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An anisotropic continuum material model was developed to describe the thermomechanical response of unreacted pentaerythritol tetranitrate (PETN) single crystals to shock wave loading. Using this model, which incorporates nonlinear elasticity and crystal plasticity in a thermodynamically consistent tensor formulation, wave propagation simulations were performed to compare to experimental wave profiles [J. J. Dick and J. P. Ritchie, J. Appl. Phys. 76, 2726 (1994)] for PETN crystals under plate impact loading to 1.2 GPa. Our simulations show that for shock propagation along the [100] orientation where deformation across shear planes is sterically unhindered, a dislocation-based model provides a good match to the wave profile data. For shock propagation along the [110] direction, where deformation across shear planes is sterically hindered, a dislocation-based model cannot account for the observed strain-softening behavior. Instead, a shear cracking model was developed, providing good agreement with the data for [110] and [001] shock orientations. These results show that inelastic deformation due to hindered and unhindered shear in PETN occurs through mechanisms that are physically different. In addition, results for shock propagation normal to the (101) crystal plane suggest that the primary slip system identified from quasistatic indentation tests is not activated under shock wave loading. Overall, results from our continuum simulations are consistent with a previously proposed molecular mechanism for shock-induced chemical reaction in PETN in which the formation of polar conformers, due to hindered shear, facilitates the development of ionic reaction pathways. [ABSTRACT FROM AUTHOR]

Thin polycrystalline aluminum (1050 and 6061-T6 alloys) samples were shocked to 4 GPa to examine elastic wave attenuation not observed in thicker samples (1–10 mm). Using laser interferometry in plate impact experiments, particle velocity histories were obtained for 0.08–1 mm thick samples, thinned from bulk material. Unlike past work on thicker samples, thin 1050 Al samples reveal large and rapidly attenuating elastic wave amplitudes, indicating a time-dependent elastic-plastic response. Extrapolation of measured elastic wave amplitudes to larger sample thicknesses agrees well with previously observed amplitudes for thicker 1050 and 1060 Al samples. Thus, all of the results for relatively pure polycrystalline Al can be reconciled into a single consistent picture: elastic wave attenuation, due to time-dependent elastic-plastic response, is confined to material close to the impact surface. In contrast to the 1050 Al results, thin 6061-T6 Al samples reveal an elastic wave amplitude of ∼0.7 GPa with no attenuation, in quantitative agreement with previous results for thick 6061-T6 Al samples. The lack of elastic wave attenuation even in thin samples suggests that elastic wave amplitudes in shocked 6061-T6 Al are governed by different plastic deformation mechanisms than those for shocked pure Al. [ABSTRACT FROM AUTHOR]

To examine the effect of compressive loading rate on the elastic limit of brittle solids, shockless and shock wave uniaxial strain experiments were conducted on x-cut quartz to a peak stress of 11 GPa. Using a compact pulsed power generator, x-cut quartz crystals were subjected to shockless compression (loading rate of ∼3×105/s). Plate impact experiments were used to subject samples to shock wave compression (loading rate >=4×107/s). Particle velocity histories, measured at propagation distances of 1.5–3.5 mm, demonstrated that the elastic limit of x-cut quartz under shockless compression was 85%–90% higher than the elastic limit under shock wave compression. The substantial increase in the elastic limit with decreasing loading rate is contrary to the expected loading rate dependence of material strength. Mechanistic implications of this finding are discussed. [ABSTRACT FROM AUTHOR]

The second-order elastic constants for cyclotetramethylene tetranitramine (β-HMX) single crystals were determined using the impulsive stimulated thermal scattering (ISTS) method. Despite the low symmetry of these crystals, the complete set of 13 elastic constants were determined accurately from acoustic velocity measurements using samples cut parallel to three different crystal planes. Our acoustic velocities are consistent with the limited sound speed data available from ultrasonic measurements. However, significant differences are observed between the elastic constants determined from our experiments and those obtained previously using Brillouin scattering. Our results demonstrate the usefulness and efficiency of the ISTS method for determining the full set of elastic constants of low-symmetry molecular crystals, including energetic crystals. [ABSTRACT FROM AUTHOR]

We present a method to use real time, synchrotron x-ray diffraction measurements to determine the strength of shocked single crystals following compression and release during uniaxial strain loading. Aluminum and copper single crystals shocked along [111] were examined to peak stresses ranging from 2 to 6 GPa. Synchrotron x rays were used to probe the longitudinal lattice strains near the rear free surface (16 and 5 μm depths for Al and Cu, respectively) of the metal crystals following shock compression and release. The 111 diffraction peaks showed broadening indicating a heterogeneous microstructure in the released state. The diffraction peaks also shifted to lower Bragg angles relative to the ambient Bragg angle; the magnitude of the shift increased with increasing impact stress. The Bragg angle shifts and appropriate averaging procedures were used to determine the macroscopic or continuum strength following compression and release. For both crystals, the strengths upon release increased with increasing impact stress and provide a quantitative measure of the strain hardening that occurs in Al(111) and Cu(111) during the shock and release process. Our results for Al(111) are in reasonable agreement with a previous determination based solely on continuum measurements. Two points are noteworthy about the developments presented here: Synchrotron x rays are needed because they provide the resolution required for analyzing the data in the released state; the method presented here can be extended to the shocked state but will require additional measurements. [ABSTRACT FROM AUTHOR]

