Two-wave Structure Research Articles

Shock-Induced Inelastic Deformation in Oriented Crystalline Pentaerythritol Tetranitrate

Molecular dynamics simulations were used to study the mechanisms of shock-induced inelastic deformation in oriented single crystals of the energetic material pentaerythritol tetranitrate (PETN). Supported planar shock waves with Rankine–Hugoniot shock pressures PR–H ∼ 9 GPa were propagated along two different crystal directions: one that is sensitive to initiation ([001]) and another that is relatively insensitive to initiation ([100]). Qualitatively, it was observed that for the sensitive orientation only elastic compression occurred, leading to the propagation of a single wave through the material, whereas for the insensitive direction elastic compression at and immediately behind the shock front was followed by inelastic deformation, leading to a two-wave structure in which the sharp elastic front moves through the crystal at a higher speed than the broader plastic wave. The detailed responses were characterized by calculating several structural and thermal properties including: relative center-of-mass...

Phase states of dynamically compressed cerium

This paper presents a multiphase equation of state for cerium, which includes the $\ensuremath{\gamma}$, $\ensuremath{\alpha}$, $\ensuremath{\varepsilon}$, and liquid phases. The $\ensuremath{\alpha}$ and $\ensuremath{\gamma}$ phases are described with the Aptekar-Ponyatovsky model for pseudobinary solutions, while the $\ensuremath{\varepsilon}$ and liquid phases are treated as pure phases. The Hugoniot and release isentropes are calculated for the solid $\ensuremath{\gamma}$, $\ensuremath{\alpha}$, liquid, and mixed phases. Based on the model developed, the Hugoniot does not cross the line of the $\ensuremath{\alpha}$-$\ensuremath{\varepsilon}$ transition and melting occurs directly from the $\ensuremath{\alpha}$ phase. The equation of state developed shows reasonable agreement with the static measurements, the experimentally determined phase diagram, and the shock experimental data. Cerium compresses isentropically through the $\ensuremath{\gamma}$-$\ensuremath{\alpha}$ transition as a result of cerium's abnormal compressibility in the region of the $\ensuremath{\gamma}$-$\ensuremath{\alpha}$ transition. The inclusion of the Aptekar-Ponyatovsky model assists in providing a way to handle both the abnormal compressibility and the anomalous melt boundary simultaneously. Experimentally under dynamic loading conditions, a three-wave structure is observed at stresses above the phase transition: an elastic wave, a phase transition wave (which appears as an isentropic compression wave), followed by a shock wave. For our model development we consider only the hydrostatic response and thus a two-wave structure would be anticipated. No phase precursor would be observed for melting. Sound velocity behind the shock front dramatically decreases in the region of the $\ensuremath{\gamma}$-$\ensuremath{\alpha}$ transition and smoothly varies through the region of melting.

Shock compression and spallation of palladium bicrystals with a Σ5 grain boundary

We investigate an elementary process of shock response of grain boundaries (GBs) using molecular dynamics simulations: shock compression and spallation in Pd bicrystals with a symmetric Σ5/(210)/〈100〉 GB. The loading direction is normal to GB. An elastic shock may induce the elastic-plastic or two-wave structure at the GB. The GB serves as a wave scattering center for the transverse motion perpendicular to the GB rotation axis and the shock direction: it induces a phase shift of 180∘, an increase in the amplitude of the particle velocity, GB sliding and grain orientation distortion. The GB is the preferred nucleation site both for dislocations and voids. Our results suggest that both microstructure and the loading geometry contribute to dynamic response of a solid.

Pressure-dependent Hugoniot elastic limit of Gd3Ga5O12 single crystals

Single-crystal Gd3Ga5O12 has been studied at high dynamic pressures generated with plate impacts. Shock-wave profiles and Hugoniot points were measured with a picosecond time-resolved Doppler Pin System. For final shock pressures in the range 8.52-113 GPa, a two-wave structure is observed below 59.3 GPa, a three-wave structure at ∼88.5 GPa, and a single shock wave is observed at ∼113 GPa. Our data show that the Hugoniot elastic limit (HEL) of single-crystal Gd3Ga5O12 is strongly dependent on final shock pressure. The HEL increases from 7.65 to 24.2 GPa as final pressure increases from 8.52 to 88.5 GPa. A shock-induced phase transformation is observed at a pressure of ∼75.9 GPa, which is a little higher than the value reported previously (Mashimo et al., Phys. Rev. Lett. 96, 105504, 2006), but is consistent with previous DAC work (Mao et al., Phys. Rev. B 83, 054114, 2011).

