Use of Time-Resolved Wave Profile Techniques for Dynamic Material Property Measurements

Review and Prospects for the Future* (U) SA/VB-. -9 7- 30 55 G &/fJ?- 920 a I 8 - -

James R. Asay Shock Physics Applications Department

Sandia National Laboratories Albuquerque, New Mexico 87185-1 181

Abstract

CEIVED

Shock wave techniques have become a standard tool for studying the high pressure dynamic response of materials. An important advance in this field is the development of techniques for making detailed measurements of the time-resolved wave structure in shock and release waves. These techniques began with the development of stress wave gauges in the early 1960s and have evolved into a variety of high-resolution techniques being used in present shock physics applications. This paper provides a brief review of the development and use of time-resolved interferometer techniques for studying the high pressure dynamic response of materials. Applications of these techniques include studies of the initial compressive yield response of materials, plastic viscosity occurring during shock compression, measurements of compressive and tensile yield strength after passage of strong shock waves, and measurements of the kinetic properties of phase transitions. Dynamic material properties obtained from these measurements are important in developing predictive material models important to Science Based Stockpile Stewardship and in validating the equation of state and constitutive response of material models being used in a variety of applications. Examples are given which illustrate the importance of these measurements in current weapon physics and in other non-weapon applications. Prospects for extending these techniques for use with pulsed radiation sources, such as z pinch accelerators, are also be'discussed.

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INTRODUCTION

There is a continuing need to determine the equation of state (EOS) and constitutive properties of materials to multi-megabar pressures in support weapons and non-weapons applications. Shock wave techniques have been a principal tool for determining the high pressure equation of state (EOS) of materials in regimes inaccessible by other methods (Asay and Kerley, 1987; Graham and Asay, 1978). A variety of shock wave techniques have been developed for producing well- controlled shock planar shock waves to study dynamic material response (Graham and Chhabildas, 1988). For ultra-high EOS measurements, underground nuclear tests have been used to produce shock wave pressures to pressures inaccessible by other methods (Ragan, et al., 1982).

1 19980406 156

DISCLAIMER

This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employm, makes any wartanty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or use- fulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any spe- cific commercial product, process, or service by trade name, trademark, manufac- turer, or otherwise docs not necessarily constitute or imply its endorsement, rccom- mendrction, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

a s work was Derformed at S-borataies was su Dofled bv the United States D e D a m of Energy under contract DE-AC04-94AL85000. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the U.S. DOE.

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High-velocity launchers remain the standard tool for making these measurements. However, conventional gun technology is limited to launch velocities of about 8 km/s. Projectile impact at these velocities will produce shock pressures in materials ranging from about 1 Mbar in low-Z materials to approximately 7 Mbar in high-Z materials. Existing scientific and programmatic problems, however, require EOS studies to shock pressures of tens of megabars. This requirement results in a need to increase the capability of gun launchers to significantly higher velocities and to develop other sources of shock wave loading for high-pressure EOS studies.

A variety of radiation sources are being explored for accessing the extremely high-pressure states of matter. The leading candidates include high intensity lasers and pulsed power methods. For example, recent results obtained with laser driven shock waves have produced promising results for high-pressure EOS studies in plastics and in deuterium. For example, Evans et al. (1 995) have developed direct-deposition laser techniques using impedance matching to produce shock waves in copper to pressures of about 20 Mbar. More recently, Cauble et al. (1 997) have developed simultaneous laser drive and back-lighting techniques for making absolute shock wave measurements of low atomic number materials, including deuterium, to extremely high pressure. A major limitation with laser shock experiments is the limited samples sizes that can be studied. This restriction limits the experimental possibilities for studying a broad range of material properties other than EOS. For example, measurement of compressive strength under shock compression is of intense interest in developing constitutive models needed in 3-D computer simulations of dynamic material response. Typically, such measurements require samples of several centimeters in diameter and several millimeters in thickness for conventional gas gun techniques.

This paper discusses the use of wave profile techniques for probing the high pressure thermophysical and mechanical properties of materials. First, a review is given of the development and status of shock wave profile techniques. These methods have matured to the state where they can yield a wide variety of thermophysical and mechanical properties. Secondly, the application of wave profile techniques to the study of dynamic material yielding and, specifically, the pressure dependence of dynamic material strength is discussed. A discussion is then given regarding the effects of shock-induced phase transitions, which include shock-induced melting and polymorphic phase transitions that occur during shock compression. The discussion of phase transitions also includes shock-induced vaporization, which is a relatively new area of shock compression science. Finally, the prospects for using wave profile techniques with pulsed radiation sources (PRS) is discussed.