Photoluminescence (PL) spectra of bound excitons were measured in uniaxially strained GaP by performing shock-wave experiments at liquid nitrogen temperatures. GaP samples doped with sulfur or nitrogen were compressed up to 3 GPa when subjected to uniaxial strains along the [100] crystallographic orientation. PL lines from shallow sulfur donors redshifted upon compression, tracking the reduction in the indirect band gap. PL lines related to the isoelectronic NN1 pairs, in contrast, exhibited splitting and nonlinear blueshift. An empirical approach was used to model the NN1 behavior. It was shown that the splitting pattern is consistent with the previously proposed symmetry of NN1 defects and nonlinearities resulting from the reduction in the exciton binding energy. At high stresses, the NN1 lines disappeared due to the ionization of bound excitons. [ABSTRACT FROM AUTHOR]

Using a recently developed compact pulsed power generator (CPPG), z-cut quartz samples were subjected to shockless uniaxial strain compression to 7 GPa peak stress. Over this stress range, the behavior of z-cut quartz under shock compression [J. Appl. Phys. 88, 5671 (2000)] is nonlinear elastic and in good agreement with predictions based on the measured values of the second and third order elastic constants. In-material and free surface velocities were measured in the present work and analyzed, using a Lagrangian analysis, to provide a continuous loading curve for z-cut quartz. The wavelet speed-particle velocity (Cu-u, where Cu≡(Δh/Δt)u) results were somewhat sensitive to the CPPG panel design details, as well as the velocity data acquisition and reduction techniques. Improvements to provide optimal data were discussed and used to provide accurate longitudinal stress-density response to 7 GPa (6% density compression). The Cu-u curves, a more stringent measure of the material response to nonlinear compression, were within 0.6% of the values predicted using shock compression measurements. This excellent agreement demonstrates that the shockless compression response of quartz is indistinguishable from the shock response in the nonlinear elastic regime and provides a good foundation for comparing the inelastic response of solids under shockless and shock compression. The present work also demonstrated the use of the CPPG as a laboratory capability for examining the shockless compression of materials. [ABSTRACT FROM AUTHOR]

We describe the use of a third generation synchrotron facility to obtain in situ, real-time, x-ray diffraction measurements in plate impact experiments. Subnanosecond duration x-ray pulses were utilized to record diffraction data from pure and magnesium-doped LiF single crystals shocked along the [111] and [100] orientations. The peak stresses were 3.0 GPa for the [111] oriented LiF and between 3.0 and 5.0 GPa for the [100] oriented LiF. For these stresses, shock compression along [111] results in elastic deformation and shock compression along [100] results in elastic-plastic deformation. Because of the quality of the synchrotron x-ray pulses, both shifting and broadening of the diffraction data were obtained simultaneously. As expected, shifts for elastic compression and elastic-plastic compression in shocked LiF were consistent with uniaxial and isotropic lattice compression, respectively. More importantly, diffraction patterns from crystals shocked along [100] exhibited substantial broadening due to elastic-plastic deformation. The broadening indicates that the shocked LiF(100) crystals developed substructure with a characteristic size for coherently diffracting domains (0.1–10 μm) and a distribution of (100) microlattice-plane rotations (∼1° wide). In contrast to the LiF(100) results, broadening of the diffraction pattern did not occur for elastically deformed LiF(111). Another important finding was that the amount of lattice disorder for shocked LiF(100) depends on the loading history; the broadening was larger for the magnesium-doped LiF(100) (large elastic precursor) than for ultrapure LiF(100) (small elastic precursor) shocked to the same peak stress. The data are simulated by calculating the diffraction pattern from LiF(100) with a model microstructure consisting of coherently diffracting domains. The lattice orientation and longitudinal strain is assumed uniform within domains, but they vary from domain to domain with Gaussian distributions. Simulations using such a model are in good agreement with the measured diffraction patterns. The principal finding from the present work is that synchrotron x-rays can provide real-time data regarding microstructure changes accompanying shock-induced deformation and structural changes. [ABSTRACT FROM AUTHOR]

The relative orientations between the lattices of the low pressure (B1) and high pressure (B2) phases of shock compressed KCl single crystals were examined using plate impact loading along the [111] and the [110] directions. The B2-phase lattice planes, perpendicular to the loading direction, were determined from transient x-ray diffraction measurements. Two closely spaced diffraction peaks were observed for the [111] loading direction. The lower Bragg angle peak is consistent with a 200 peak of a cubic B2-phase unit cell giving the orientation relation [111]B1 is parallel to [100]B2. The higher Bragg angle peak is not consistent with any peak from either a cubic B1 or a cubic B2 unit cell; the origin of this peak is unknown. Other experiments found no orientation relations; for the [111] loading direction, [111]B1 is not parallel to [211]B2 and for the [110] loading direction, [110]B1 is not parallel to [100]B2. The orientation relation determined for the [111] loading in this work is incompatible with a previously determined orientation relation obtained for the [100] loading [T. d’Almeida and Y. M. Gupta, Phys. Rev. Lett. 85, 330 (2000)]. This finding suggests that the transformation pathway between the B1 and B2 lattices in KCl crystals depends on the shock compression direction for the B1 phase. The results are discussed in terms of the compatibility between the macroscopic uniaxial strain imposed by shock wave loading and the microscopic rearrangement of atoms leading to the observed orientation relations. [ABSTRACT FROM AUTHOR]