Shock compression response of a Zr-based bulk metallic glass up to 110 GPa

Shock wave compression experiments were conducted on a Zr-based bulk metallic glass (BMG, Zr51Ti5Ni10Cu25Al9 in atomic percent) up to 110 GPa. Time-resolved free-surface velocity profiles were measured in a shock stress range from 18 to 28 GPa with velocity interferometer techniques. The shock Hugoniot data in a shock stress range from 53 to 110 GPa were obtained by using electric pin techniques. The time-resolved wave profiles showed a distinct two-wave structure consisting of an elastic precursor followed by a plastic wave. Based on the obtained wave profiles, the Hugoniot elastic limits were determined to be 6.9 to 9.6 GPa. The shock wave velocity (Ds) vs. particle velocity (up) Hugoniot data in a shock stress range from 18 to 110 GPa were linearly fitted by Ds=(4.241±0.035)+(1.015±0.024)up. No evidence of phase transition was found in the performed shock experiments of the Zr-based BMG.

An equation of state of a carbon-fibre epoxy composite under shock loading

An anisotropic equation of state (EOS) is proposed for the accurate extrapolation of high-pressure shock Hugoniot (anisotropic and isotropic) states to other thermodynamic (anisotropic and isotropic) states for a shocked carbon-fibre epoxy composite (CFC) of any symmetry. The proposed EOS, using a generalised decomposition of a stress tensor [A.A. Lukyanov, Int. J. Plasticity 24, 140 (2008)], represents a mathematical and physical generalisation of the Mie-Grüneisen EOS for isotropic material and reduces to this equation in the limit of isotropy. Although a linear relation between the generalised anisotropic bulk shock velocity Us A and particle velocity up was adequate in the through-thickness orientation, damage softening process produces discontinuities both in value and slope in the Us A-up relation. Therefore, the two-wave structure (non-linear anisotropic and isotropic elastic waves) that accompanies damage softening process was proposed for describing CFC behaviour under shock loading. The linear relationship Us A-up over the range of measurements corresponding to non-linear anisotropic elastic wave shows a value of c0 A (the intercept of the Us A-up curve) that is in the range between first and second generalised anisotropic bulk speed of sound [A.A. Lukyanov, Eur. Phys. J. B 64, 159 (2008)]. An analytical calculation showed that Hugoniot Stress Levels (HSLs) in different directions for a CFC composite subject to the two-wave structure (non-linear anisotropic elastic and isotropic elastic waves) agree with experimental measurements at low and at high shock intensities. The results are presented, discussed and future studies are outlined.

Strength effects in diamond under shock compression from 0.1 to 1 TPa

A two-wave shock structure---elastic precursor followed by an inelastic compression wave---is observed in single crystal and polycrystalline diamond laser shock compressed to peak stresses as high as 800 GPa. The Hugoniot elastic limits are measured to be 80 $(\ifmmode\pm\else\textpm\fi{}12)$, 81 $(\ifmmode\pm\else\textpm\fi{}6)$, and 60 $(\ifmmode\pm\else\textpm\fi{}3)\text{ }\text{GPa}$ for the $⟨100⟩$, $⟨110⟩$, and $⟨111⟩$ orientations of single crystals with the directional dependence attributable to the relative increase in strength under confining stress. These values imply a single crystal yield strength approximately 1/3 of theoretical predictions. The measurements reveal clear deviations from an elastic-plastic response upon dynamic yielding with significant relaxation toward an isotropic stress state for shock stresses of at least 160 GPa. Previously reported signatures of melting at 700--800 GPa along the diamond Hugoniot may be related to the transition from a two-wave to a single-wave structure, supporting the interpretation that melting begins at lower stresses $(\ensuremath{\sim}600\text{ }\text{GPa})$ with the appearance of an optically reflecting phase of carbon.