Early shock wave research focused on the pressure-volume states achieved by a single shock that transitions from the initial to final state; typically shock pressures achieved in these early experiments ranged from several tens of kbar to several Mbar using explosive loading techniques (Graham and Asay, 1978). At that time, parallel efforts at Sandia National Laboratories and at Los Alamos National Laboratory focused on the development of smooth-bore gun loading techniques to introduce well-controlled planar loading conditions into materials and in the development of advanced wave profile techniques to study the fine structure of shock waves (Graham and Asay, 1978; Graham and Chhabildas, 1988). These new diagnostics enabled a whole new range of dynamic material property information for off-Hugoniot states (Le., release states or reshock states), in addition to the initial shock response.

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Figure 1 illustrates schematically the technique for producing principal Hugoniot states using gas gun techniques. In the upper part of the figure, a gun-launched projectile with a flat facing is shown impacting a specimen in the form of a flat disk. For symmetric impact experiments, the facing on the projectile is identical to the sample. In this case, measurement of the impactor velocity defines the particle velocity induced in the specimen; simultaneously, the shock velocity produced in the sample is measured. The use of these two independent variables in the conservation equations for mass, momentum and energy achieved by shock loading defines the pressure and volume state - Le., the Hugoniot state - produced in the experiment.

In the mid- 1960s, several groups began developing gauges to make a time-resolved measurement of shock wave structure . At pressures on the order of tens of kbar, the shock wave is not discontinuous but has considerable structure containing information about the shock deformation process and the mechanical and physical properties of the shocked material. This approach is shown schematically in the lower part of Fig. 1. For illustrative purposes, the figure represents the phenomenon of initial yielding, followed by plastic compression; subsequent release from the Hugoniot state results in the wave structure appropriate to elastic-plastic unloading (Asay and Kerley, 1987).

Pins - -- .II .I

-1 *.. " . Time-resolved

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Fig. 1. Time-resolved shock wave techniques increase accessibility to thermophysical and mechanical properties under shock compression.

A large variety of time-resolved gauges have been developed for studying shock wave structure (Graham and Chhabildas, 1988). Early gauges included piezoelectric quartz transducers, piezoresistive gauges, velocity interferometers and magnetic particle velocity gauges. A key development that enabled interferometer measurements at Mbar pressures is the Velocity - Interferometer System for Any Reflector (VISAR) developed by Barker and HolGnbach (1 974). Most of the examples desczbedbelow have been made with this instrument.

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In tandem with the evolution of time-resolved techniques, a variety of new experimental methods were also developed to probe dynamic material properties. Several of the loading techniques developed to study off-Hugoniot properties are illustrated in Figure 2.

By placing an appropriate backing material to the impacting plate in an impact experiment, it is possible to control the subsequent loading process after the initial shock wave has passed through a sample. If the back surface is vacuum or a low-impedance material, full unloading from the shocked state or partial unloading to a lower pressure can be achieved (Asay and Chhabildas, 1979). If the backing plate is higher impedance, it is possible to reload the sample from the initial (principal Hugoniot) state (Lawrence and Asay, 1977). The final state achieved during reshocking of a material from a specific state on the principal Hugoniot is referred to as a recentered Hugoniot from that state.

I I L \ Sample X Graded’ Density

Impactor

Impactor / Window Ox

\ Sample Backing

ock

Fig. 2. Experimental techniques for making off-Hugoniot measurements using gun-launched projectiles.

In general, the recentered Hugoniot will be offset to the principal Hugoniot; typically, the resulting P-V states fall below the principal Hugoniot. Similarly, unloading the specimen from

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the shocked state produces P-V states that approach isentropic behavior (Chhabildas and Asay, 1992). Thus, unloading and reloading wave structures provide valuable information about EOS properties off the principal Hugoniot and also about the mechanical properties of materials at high pressure.