To gain insight into the instability and trajectory change in projectiles penetrating dry sand at high velocities, two dimensional plane strain mesoscale simulations were carried out using representative models of a particulate system and of a small projectile. A program, ISP-SAND, was developed and used to generate the representative particulate system with mean grain sizes of 60 and 120 μm as well as ±30% uniform size distribution from the mean. Target porosities ranged from 30% to 40%. The penetration of ogive nose steel projectiles with caliber radius head of 3.5 and length-to-diameter (l/d) ratio of 3.85 was simulated using the updated Lagrangian explicit parallel finite element code ISP-TROTP. Deformation of the projectile and individual sand grains was analyzed using a nonlinear elastic-inelastic model for these materials. Grain-grain and grain-projectile interactions were analyzed using a contact algorithm with and without friction. Projectile instability was quantified and compared using the lateral displacement of the center of mass, lateral force acting on the projectile, and its rotational momentum about the center of mass. The main source of projectile instability and the ensuing trajectory change in the penetration simulations was found to be the inhomogeneous loading of the projectile due to the heterogeneities and randomness inherent in a particulate media like sand. The granularity of the media has not been considered explicitly in previous work. Projectile instability increased with impact velocity, as expected. However, it also increased for the case of elastic impactor that preserved the nose shape, with an increase in grain size, and for uniform grain sizes. Moreover, friction, inherently present in geologic materials, was found to be a major contributor to instability. Conclusions derived from one projectile depth simulations were confirmed by two deeper penetration simulations considering up to three full lengths of penetration (requiring a larger sand target). The deep penetration simulation predicted considerable instability with a trajectory change of approximately 45° when friction was considered in the dry sand medium. An overall conclusion of this work is that projectile penetration studies in geologic materials need to explicitly consider the heterogeneous or particulate nature of these materials. [ABSTRACT FROM AUTHOR]

Impulsive stimulated thermal scattering (ISTS) was used to determine the complete set of second-order elastic constants for pentaerythritol tetranitrate (PETN) and cyclotrimethylene trinitramine (RDX) single crystals. Despite the weak scattering efficiency of these materials, excellent signal quality was obtained by using an optical heterodyne detection approach. The elastic constants for PETN agree well with previous values obtained from ultrasonic velocity measurements. The elastic constants for RDX are consistent with previous values obtained from ultrasonic velocity measurements and from resonant ultrasound spectroscopy, but show significant differences with values obtained from Brillouin scattering data. The present results demonstrate that the ISTS method, with optical heterodyne detection, provides a useful and accurate approach for determining the elastic constants of energetic crystals. [ABSTRACT FROM AUTHOR]

Time-resolved x-ray diffraction measurements were used to examine the lattice deformation during elastic-plastic deformation in Mg-doped (approximately 100 ppm) LiF single crystals shocked along [100]. The magnesium impurities significantly increase the elastic limit of the LiF crystals, as compared to the low values observed for ultrapure LiF crystals, leading to a large amplitude elastic wave and significant stress relaxation behind the elastic wave. The objective of the current work was to examine lattice deformation throughout this wave profile using time-resolved, x-ray diffraction methods (2 ns resolution) for plate impact experiments to gain insight into time-dependent, elastic-plastic deformation at the microscopic level. The diffraction data were analyzed using an x-ray model coupled to an existing wave propagation code that incorporated dislocation mechanisms for elastic-plastic deformation including stress relaxation. All experimental results revealed a uniaxial lattice compression at the elastic wave front followed by a rapid transition toward isotropic unit cell compression during stress relaxation. Furthermore, comparison between the experimental data and the calculated streak records indicated that the lattice transition proceeds at a faster rate than predicted by the model. Further implications of these results are discussed. [ABSTRACT FROM AUTHOR]

Plate impact experiments were conducted to produce two and three step shock wave loadings in [100] ultrapure, lithium fluoride (LiF) crystals to examine the role of loading history on optical window response in laser interferometry measurements. Peak compressive stresses ranged between 5.0 and 17.5 GPa, and the window response was characterized by measuring the difference between the apparent and actual velocities of reflecting surfaces by using a velocity interferometer. In some experimental configurations, this velocity correction was obtained independently from the projectile velocity. Our results show that the velocity correction in [100] lithium fluoride windows can be described in all cases by a single linear relation, Δu=(0.2739±0.0016)u. Because this correction is independent of the loading history, it is applicable to arbitrary loading, which includes ramp-wave or shockless compression. By using the velocity correction and the measured particle and shock velocities, we have also determined the density dependence of the refractive index for [100] lithium fluoride at 532 nm to be n=(1.2769±0.0024)+(0.0443±0.000 82)ρ. [ABSTRACT FROM AUTHOR]