Modeling the elastic wave propagation in a block medium under the impulse loading

The wave propagation analysis revealed that the low-frequency pendulum wave propagating in a 2D block medium with periodic structure due to the action of local impulse has a two-wave structure. The shape of such wave depends on its propagation direction. Modeling the blast-induced seismic wave propagation in a two-layer block rock mass with the weak upper layer and stiff lower layer showed that the far distant point from the wave excitation source is first reached by the small amplitude pendulum wave running in the stiffer lower layer and then by the delayed maximum-amplitude wave propagating in the upper layer.

Two-wave structure of liquid film and wave interrelation in annular gas-liquid flow with and without entrainment

The wavy structure of liquid film in downward annular gas-liquid flow with and without liquid entrainment is examined for a wide range of gas velocities using high-speed laser-induced fluorescence technique. It is shown that the wavy structure is always represented by two types of waves, long-lived and short-lived waves with the latter always generated at the back slopes of the long-lived waves. Main regularities of short-lived wave generation and evolution are also described.

On the structure of the Hugoniot relation for a shock-induced martensitic phase transition

The Hugoniot curve relates the pressure and volume behind a shock wave, with the temperature having been eliminated. This paper studies the Hugoniot curve behind a propagating sharp interface between two material phases for a solid in which an impact-induced phase transition has taken place. For a solid capable of existing in only one phase, compressive impact produces a shock wave moving into material, say, at rest in an unstressed state at the ambient temperature. If the specimen can exist in either of two material phases, sufficiently severe impact may produce a disturbance with a two-wave structure: a shock wave in the low-pressure phase of the material, followed by a phase boundary separating the low- and high-pressure phases. We use a theory of phase transitions in thermoelastic materials to construct the Hugoniot curve behind the phase boundary in this two-wave circumstance. The kinetic relation controlling the evolution of the phase transition is an essential ingredient in this process.

A shock-induced phase transformation in a LiTaO3 crystal

The high-pressure phase transformation behavior of LiTaO3 crystal has been studied by both Hugoniot measurements and first-principle calculations. We observe a discontinuity in shock velocity (D) versus particle velocity (UP) relation, a two-wave structure below 37.9 GPa, and a three-wave structure above 37.9 GPa. These data confirm that a shock-induced phase transformation of LiTaO3 occurs. The onset pressure of the phase transformation (37.9 GPa) defined by our new shock compression data is higher than the early shock wave value (19 GPa) reported by Stantonand Graham [P. L. Stanton and R. A. Graham, J. Appl. Phys. 50, 6892 (1979)]. A first-principle calculation of the zero degree isotherm for rhombohedral phase (R3c space group) is in good agreement with our low-pressure experimental data. The calculated zero degree isotherm for orthorhombic phase (Pbnm space group) is in concord with our high-pressure shock compression data.

Shock Compression of Monocrystalline Copper: Atomistic Simulations

Molecular dynamics (MD) simulations were used to model the effects of shock compression on [001] and [221] monocrystals. We obtained the Hugoniot for both directions, and analyzed the formation of a two-wave structure for the [221] monocrystal. We also analyzed the dislocation structure induced by the shock compression along these two crystal orientations. The topology of this structure compares extremely well with that observed in recent transmission electron microscopy (TEM) studies of shock-induced plasticity in samples recovered from flyer plate and laser shock experiments. However, the density of stacking faults in our simulations is 102 to 104 times larger than in the experimental observations of recovered samples. The difference between experimentally observed TEM and calculated MD results is attributed to two effects: (1) the annihilation of dislocations during post-shock relaxation (including unloading) and recovery processes and (2) a much shorter stress rise time at the front in MD (<1 ps) in comparison with flyer-plate shock compression (∼1 ns).