Another method €or studying dynamic material response is the shockless loading technique shown in the lower part of Figure 2. In this case, the impactor has a graded density, beginning with a low impedance (e.g., plastic) at the impacting surface and increasing to a high shock impedance at the far side (copper or tungsten). Barker (1 983) developed a process for making graded density impactors using powder metallurgy techniques that provides essentially smooth compression to the final state after an initial low amplitude shock upon impact. Chhabildas (1 992) extended this approach to a graded density layered-plate impactor; which produces a series of small initial steps in the loading followed by transition to smooth compression as a result of wave interactions. An alternate approach used for shockless loading of specimens involves use of a ceramic material with negative stress-strain curvature for plane shock loading to 200 kbar (Asay and Chhabildas, 1979). Because of this curvature, a steady shock wave is not possible and a shock input will quickly disperse into a ramp wave having a risetime proportional to the propagation distance in the ramp wave generator.

DYNAMIC MATERIAL STRENGTH

There are several issues related to the strength of materials during shock compression, including (1) the physical mechanisms occurring during dynamic yielding, (2) the effects of high shock pressure, and (3) the effects of initial loading rate on thermophysical and mechanical properties. Wave profile techniques can address most of these issues, as well as several other material properties and kinetic effects important in shock wave experiments. Figure 3 illustrates the shock wave features that can be studied in shock-wave studies. These include initial yielding which can be rate dependent, viscoplastic effects of compression, polymorphic (solid-solid) phase transitions represented by the break in the plastic wave, elastic effects during unloading from the Hugoniot state, hydrodynamic release which provides information on release isentropes, and the final pull-back signal which gives information on dynamic spa11 strength.

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Fig. 3. A typical shock wave profile which illustrates the physical and mechanical properties that can be determined from these measurements.

Figure 4 illustrates the phenomenological effects of elastic-plastic compression that can occur during dynamic yielding (Asay, et al., 1972). The graph on the left shows the hydrostatic response, P(V), expected for fluids and the stress state obtained by uniaxial shock compression, which is offset from the hydrostat by two-thirds the yield strength. The dashed line in the figure illustrates the path that would be followed if there is rate dependence to the yield process.

Figure 5 shows the effect of rate dependence on shock structure for different propagation distances. This effect can be described in terms of the stress relaxation rate equation shown in the figure, where ox is the longitudinal stress, E is the total strain, y is plastic shear strain, E is the elastic longitudinal modulus and p the elastic shear modulus. This representation for stress relaxation is appropriate for polycrystalline materials and has been used primarily to study elastic-plastic transitions in metals.

,'- Cyclic Loading Dissipation

Real Material

?Or

3 Strain Hardening Visco-

* U

Elastic Precursor /

Propagation Distance, X

Fig. 4. The elastic-plastic model for solids predicts that the uniaxial strain compression curve is offset from the hydrostat by two thirds of the compressive yield strength. The offset is negative for release from the shocked state. The corresponding wave structure expected is illustrated on the right side of the figure.

Elastic precursor decay experiments have been conducted on a large number of materials, including single crystals, to study the dislocation mechanisms responsible for dynamic yielding (see for example, Asay et al., 1972).

The discussion above concerns initial yielding of materials subjected to shock compression and the use of wave profile techniques to study this behavior. Another issue is the strength of materials after shock compression. There has been considerable uncertainty regarding the strength of materials in the shocked state. Prior to the early 1970s there were limited data

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available to address this issue. At that time, investigators at Los Alamos and in the Soviet Union had shown that elastic compression persists in materials shocked to very high pressures. However, quantitative data of shock-induced strength effects were not available. In many cases, it was assumed that material strength was either negligible for EOS applications or very large in applications such as plate launcher methods where the observed stability of accelerated plates implied strength-stabilizing response.

V

Steady Wave

1-11

X

Elastic Precursor Decay Determines Initial Stress Relaxation Steady-Wave Structure Determines Shock Viscosity

Fig. 5. Effects of rate dependence in dynamic elastic response.

An approach developed (Asay and Lipkin, 1978; Asay and Chhabildas, 1979) for determining high-pressure compressive strength involves measurement of the complete wave structure, especially the unloading wave. structure, as illustrated in Figure 4. The figure shows the initial elastic precursor, followed by the plastic compression wave that can induce strain hardening and other material effects due to the introduction of defects occurring during viscoplastic deformation. If the material is allowed to come into thermal and mechanical equilibrium after shock compression, as illustrated by the constant portion of the wave structure, and then unloaded it is possible to obtain information about the compressive yield strength, Y, in the shocked state. The figure shows the stress path followed during unloading and the resulting elastic-plastic structure expected in the wave profile. The ideal structure is never fully realized because of non-elastic mechanisms, such as the Bauschinger effect (pre-yielding).