Plate-impact experiments were performed to examine the influence of grain size on the dynamic tensile (or spall) behavior of shocked polycrystalline aluminum. Ultrapure and commercially pure 1050 aluminum plates were cold rolled to 80% strain and heat treated under predetermined conditions to produce recrystallized samples with average grain sizes varying between 49 and 453 μm. Well-characterized samples were subjected to plane wave loading at peak compressive stresses of 4 and 21 GPa, and free-surface velocity profiles were obtained using velocity interferometry. At 4 GPa, the observed pullback velocity, a characteristic feature of the spall response, was similar for different grain sizes of 1050 and ultrapure Al, suggesting that the preferential failure mode is intragranular. At 21 GPa, the spall response (i.e., the pullback velocity and the signal structure) depended on the alloy content; the pullback velocity of ultrapure Al increased with increase in grain size, while it remained constant for 1050 Al. In addition, the structure of pullback signals showed a well-defined change in slope for different grain size samples in ultrapure Al, while no such feature was observed for 1050 Al. For the grain sizes examined, the σHEL was nearly independent of the grain size for 1050 Al and beyond a certain grain size for ultrapure Al. [ABSTRACT FROM AUTHOR]

Dynamic tensile response and fracture of a Zr-based bulk amorphous alloy (BAA) were examined by subjecting samples to uniaxial tensile strain in plate-impact experiments. Following elastic compressive loading to peak stresses ranging between 3.9 and 6.1 GPa, wave interactions produced tensile loading resulting in spallation in the BAA samples. Rear-surface velocity histories, obtained using laser interferometry, provided a real-time measure of the tensile response including spallation. The initial tensile loading was elastic (loading rates approximately 8×105 s-1) and the data were analyzed to obtain a nonlinear, tensile stress-strain relation. Tensile fracture or spall, observed in all experiments, was initiated at a tensile stress of 3.8±0.3 GPa; this initiation value was independent of the impact stress and is significantly higher than that observed for crystalline metals. A phenomenological tensile fracture model was incorporated into one-dimensional wave propagation simulations to gain insight into the BAA tensile response and damage. Good agreement was obtained between the numerical simulations and the experimental measurements. With increasing impact stress, the BAA samples exhibited a change from ductile to brittle tensile response. [ABSTRACT FROM AUTHOR]

Two-dimensional (2D) mesoscale simulations of planar shock compression, followed by either reloading or unloading, are presented to examine and understand the quasielastic response observed experimentally in shocked polycrystalline aluminum. The simulations included a realistic representation of the grain ensembles in polycrystalline samples to identify heterogeneous deformation features deemed important to model the continuum measurements. The simulations were carried out using a 2D Lagrangian finite element code (ISP-TROTP) that incorporated elastic-plastic deformation in grain interiors and utilized a contact/cohesive methodology to analyze the response of finite strength grain boundaries. Local heterogeneous response due to mesoscale features was quantified by calculating appropriate material variables along in situ Lagrangian tracer lines and comparing the temporal variation of their mean values with results from 2D continuum simulations. A series of initial calculations ruled out effects due to finite element size and width of the representative volume element used in our simulations. Simulations using a variety of heterogeneities were performed to identify the heterogeneities that were most important for simulating the experimentally observed quasielastic response. These were inclusions, hardened grain boundaries, and microporosity. Mesoscale simulations incorporating these effects demonstrate that the shock-deformed state in polycrystalline aluminum is strongly heterogeneous with considerable variations in lateral stresses. The simulated velocity profiles for a representative reloading and unloading experimental configuration were found to agree well with experimental data, and suggest that hardened grain boundaries are the most likely source of mesoscale heterogeneities in shocked 6061-T6 aluminum. The calculated shear strength and shear stresses were also found to be in good agreement with the reported experimental values. [ABSTRACT FROM AUTHOR]

Plane shock wave experiments were performed on bulk amorphous alloy (BAA) samples having a nominal composition of Zr56.7Cu15.3Ni12.5Nb5.0Al10.0Y0.5. Peak compressive stresses ranged from 4 to 16.4 GPa. Piezoelectric pins and a velocity interferometer were used to measure elastic shock speeds and particle velocity histories, respectively. The elastic Hugoniot curve was determined and the Hugoniot elastic limit (HEL) was measured to be approximately 7.0 GPa, a value significantly higher than expected from quasistatic uniaxial stress data. Impact loading beyond the HEL results in a distinct two wave structure due to elastic-plastic deformation. Our data also show clear evidence for strength loss under shock loading above the HEL. Unlike most metals, the present data show distinct elastic response during unloading. We present a continuum model to describe the deformation response of the BAA to shock loading. Simulations using this time-dependent, strain-softening strength model were able to successfully match the measured wave profiles. The calculated profiles indicate that the characteristic time for stress relaxation is very small (few nanoseconds) and confirm that a significant loss of strength occurs as the plastic wave propagates through the material. When the material is shocked to a peak stress of 16.4 GPa, our model indicates that the yield stress in the shocked state is reduced by at least 0.7 GPa from its value of 2.7 GPa at the HEL. [ABSTRACT FROM AUTHOR]