Observation of Two-Wave Structure in Strongly Nonlinear Dissipative Granular Chains

In a strongly nonlinear viscous granular chain impacted by a single grain we observe a wave disturbance that consists of two parts exhibiting two time scales of dissipation. Above a critical viscosity there is no separation of the two pulses, and the dissipation and nonlinearity dominate the shocklike attenuating pulse.

Shock-induced phase transition of z-cut lithium tantalate single crystal

High-pressure phase-transition behaviors of z-cut lithium tantalate single-crystal have been studied by Hugoniot measurements at our two-stage light-gas gun and DFT-PWP calculations. A distinct discontinuity was discovered on the D-u (shock-wave velocity versus particle velocity) relation. An elastic-plastic two-wave structure was observed from the VISAR measured particle velocity profiles at low pressures (25.9 GPa and 32.6 GPa), while three-wave structure appeared in the measured particle velocity profiles at the final pressure of 42.9 GPa and 53.0 GPa. Both facts indicate a shock-induced phase transition of LiTaO3 samples occurred with an onset pressure of 37.9GPa. The theoretically calculated 0K pressure versus compression ratio (P-V/V0) curve for the rhombohedral phase (R3c space group) is in good agreement with the low-pressure experimental data, while that for orthorhombic phase (Pbnm space group) is in accord with the results by deducing thermal pressure contribution from the measured shock-compression data at high pressures. This suggests that the high-pressure phase has orthorhombic symmetry. High-pressure phase transformation behaviors including the transition pressure and structures, which are unclear in current literature, have been clarified in this paper by our new shock-wave data and ab-initio calculations. These behaviors were demonstrated to be in close similarity with that of its isomorphous crystal LiNbO3. The present work is significant for the investigations of shock-induced phase-transition of similar single-crystal materials.

Strength behavior of materials at high pressures

Strength is an important aspect of material behavior for armor performance, planetary science, and accurate property measurement under quasi-isentropic loading and static high pressure. The advent of time-resolved diagnostics allowed the elastic–plastic behavior of solids under shock loading to be detected for the first time. These early experiments revealed a two-wave structure of elastic and plastic shock waves for stresses above the elastic limit. However, the full stress state in the shocked state remained unknown because the conservation equations provide only the longitudinal stress. Since then, a variety of techniques has been used to determine strength in the shocked state. One of the most successful has been using shock/release and shock/reload to find the stress state and strength in the shocked condition. This technique has been applied to a variety of metals and ceramics at stresses of 100 GPa or higher. These experiments have revealed a rich set of behaviors, many of which are still not fully understood. Recently, there has been significant interest in isentropic loading where the material can be significantly cooler and strength even more important. In this paper, we present a current perspective on strength under high pressures, particularly in the dynamic regime, with emphasis on the techniques used to measure strength and their advantages and disadvantages. Results of strength measurements on several materials will be discussed, and interesting aspects of behavior will be highlighted. In addition, shock results will be contrasted with those under isentropic loading. Finally, some new directions in the study of strength will be outlined.

Multiscale Shock Heating Analysis of a Granular Explosive

AbstractA multiscale model is formulated and used to characterize the duration and amplitude of temperature peaks (i.e., hot spots) at intergranular contact surfaces generated by shock compaction of the granular high explosive HMX (octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine). The model tracks the evolution of both bulk variables and localized temperature subject to a consistent thermal energy localization strategy that accounts for inelastic and compressive heating, phase change, and thermal conduction at the grain scale (grain size ∼50μm). Steady subsonic compaction waves having a dispersed two-wave structure are predicted for mild impact of dense HMX (porosity ∼19%), and steady supersonic compaction waves having a discontinuous solid shock followed by a thin compaction zone are predicted for stronger impact. Short duration hot spots having peak temperatures in excess of 900K are predicted near intergranular contact surfaces for impact speeds as low as 100m∕s; these hot spots are sufficient to induce sustained combustion as determined by a two-phase thermal explosion theory. Thermal conduction and phase change significantly affect hot-spot formation for low impact speeds (∼100m∕s), whereas bulk inelastic heating dominates the thermal response at higher speeds resulting in longer duration hot spots. Compressive grain heating is shown to be largely inconsequential for the range of impact speeds considered in this work (100⩽up⩽1000m∕s). Predictions for the variation in inelastic strain, pressure, and porosity through the compaction zone are also shown to qualitatively agree with the results of detailed mesoscale simulations.