Figure 6 presents a compilation of wave profile measurements used to deduce the strength of materials in the shocked state (Asay, et al., 1980; Asay and Chhabildas, 1980; Asay, et al., 1985; Chhabildas, et al., 1981; Wise, et al., 1981). The inset shows an experiment performed on aluminum at about 200 kbar which illustrates the elastic-plastic nature of unloading from that pressure and a numerical simulation of the experiment (Asay and Chhabildas, 1980). As shown,

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the dynamic compressive strength of materials can increase substantially after shock compression. For example, in copper (Chhabildas and Asay, 198 l), the compressive yield strength at a shock pressure of 300 kbar is over an order of magnitude larger than the ambient value. However, since the initial yield strength of all materials studied was on the order of a few kbar, the final values are still a few tens of kbar, rather than the Mbar values speculated by some investigators.

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Fig. 6. Normalized dynamic yield strength versus shock pressure to over Mbar pressures for several metals. The inset shows an experiment on aluminum at about 200 kbar and the resulting numerical calculation used to estimate the strength effects.

In addition to the determination of high-pressure material strength, the unloading profiles provide information on the isentropic response during unloading (Asay and Chhabildas, 1979). Figure 7 shows a schematic representation of the relationship of the principal Hugoniot to other equation of state paths, including the cold curve (isothermal compression at absolute zero), the room temperature isentrope and the release isentrope from the shocked state. With the exception of the initial elastic unloading from the shocked state, the lower portion of the unloading wave follows thermodynamic states that are essentially isentropic. The set of three wave profiles shown on the right side of Figure 8 represent data obtained on aluminum to about 1 Mbar (Asay, et al., 1985). Shown with the experimental results are numerical calculations using an EOS model for aluminum. The good agreement between calculation and experiment indicates that the isentropes in aluminum are accurately known to pressures of about 1 Mbar. This EOS information adds much more to the knowledge of the aluminum EOS than a principal Hugoniot.

In Figure 6, note that the strength of beryllium and the three aluminum alloys studied initially increases with shock pressures to about 300 kbar. However, the aluminum alloys exhibit anomalous response at the higher pressures in that the precipitation-hardened alloy, 6061 -T6, shows premature softening compared to pure aluminum and the 2024 alloy. The softening of the

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latter two alloys can be partially attributed to shock-induced melting, since aluminum undergoes a melting transition at shock pressures of about 1.2 Mbar.

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Wave profile experiments performed on this alloy showed that the standard elastic-plastic theory is appropriate for this alloy to shock pressures (technically, shock stresses) of about 80 kbar, but that a definite softening effect occurs at the higher pressures (Asay and Lipkin, 1978). For

L

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-

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Fig. 7. The relationship between the Hugoniot curve, a room temperature isotherm and a release isentrope. The release wave profiles on the right hand side represent unloading along isentropes from appropriate shock pressures.

recompression from shock stresses less than 8 GPa, only a very small elastic wave is observed. However, at higher shock stresses, the shear stress developed during reloading increases rapidly. This is associated with a rapid increase in the reverse shear stress measured independently in unloading experiments. Both of these transitions occur near 8 Gpa, which corresponds to a strain rate of about 1 08/s in the initial shock loading.

Current understanding of this effect is that shock-induced softening results from the high rate of loading achieved in higher amplitude shock waves. In aluminum, the onset of softening is thought to occur at strain rates of about 1 08/s in the shock wave. Several hypotheses for micro- mechanical mechanisms of deformation have been advanced to account for this observation. (Grady and Asay, 1982) proposed that the effect is due to localized heating in shock-induced defects, such as micro shear bands that cannot be dissipated during the very high rates occurring in a shock wave, but can be continually dissipated during shockless loading at low strain rates, thus maintaining an equilibrium thermal state. The effect of shock-induced softening is potentially important in a number of applications, including the stability of shocked surfaces and the integrity of components subjected to high dynamic loads.

The effect of shock-induced softening illustrated in figure 8 shows the change in dynamic yield strength for tungsten (Chhabildas, et al., 1988, 1989) to 2 Mbar for both shock loading and

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shockless loading. For shock compression, the yield strength of tungsten is observed to remain fairly constant at about 2 GPa (20 kbar). For shockless loading and corresponding strain rates of about 105/s, the strength is observed to increase rapidly to over 10 GPa (100 kbar) at 2 Mbar.