X-ray diffraction measurements, utilizing multiple and single diffraction methods, were used to examine lattice compression of magnesium doped (approximately 100 ppm) LiF single crystals shocked along the [100] direction. Unlike ultrapure LiF crystals, examined in previous x-ray diffraction studies, magnesium doped crystals display large elastic wave amplitudes under shock wave compression. Analysis of multiple diffraction data from the (200) and (202) planes and single diffraction data from the (200) planes showed that the crystal lattice for doped crystals was compressed isotropically in the peak state, similar to that observed for ultrapure crystals. This agreement demonstrates that the large elastic wave amplitude and subsequent stress relaxation observed in wave propagation measurements for the doped LiF crystals are a transient phenomenon and do not appear to affect the lattice compression in the final state. Implications of this finding are discussed. [ABSTRACT FROM AUTHOR]

A nonlinear anisotropic continuum framework for describing the thermoelastic-plastic response of single crystals shocked along arbitrary orientations has been developed. Our modeling approach incorporates nonlinear elasticity, crystal plasticity, and thermodynamic consistency within an incremental tensor formulation. Crystal plasticity was incorporated by considering dislocation motion along specified slip planes. The theoretical developments presented here are sufficiently general to also accommodate other types of inelastic deformation mechanisms. As representative applications of the theoretical developments, numerical simulations of shock wave propagation in lithium fluoride (LiF) and copper single crystals are presented and compared to wave profile data for several crystal orientations. Simulations of shock wave propagation along low-symmetry directions, where data are not available, are also presented to examine the propagation of quasilongitudinal and quasishear waves in crystals undergoing elastic-plastic deformation. Temperature calculations for the shocked single crystals are discussed. [ABSTRACT FROM AUTHOR]

Using real time optical transmission and imaging measurements in multiple shock wave compression experiments, water was shown to solidify on nanosecond time scales [D. H. Dolan and Y. M. Gupta, J. Chem. Phys. 121, 9050 (2004)]. Continuum modeling and wave profile measurements, presented here, provide a complementary approach to examine the freezing of shocked water. The water model consisted of thermodynamically consistent descriptions of liquid and solid (ice VII) water, relationships for phase coexistence, and a time-dependent transition description to simulate freezing dynamics. Continuum calculations using the water model demonstrate that, unlike single shock compression, multiple shock compression results in pressure-temperature conditions where the ice VIII phase is thermodynamically favored over the liquid phase. Wave profile measurements, using laser interferometry, were obtained with quartz and sapphire windows at a peak pressure of 5 GPa. For water confined between sapphire windows, numerical simulations corresponding to a purely liquid response are in excellent agreement with the measured wave profile. For water confined between quartz windows (to provide a nucleating surface), wave profile measurements demonstrate a pure liquid response for an incubation time of approximately 100 ns followed by a time-dependent transformation. Analysis of the wave profiles after the onset of transformation suggests that water changes from a metastable liquid to a denser phase, consistent with the formation of a high-pressure ice phase. Continuum analyses and simulations underscore the need for multiple time scales to model the freezing transition. Findings from the present continuum work are extremely consistent with optical results reported previously. These studies constitute the first comprehensive investigation reported for freezing of a liquid at very short time scales. [ABSTRACT FROM AUTHOR]

Plane shock wave experiments were performed to examine optical transmission in sapphire single crystals (c cut, a cut, and r cut) compressed to longitudinal stresses ranging between 119 and 260 kbar. Peak stress and particle velocity values in our experiments were obtained by compiling and analyzing published continuum data on shocked sapphire crystals. Time-resolved measurements, with nanosecond resolution, showed time-, stress-, and orientation-dependent changes in optical transmission beyond the Hugoniot elastic limit. Over the 300–680-nm range examined in our work, no wavelength dependence was observed. Loss of optical transmission in the stress range examined is due to inelastic deformation in shocked sapphire crystals. The present data reveal that inelastic deformation mechanisms are different in r-cut sapphire compared to a-cut and c-cut sapphire, and may be different for all three orientations examined. Although quantitative analysis of the time-dependent optical transmission data is not possible at present, optical transmission results have provided insight into inelastic deformation mechanisms in shocked sapphire. Present results are expected to be valuable for use of sapphire windows in shock wave experiments. [ABSTRACT FROM AUTHOR]

