenter Calculated Measurec

Optimized fPZT Model A/

PZT Rod CenterCalculated . Measured

3 4 5 6 7Time after impact (is)

Figure 7. Experiment results compared with calculated wavehistories for ALOX-encapsulated PZT rod experiment ECF 301.

REFERENCES

Chhabildas, L. C., Dynamic shock studies of PZT95/5 ferroelectric ceramic, Sandia NationalLaboratories Report SAND84-1729, 1984.Chhabildas, L. C., M. J. Carr, S. C. Kunz and B.Morrison, Shock-recovery experiments on PZT95/5, pp. 785-790 in Shock Waves in CondensedMatter, Y. M. Gupta (ed.), Plenum, 1986.Furnish, M. D., L. C. Chhabildas, R. E. Setchell andS. T. Montgomery, Dynamic electromechanicalcharacterization of axially poled PZT 95/5, pp. 975-978, in Shock Compression of Condensed Matter-1999, edited by M.D. Furnish, L.C. Chhabildas, andR.S. Hixson (AIP Press, 2000).R. E. Setchell, Recent progress in understanding theshock response of ferroelectric ceramics, in thisvolume.D. S. Drumheller, On the dynamical response ofparticulate-loaded materials. II. A theory withapplication to alumina particles in an epoxy matrix.J. Appl. Phys., 53, 957-969, 1982Brannon, R. M,. S. T. Montgomery, J. B. Aidun andA. C. Robinson, Macro- and mesoscale modeling ofPZT ferroelectric ceramics, in this volume.M. Wong (Sandia National Laboratories), personalcommunication, 2001Furnish, M. D., R. E. Setchell, L. C. Chhabildas andS. T., Montgomery, Gas gun impact testing of PZT95/5 part I: unpoled state, Sandia NationalLaboratories Report, SAND99-1930, 2000.

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