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. e Shock Loading . I Isentropic Loading

.. - m

0 0 50 100 150 200 250

0, GPa

Fig. 8. The effect of initial strain rate in the compressive yield strength of tungsten for both shock and isentropic loading.

Since the strain rate in a shock wave can have major consequences on the subsequent thermophysical and mechanical behavior of the material, it is important to understand and predict the strain rates achieved through shock loading. Grady has advanced a theory which predicts that strain rate in steady shock waves should be proportional to the fourth power of the shock stress (Grady and Asay, 1982). This prediction is represented in Fig. 9, which shows total strain rates attained in plastic shock waves for several metals and two oxides. The experimental data acquired on these materials is in good agreement with the predicted fourth power dependence. A consequence is that the effective viscosity for strong shocks should vary as the inverse one-half power of shear stress rather than the linear power predicted by Newtonian viscosity. This phenomenological observation can be used in computer simulations instead of the usual assumption of linear or quadratic viscosity commonly used.

105 10s 107 Id

Strain Rate (SI)

11

Fig. 9. The dependence of peak strain rate achieved during shock compression versus stress in steady shock waves..

DYNAMIC PHASE TRANSITIONS

Wave profile techniques have been a major advance for studying phase transition occurring during shock compression. One application has been the study of shock-induced melting. The first work in this area was conducted by Asay (1 974) on shock melting and refreezing in bismuth which illustrated the capability. Bismuth has a complex phase diagram, as illustrated in Figure 10, including a negative Clausius-Clapyeron slope for melting.

0.0 1 .o 2.0 Pressure (GPa)

0.98

0.97

0.96 c ;; 0.93

0.92_b I I . I . I . 1

300 350 400 450 500

Initial Temperature ("K)

Validation of theories Kinetic effects Effects of strength on transition

Fig. 10. Phase diagram for bismuth and the wave profiles expected for different initial temperatures and final pressure.

The insets shown in the figure illustrate the type of shock wave structures expected for the different initial conditions. For regions where the Hugoniot intersects the solid I-solid I1 phase boundary, a two-wave structure (neglecting elastic compression effects) is expected. When a correction is made for strength effects good agreement was achieved between the amplitude of the first wave and the established temperature-dependent pressure defining the phase boundary, as shown by the graph on the right side (Asay, 1974). These experiments also allowed an estimation of kinetic effects associated with the phase transition. Comparisons with computer simulations using a rate law for the transition indicated negligible kinetic effects.

For initial temperatures above about 470 K, the Hugoniot intersects the solid I-liquid phase boundary. For these experiments, a three-wave structure should occur in the transmitted shock waves for final pressures residing in the solid I1 region (again neglecting elastic wave effects). However, a large number of experiments conducted in this region revealed that only a two-wave structure occurred and that the resulting waves were highly dispersed. This effect was probably due to increased viscoplastic effects occurring at high temperatures. Although the onset of melting (point b in the inset) could not be detected, it was possible to determine that melting indeed occurred by comparing the pressure at which the second wave arrived. If melting were

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completely suppressed over the time duration of these experiments, transition to the high pressure solid phase would occur at the metastable extension of the solid I1 phase into the liquid regime. However, the experimental results showed that transition to the solid I1 phase occurred at the triple point, independent of starting temperature. This response is expected if melting occurred on the time scale of the experiments. Thus, these experiments were the first to establish that melting occurred in the sub-microsecond time scale of shock wave experiments.

Although early experiments on bismuth established that shock-induced melting occurred, it was not possible to quantify the location of the melt boundary. However, unloading wave experiments provide a method for detecting the melt boundary at high pressure (Asay, 1977). Figure 11 presents the results of release-wave experiments conducted on bismuth. Since this was one of the first applications of interferometry to determine unloading wave speeds the early measurements had error bars of 34%; however, it has been possible to reduce these errors to 1- 2% with later improvements. The graph on the right illustrates the sensitivity of the technique, which could easily detect a 1 % decrease in particle velocity or pressure at the shocked state. With these measurements it was possible to compare with theoretically predicted longitudinal and bulk sound speeds in the solid-liquid mixed phase region. More importantly, by observing the transition from elastic longitudinal to bulk sound speeds, it was possible to identify where melting occurred in the shocked state. As shown in the figure, the onset of melting that was experimentally measured was in excellent agreement with theoretical predictions based on a complete thermodynamic equation of state for bismuth.