Water samples were subjected to multiple shock wave compressions, generating peak pressures of 1–5 GPa on nanosecond time scales. This loading process approximates isentropic compression and leads to temperatures where the ice VII phase is more stable than the liquid phase above 2 GPa. Time resolved optical transmission and imaging measurements were performed to determine the solidification rate under such conditions. Freezing occurred faster at higher pressures as water was compressed further into the ice VII phase, in agreement with classical micleation theory. Water consistently froze when in contact with a silica window, whereas no solidification occurred in the presence of sapphire windows. The transition was determined to be a surface initiated process—freezing began via heterogeneous nucleation at the water/window interface and propagated over thicknesses greater than 0.01 mm. The first optical images of freezing on nanosecond time scales were obtained. These images demonstrate heterogeneous nucleation and irregular solid growth over 0.01–0.10 mm lateral length scales and are consistent with latent heat emission during the transformation. The combination of optical transmission and imaging measurements presented here provide the first consistent evidence for freezing on short time scales. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Plate impact experiments were carried out to understand inelastic deformation in soda-lime glass shocked between 3 and 10.8 GPa. In-material, wave profile measurements were obtained using longitudinal and lateral stress gauges (4.6–10.8 GPa), and electromagnetic particle velocity gauges (2.9–6 GPa) at comparable sample thicknesses. The 4.6 and 6 GPa experiments revealed time-dependent material inelastic response along with time-dependent loss of material strength. Because of the unsteady, two wave structure observed in the longitudinal wave profiles in conjunction with the time-dependent changes in the lateral stress data, previous interpretations of the shocked soda-lime glass response in terms of a propagating failure wave are not valid. At higher peak stresses (∼10 GPa), the experimental results do not display time-dependent strength loss. The shock wave response of soda-lime glass over the 4–10 GPa range is complex, and material strength and inelastic deformation features depend significantly on the peak stress. Using the experimental results, a phenomenological continuum model incorporating the various material phenomena was developed. Wave profile simulations using the continuum model show reasonable overall agreement with the experimental profiles at different stress levels. Because of the approximate nature of the continuum model, all of the experimental details were not reproduced in the wave propagation simulations. It is likely that around and above 10 GPa, other material phenomena not included in our model may need to be considered. [ABSTRACT FROM AUTHOR]

An anisotropic continuum framework for describing the nonlinear thermoelastic response of shocked single crystals has been developed. Using this framework, the propagation of large amplitude stress waves along arbitrary directions in crystals of any symmetry can be examined. We developed an incremental approach, where the reference state for the dynamical variables and the material properties is updated throughout the calculation. Results from our incremental approach are in excellent agreement with the results from a finite strain formulation. Using a finite-difference wave propagation code, we performed numerical simulations of large amplitude elastic wave propagation in single crystals. Results of impact loading simulations for quartz and sapphire single crystals are presented. The framework developed was also useful for examining the propagation of pure mode nonlinear waves for various crystal symmetries. Our calculations showed that pure longitudinal waves resulted from impact loading along any rotational symmetry axis for all crystal symmetry classes. Differences between pure mode wave propagation for linear and nonlinear elastic deformation are discussed. [ABSTRACT FROM AUTHOR]

Experimental methods to permit continuous, time-resolved x-ray diffraction measurements in plate impact experiments were developed and used to examine lattice deformation in shock compressed LiF single crystals. Using an x-ray streak camera diffraction data with 2-4 ns resolution were obtained from crystals subjected to both shock and ramp wave loading along the [111] direction. Because of the penetration depth of x rays into the sample, interpretation of the ramp wave loading data required an analytic model to simulate the results. The penetration depth used in the model was determined experimentally from the time-resolved shock wave loading data. Good agreement between the simulations and experimental data was found for both loading conditions, suggesting that the analytic model has broad applicability. [ABSTRACT FROM AUTHOR]

The ordinary refractive index of sapphire, at 532 nm, was measured in single crystals subjected to elastic, uniaxial tensile (and compressive) strain along the c axis in plate impact experiments. The refractive index under both tension and compression was determined from the difference between the uncorrected particle velocities from velocity interferometer measurements and the known particle velocities in symmetric impact experiments. Results to a peak stress of 100 kbar in tension and compression show that the refractive index has an overall monotonic, nonlinear dependence on density that is asymmetric about the ambient density. In compression, the refractive index decreases by an extremely small amount; in contrast, the change is relatively larger in tension. These refractive index results at large tensile stresses suggest that sapphire polarizability is quite different under compression and tension. Compression measurements by themselves can be approximated well by a linear refractive index-density relation, resulting in a window correction (at 532 nm) that is a constant fraction of the true particle velocity up to at least 115 kbar longitudinal stress. The present data also provide high-precision shock velocity results in compression and demonstrate the appropriateness of using second and third order elastic constants for calculating the elastic response of sapphire under uniaxial tensile strain loading. [ABSTRACT FROM AUTHOR]

Initial stage kinetics of the cadmium sulfide (CdS) phase transition was investigated using picosecond time-resolved electronic spectroscopy in plate-impact shock wave experiments. Real-time changes in the electronic spectra were observed, with 100 ps time resolution, in CdS single crystals shocked along a and c axes to stresses ranging between 35 and 90 kbar, which is above the phase-transition threshold stress of approximately 30 kbar. Significant difference in the transformation kinetics was observed for the two crystal orientations. At sufficiently high instantaneous stress, above approximately 60 to 70 kbar for a axis and 50 kbar for c axis, transformation to a metastable state appears to reach a constant state within the 100 ps time resolution. At lower instantaneous stresses, an incubation period on the order of several nanoseconds is observed prior to the onset of electronic changes that mark the onset of the structural change. The subsequent increase in absorbance was quite rapid, with a constant state being reached within the first few nanoseconds after the onset of the structural changes. These results suggest that the nucleation process determines the transformation rate. This insight into transformation kinetics, along with the transformation mechanism obtained from the high-stress experiments, was used to develop a phenomenological model, incorporating ideas of nucleation and growth in martensitic transformations, to simulate the time-dependent extinction of light observed in our experiments. The calculational results incorporating both extinction due to light absorption by the daughter phase volumes and scattering of light by small volumes of the daughter phase were in good agreement with experimental observations. Finally, the orientational differences observed in the transformation kinetics were interpreted in terms of the differences in the elastic-plastic response for the two orientations. [ABSTRACT FROM AUTHOR]