Nanoscale view of shock-wave splitting in diamond

Molecular dynamics (MD) simulations of shock wave propagation in the 〈110〉 crystallographic direction of diamond were carried out using a reactive empirical bond order potential. A split two-wave shock structure due to a lattice transformation is observed above a piston velocity threshold of up ≈ 1.8 km/s corresponding to the Hugoniot elastic limit of 125 ± 15 GPa. This transition is triggered while the temperature increase in the leading shock remains negligibly small in comparison to the melting temperature of diamond and is limited to moderate shock strengths.

Structure of weak shock waves in 2-D layered material systems

Shock waves in homogeneous materials in the absence of phase transitions are understood to have a one-wave structure. However, upon loading of a layered heterogeneous material system a two-wave structure is obtained––a leading shock front followed by a complex pattern that varies with time. This dual shock-wave pattern can be attributed to material architecture through which the shock wave propagates, i.e. the impedance (and geometric) mismatch present at various length scales, and nonlinearities arising from material inelasticity and failure. The objective of the present paper is to provide a better understanding of the role of material architecture in determining the structure of weak shock waves in 2-D layered material systems. Normal plate-impact experiments are conducted on 2-D layered material targets to obtain both the precursor decay and the late-time dispersion. The particle velocity at the free surface of the target plate is measured by using a multi-beam VALYN VISAR. In order to understand the effects of layer thickness and the distance of wave propagation on elastic precursor decay and late-time dispersion several different targets with various layer and target thicknesses are employed. Moreover, in order to understand the effects of material inelasticity both elastic–elastic and elastic–viscoelastic bilaminates are utilized. The results of these experiments are interpreted by using asymptotic techniques to analyze propagation of acceleration waves in 2-D layered material systems. The analysis makes use of the Laplace transform and Floquet theory for ODE’s with periodic coefficients [Asymptotic solutions for wave propagation in elastic and viscoelastic bilaminates. In: Developments in Mechanics, Proceedings of the 14th Mid-Eastern Mechanics Conference, vol. 26, no. 8, pp. 399–417]. Both wave-front and late-time solutions for step-pulse loading on layered half-space are compared with the experimental observations. The results of the study indicate that the structure of acceleration waves is strongly influenced by impedance mismatch of the layers constituting the laminates, density of interfaces, distance of wave propagation, and the material inelasticity.

Compressive shock wave response of a Zr-based bulk amorphous alloy

Plane shock wave experiments were performed at peak stresses up to 13 GPa on Zr-based bulk amorphous alloy (BAA) samples. A velocity interferometer was used to measure the particle velocity history either at the impact surface or at the rear surface of the BAA samples. From the measured particle velocity histories, the Hugoniot elastic limit (HEL) was determined to be 7.1±0.3 GPa, corresponding to an elastic strain of approximately 4%. For experiments in which the peak stress exceeded the HEL, a clear two-wave structure consisting of an elastic precursor followed by a plastic wave was observed. Measurements of the transmitted wave profiles, along with direct determination of the longitudinal stress and particle velocity at the impact surface, suggest that the shear strength of the Zr-based BAA is reduced as it is shocked above the elastic limit.

Microscopic View of Structural Phase Transitions Induced by Shock Waves

Multimillion-atom molecular-dynamics simulations are used to investigate the shock-induced phase transformation of solid iron. Above a critical shock strength, many small close-packed grains nucleate in the shock-compressed body-centered cubic crystal growing on a picosecond time scale to form larger, energetically favored grains. A split two-wave shock structure is observed immediately above this threshold, with an elastic precursor ahead of the lagging transformation wave. For even higher shock strengths, a single, overdriven wave is obtained. The dynamics and orientation of the developing close-packed grains depend on the shock strength and especially on the crystallographic shock direction. Orientational relations between the unshocked and shocked regions are similar to those found for the temperature-driven martensitic transformation in iron and its alloys.