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A notable observation was that the bulk sound speeds measured in the solid-liquid mixed phase region corresponded to a mixed of frozen concentration of solid and liquid, versus a mixture of these two phases in thermodynamic equilibrium. This suggests that refreezing back to the initial solid phase upon release, as predicted from the theory, is not instantaneous or even as fast as the initial melting rates. This observation was firther confirmed by calculating the unloading paths from the release wave profiles. These results suggested that the unloading response remains as a fixed concentration of liquid and solid during most of the release.

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Figure 12 gives the temperature-pressure phase diagram for aluminum and the results of shock loading and unloading experiments to determine the initial unloading velocities in the shocked state (Asay and Hayes, 1975). It is possible to shock melt porous aluminum for Hugoniot pressures significantly lower that that required for solid aluminum (about 1.2 Mbar). The graph on the right shows the initial release wave speeds that I measured for a series of experiments in the vicinity of the melt boundary. A clearly defined decrease in the release speed was observed in these experiments at shock pressures corresponding to theoretical predictions. As for the bismuth studies, the release speed approached predicted bulk velocities in the mixed phase region. In this case, the measured bulk velocities were in better agreement with predictions of equilibrium response, although the difference between frozen and equilibrium response was significantly less than that for bismuth. The apparent agreement with equilibrium response in aluminum results from the fact that unloading from shocked states in the mixed phase region causes further melting; in contrast to bismuth where unloading from mixed phases causes refreezing.

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Fig. 12. Melting along the Hugoniot of shock-compressed porous aluminum.

The final area of shock-induced phase transitions to be discussed concerns the issue of shock- induced vaporization. There has been only limited research performed on shock-induced vaporization. The majority of work had been done in the former Soviet Union by Bushman, Fortov and their colleagues (Bushman and Fortov, 1983). These experiments were confined to equilibrium measurements of pressure-volume states achieved by unloading shocked samples into the liquid-vapor coexistence region. Wave profile methods provide a technique for examining the kinetic effects of shock-induced vaporization, the effects of mixed phase flow of liquid-vapor products, and the transfer of momentum from vapor products to solid materials (Asay et al., 1987; Asay and Trucano, 1990; Brannon and Chhabildas, 1995).

Figure 13 summarizes the different approaches previously pursued for studying materials in expanded thermodynamic states. The graph on the left illustrates the behavior of release isentropes in the vicinity of the liquid-vapor coexistence region. Upon intersection of the release isentrope with the liquid-vapor boundary, the isentrope will assume a very low slope in the mixed phase region if the material remains in thermodynamic equilibrium. Since the critical

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point is at a very low pressures of a few kbar and the initial shock pressure corresponding to intersection of the release isentrope with the principal Hugoniot is very high, typically a few Mbar, it has been very difficult to study this region. Russian investigators used an impedance matching technique as illustrated in the figure to measure discrete P-V states in the mixed-phase region.

Time-resolved wave profile measurements can be used to measure stagnation pressures from shock-induced vapor expansions and to evaluate effects of vaporization kinetics and mixed phase liquid-vapor propagation. In previous work conducted at Sandia National Laboratories, a two- stage light gas gun was used to shock a thin specimen with a low melting point. Lead and cadmium were studied initially because they satisfied this requirement. To induce shock vaporization, a specimen of one of these materials was shocked to pressures on the order of 1-3 Mbar with a tantalum impactor. The resulting shock wave reflected from a free surface in vacuum which instantaneously resulted in temperature states sufficient to partially vaporize the material. If vaporization did not occur, the specimen impacted the material as a liquid sheet of uniform density with a characteristic impact for condensed materials. If it did, a gradual increase in pressure was observed at the gauge, signifying vaporous material.

Impedance Mismatch Specimen JBuffer 0 Discrete

P-V States During Unloading

P + + --+

Isobaric Measurements + Wire *P-v States in ;k specimen coexistence Stagnation Pressure

Crltical Liquid-Vapor Coexistence

Region I

Final State in Coexistence Region

Shock-Unloaded Specimen

Fig. 13. Experimental methods for studying shock-induced vaporization.

Figure 14 shows the experimental method and the calculated liquid-vapor coexistence regions for cadmium and lead. Release isentropes from shock pressures of 1 10 GPa (1.1 Mbar) and 350 GPa are shown intersecting the mixed phase region at different positions along the vapor dome. The percentages of vapor formed for these loading conditions is listed in the figure. As illustrated, about 35% vapor is produced in both materials after unloading from these shock pressures.