A consistent thermomechanical material model was developed for unreacted ammonium perchlorate (AP) single crystals for shock compression normal to the (210) and (001) crystal planes. Building on previous work, the mechanical response for both orientations was described using a single isotropic elastic-plastic model and an overstress model to describe rate-dependent yielding. Velocity interferometer measurements to 12 GPa were performed to extend the AP Hugoniot curve to higher stresses. The specific heat c[sub v], the coefficient of thermal pressure (∂P/∂T)[sub V], and the isothermal bulk modulus B[sub T] were determined from Hugoniot and isothermal compression curves, along with available data at atmospheric pressure. Time-resolved Raman spectroscopy experiments were carried out under stepwise loading to obtain temperatures in the shocked state. Calculated temperatures using our material model are in good agreement with the temperatures obtained from our experiments, thus providing validation for our modeling approach. © 2002 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Sapphire crystals were shocked to 190 kbar along the a axis to characterize their use as optical windows, for velocity interferometry measurements, up to their Hugoniot elastic limit. When partially polarized light is incident on the samples, birefringence in the material is manifested as a beat frequency in the probe light that is returned from the specimens. Proper procedures for interpreting the velocity interferometry data for various polarization conditions were developed. The refractive indices at 514.5 nm wavelength decreased linearly with the density. The data were analyzed to yield three photoelastic coefficients: p[sub 12], p[sub 31], and p[sub 41]. Calibration is developed for any polarization state of the probe light. Particle velocity wave forms are consistent with elastic behavior up to 170 kbar shock stress, and evidence of deviation from elastic behavior is present at 190 kbar impact stress. High precision shock velocity measurements are reported to 170 kbar stress along the a axis. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Compression and shear wave experiments using plate impact loading were conducted on polycrystalline silicon carbide (SiC). The material was subjected to combined compression-shear loading to peak compressive stresses ranging from 3 to 18 GPa. The compression (shock) wave profiles and the propagation velocities of shear and longitudinal release waves in the shocked SiC were measured using in situ, electromagnetic velocity gauges. The Hugoniot elastic limit (HEL) of the material was found to be 11.5±0.4 GPa. The measured wave velocities were used to determine the elastic moduli of the material as functions of density compression in the shocked state. The data were further analyzed to obtain the mean stress response of the SiC under uniaxial-strain compression. The longitudinal and mean stress results completely characterize the material stress state. Numerical simulations were also carried out to verify the peak-state data analysis. Our results show that the Poisson's ratio of the material increases with elastic shock compression from an ambient value of 0.161 to 0.192 at the HEL. Above the elastic limit, the maximum shear stress supported by the material increases from 4.5 to 6.4 GPa at a peak stress of 18 GPa. This finding verifies independently the results from lateral manganin gauge measurements in the same material [R. Feng et al., J. Appl. Phys. 83, 79 (1998)]. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Presents a study that examined the loading and unloading response of manganin gauges oriented parallel and perpendicular to the shock front and embedded in an aluminum-oxide matrix. Details of the application of an analytic model for piezoresistance response coupled with electromechanical constants in calculating the gauge response; Analysis of residual resistance measurements; Results and implications.

Presents a study which determined the resistance change at peak stress and the residual resistance change of ytterbium foil gauges embedded at different depths in fused silica matrix. Material characterization; Experimentation dynamics; Profiles of resistance change versus time.

Presents a study that described a model that incorporated data on strain hardening in piezoresistance analysis. Features of the model; Analysis of the dynamic and quasi-static experiments; Application of the model in calculating the response of ytterbium foils in a polymethylmethacrylate matrix in both shock wave and quasi-static experiments.

Presents information on a study which described a method for the measurement of pressure-time profile of a carbon disulfide liquid in a reverberation or multiple-shock experiment. Description of the experimental method; Conclusions.

Presents a study which investigated the resistance change measurements in ytterbium foils, encapsulated in a polymethylmethacrylate matrix and subjected to impact loading and quasi-static triaxial loading. Factors that affect residual resistance; Result of an analysis of resistance measurements; Sensitivity of ytterbium; Difficulty in ytterbium response analysis.