Figure 15 shows the experimental and calculated results for two different initial shock pressures. The two upper curves give results for experiments where less than 10% vapor is expected to

15

occur during unloading into the liquid-vapor coexistence region. As shown, the agreement between experiment and calculation is very good for early times in the wave profiles. Late time effects are influenced by yielding in the projectile facing and other effects not understood in these experiments.

Tirget Holder

10’0

1 0 2 10’ 10’0 I O + ’ 10’2 1 0 2 10 ’ 1 0 4 10’’ 10.2

Density (grn/cm3) Density (gmlcrn3)

Fig. 14. Wave profile technique for studying shock-induced vaporization. The two graphs on the right show the calculated liquid-vapor coexistence regions for cadmium and lead and the experimental release isentropes (dotted and dashed curves) for unloading from the shock pressures indicated.

The two lower graphs in Figure 15 give the results for experiments in which about 35% vapor is produced during unloading. In these cases, there is significant disagreement between the experimental and computational results, particularly for lead. In this material, the difference in peak pressure produced by the stagnation of liquid-vaporous products of lead on the gauge differs by a factor of two. The calculated peak pressure is about 1 Mbar; experimentally it is about 500 kbar. The experimental results also show a significant precursor to the main pulse, which is barely observed in the figure. Similar results are apparent in cadmium.

Chhabildas et al. (1991) extended the vaporization technique to essentially full vaporization using zinc and the three-stage hypervelocity launcher (HVL) developed at Sandia. With the HVL, it is possible to achieve full vaporization in both lead, cadmium and zinc. Furthermore, it is possible to vaporize materials of more interest in engineering applications, including tungsten and aluminum. These experiments are thus useful for validating computer codes in the regime where full vaporization is expected to occur and to begin studies of vaporization in regions corresponding to partly ionized plasmas.

Prospects for Pulsed Radiation Sources

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Light gas guns have been an important tool for studying the dynamic response of materials in regimes previously inaccessible in the laboratory. Primarily, regions of the thermodynamic surface easily accessible by shock wave techniques include states achieved by shock and isentropic decompression, but states of isentropic compression are difficult to achieve with gas guns. This limitation prevents access of material response in the very high pressure solid phase of most materials because of shock-induced melting that typically occurs at pressures of a few

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$ 1.5 r 1.0 8 0.5 .-

0.0

Fig. 15. Experimental and calculated profiles in cadmium and lead for partial degrees of vaporization. The top two graphs represent about 9% vaporization. The lower two curves correspond to a vapor concentration of about 35%.

Mbar. As previously noted, in the solid range of material response a wide variety of dynamic material properties can be studied, including high pressure material strength, tensile failure, polymorphic phase transitions, melt transition and vaporization. In the near term, three-stage light gas guns offer the potential for expanding the pressure regimes accessible in the laboratory. However, the recent advent of pulsed radiation sources for EOS studies offers the possibility of substantially increasing this range (Rothman and Evans, 1997; Cauble et al., 1997). Specifically, lasers and other pulsed radiation sources offer the opportunity to access pressure regions of several hundred kbar in the laboratory. The integrated use of high velocity launchers and pulsed radiation sources thus offers new opportunities for studying EOS and constitutive material properties in previously inaccessible regions.

As example, Z pinch sources can be used to produce x-ray temperatures in hohlraums and to drive high pressure shock waves (Olson, et al., 1997) to pressures significantly larger than possible with light gas guns. X-ray temperatures approaching 150 eV have recently been

17

produced, which allows shock pressures to about 12 Mbar in low impedance materials such as aluminum and plastics and to 45 Mbar in high Z materials (Trucano et al., 1998).

The relatively large samples possible with Z pinch sources and lasers under development such as the National Ignition Facility (NIF) offer the possibility of performing many of the time-resolved wave profile measurements discussed previously. An approach for performing such studies is illustrated conceptually in Figure 16. The figure illustrates the concept of controlled ablation loading of a specimen to structure input waves consisting of either shock loading followed by unloading or ramp loading followed by unloading. Measurement of the resulting wave profile with velocity interferometry or a similar technique can then be used to determine a variety of EOS and constitutive material properties. Examples include Hugoniot states, compression and decompression isentropes, mechanical properties such as compressive and tensile strength, phase transitions and surface stability.

Input

Controlled loading history

n Shock B/O

+

output

Time-resolved wave profiles

Fig. 16. Pulsed radiation sources can be used to study a variety of EOS and constitutive properties with the use of wave profile techniques.