Time resolved, spectroscopic reflection measurements (300–500 nm) have been used to examine the electronic and chemical changes in liquid carbon disulfide shocked to peak pressures as high as 110 kbar. Multiple-shock loading and unloading and double-shock experiments were performed to examine the influence of temperature, and to compare the present data with previous absorption and continuum measurements. The reflectance increases markedly with pressure in multiple-shock loading experiments. At 300 nm, the reflectance increases from less than 0.33% at ambient conditions to 10% at 105 kbar. However, the reflectance changes exhibit wavelength dependence, being smaller for longer wavelengths, and are reversible upon pressure unloading. A phenomenological model was developed to calculate the complex refractive index for carbon disulfide. This model in conjunction with Fresnel’s reflection equations can be used to analyze the multiple-shock reflection and absorption data in a consistent manner. The experimental results can be understood in terms of the growth of absorption bands due to increasing overlap of the π electron wave functions of neighboring molecules due to compression; this overlap is likely a precursor to associative chemical reactions.The complete reversal in reflectance at pressures above 90 kbar is in contrast to the absorption data and arises because the present reflection measurements do not sample the bulk material, but, instead, are collected from a very thin, cooled, unreacted layer of carbon disulfide. The double-shock experiments show no evidence of a chemical reaction below 90 kbar and are in agreement with multiple-shock data. At higher pressures, the double-shock experiments show evidence of chemical reactions and display a complicated reflectance history that depends markedly on the wavelength. The wavelength dependence and associated complexities in the double-shock experiments are consequences of pressure dependent... [ABSTRACT FROM AUTHOR]

The effect of initial phase on shock-induced spectral changes in carbon disulfide/hexane has been examined by monitoring the edge shift of the V-band. Experiments were carried out to a peak pressure of 10 GPa for three different concentrations of carbon disulfide. Shifts of the absorption band in solid mixtures differ markedly from those in liquid mixtures at high pressures. The rate of edge shift with pressure in solid mixtures becomes independent of the carbon disulfide concentration and approaches the rate of shift in pure carbon disulfide. Similar results are not obtained for liquid mixtures. Temperature results cannot explain the observed differences. The experimental data suggest the occurrence of phase separation in the solid mixtures and two possible mechanisms for phase separation are indicated. The present results show the importance of the initial phase in understanding the spectral differences observed for these mixtures under shock and static loading. [ABSTRACT FROM AUTHOR]

Cadmium sulfide crystals were shocked along the crystal c axis to peak stresses ranging between 18 and 75 kbar. Stress-time profiles were measured both at the impact surface and after transmission through 1 to 2-mm-thick samples. Detailed analysis of the present data in combination with published static results makes a persuasive case for the completion of the wurtzite to rocksalt phase change in less than 0.2 μs under shock loading. The main findings are: the transition stress is measured to be 32.5 ± 1 kbar; transformation to the final state is a two step process with the first step being too rapid (less than 10 ns) to be observed in our experiments and the second step occurring in 0.1 to 0.2 μs; the transition occurs directly from the elastic state prior to any plastic deformation. The calculated mean stress for the transition is 22.9 kbar in good agreement with the 23 kbar pressure reported in static high pressure studies; the presence of large shear stress has no effect on the transition pressure. Our results suggest that the onset of the phase transition results in plastic deformation and, subsequently, the phase transition and plasticity are coupled under shock loading. [ABSTRACT FROM AUTHOR]

We report on the use of time-resolved Raman scattering data to determine temperatures in liquid carbon tetrachloride shocked by step-wise loading to a peak pressure of 12 GPa. Changes in our previously reported experimental configuration have resulted in a significant improvement in the signal-to-noise ratio in the data and permitted us to analyze the stokes and antistokes intensities for more than one vibrational mode (314 and 460 cm[sup -1] modes). Hence, better precision can be obtained for shock temperatures on the nanosecond time scales. Temperatures are reported in the 500–1000 K range with an experimental precision of approximately 8%–10%. Our data show that the equation of state for carbon tetrachloride reported in the literature provides temperature values that are significantly lower than the measured values. Various aspects of using Raman scattering data for determination of shock temperatures are discussed. © 1997 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Features a study that developed an experimental method to use time resolved Raman spectroscopy as a microscopic probe of tensile deformation in shocked crystals. Production of tension in the sample interior by the interaction of rarefaction waves generated in plate impact, uniaxial strain experiments; Use of the optical fibers to transmit visible light from a pulsed laser to the sample; Measurement of the strain-induced shift of a line of α-quartz.

Focuses on a study which analyzed the wavelength shift of R lines in ruby samples subjected to tensile stresses. Uses of the wavelength shift of the ruby luminescence R lines; Information on the development of a method to permit an examination of the R-line shifts under tensile deformations; Examination of shock induced tensile states.

Describes a study on an experimental method of obtaining time resolved Raman spectra in shock wave experiments. Compression mechanisms in quartz; Correlation of spectral and structural changes; Nonlinear elastic relations for uniaxial strain compression of quartz.

Presents information on a study which described an experimental method for measuring the time-resolved fluorescence spectrum of a dye in a liquid subjected to shock wave, uniaxial strain compression. Description of the method; Results and discussion; Conclusions.

Addresses the analysis of Lagrangian gauge measurements of simple and nonsimple plane waves. Importance of the in-material wave measurements; Equations governing the experiment; Practical considerations of embedded guage measurements.