The small samples necessary for use with pulsed radiation sources compared to conventional gun techniques make the task of obtaining accurate wave profile data more difficult. However, it appears feasible to make these measurements with reasonable accuracy. For example, Figure 17 illustrates that it should be possible to make isentropic loading experiments in aluminum with velocity accuracies approaching 1 %. However, it will be necessary to produce a ramp load that will not converge into a shock over the sample distances studied. For isentropic compression experiments on aluminum, the minimum risetimes necessary to prevent shock formation vary from about 17 ns to 45 ns for sample thickness ranging from 100 pm to 300 pm. The resulting average transit times range from about 20-60 ns. With modem instrumentation, it should be possible to measure wave velocities to 1% for these transit times. With similar accuracy in particle velocity it should be possible to determine pressure-volume states to a few percent to isentropic pressures of several Mbar

The new PRS techniques being developed offer expanded opportunities for studying materials at the extremes of pressure and temperature. It is expected that these new techniques will allow the study of new regimes of material response, result in the development of new theories of material

18

response over the complete EOS surface of interest in applications, and enable use of shock- compression techniques in material synthesis and applications not yet conceived. A specific example is that hypervelocity impact experiments at velocities of 15 km/s produce thermodynamic equation of state response in the condensed phase to pressures in the 6 Mbar in aluminum. This region of the equation of state cannot be easily accessed in laboratory static experiments. Recent theories have predicted that aluminum should undergo a polymorphic phase change from FCC crystalline order to HCP and then BCC in this region of solid response. Thus, isentropic impact experiments conducted with either hypervelocity launchers or pulsed radiation sources offer new opportunities for studying the physics of condensed phases.

60 1 I 4 Ax = 300 pm, At - 60 ns I

Shock Ax = 200 pm, At - 40 ns

J *

Ax = 100 pm, At - 20 ns

0 2 4 6 8 10 12

Pressure, Mbar

Fig. 17. Input pressure profiles necessary to produce isentropic compression in aluminum samples over the propagation range of 100 - 300 pm

In summary, wave profile techniques have played an important role in traditional shock compression science studies and applications for many years. It is expected that they will also be an important contribution to future applications involving pulsed radiation sources; which presents several challenges and opportunities. A pressing need at present is to perfect loading and sample configurations to produce controlled loading conditions that result in uniformity of the pressure loading and steadiness of the resulting shock waves. A specific application is the issue of shock risetime dependence on shock pressure. The fast diagnostics developed for laser and other PRS applications would be particularly useful for studying this issue at pressures much higher than previously possible. A systematic study of shock risetime versus shock pressure to significantly higher pressures would provide a solid foundation for theoretical understanding of the fourth-power relationship previously discussed. Diagnostics developed for the laser and pulsed power programs would also be useful for evaluating phase transition rates, such as solid- solid, melting and vaporization.

An area of special interest is isentropic loading. Pulsed radiation sources could play an important role in the generation and study of isentropic compression because of the inherent nature of the

19

loading process and the ability to produce extremely high pressures. The combination of these new sources with wave profile techniques would add a new dimension to scientific and programmatic applications. A specific application would be the study of condensed matter physics to pressures of several tens of Mbar. In addition to EOS applications, these techniques would allow determination of constitutive material properties to pressures higher than presently possible.

The high pressures and temperatures possible with pulsed radiation sources also permit study of vapor and plasma states, which are difficult to achieve with conventional light gas gun technologies although three-stage light gas guns provide several options for these studies. However, pulsed radiation sources can augment and significantly extend the study of full vaporization and dense plasma states.

Finally, the ability to simultaneously load a specimen and perform x-ray diffraction measurements in the shocked state (Hauer et al, 1998) offers new opportunities for probing the micromechanical states produced by shock compression. These studies could help resolve the mechanisms for shock-induced softening previously discussed and could also identify phase transitions occurring at high pressures.

In addition to providing basic scientific information, the combination of pulsed radiation sources and wave profile technologies will also provide more critical evaluation of models being used in ICF and weapons applications. Examples include physical processes occurring during ablatively driven shocks, such as determination of preheat levels in ablators, opacity and radiation flow. Wave profile techniques are particularly useful in detecting multiple shocks and should prove useful in validating rad-hydro calculations of laser drives to optimize convergence of ICF pellets. Finally, these techniques can be applied to studies of magneto-hydrodynamic processes.

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