Elastic Precursor Research Articles

Yield stress, polymorphic transformation, and spall fracture of shock-loaded iron in various structural states and at various temperatures

The response of polycrystalline 99.5% pure iron was studied in a series of planar impact experiments, with samples of different thickness having an initial temperature that ranged between 300 and 1233 K. The free surface velocity histories of the shocked samples were recorded in the course of the experiments. Almost all recorded histories are characterized by a three-wave structure containing an elastic precursor Pel and two plastic, P1 and P2, waves. It was found that at 300, 900, and 1039 K (some 5 K away from iron's Curie point), the decay of the Pel wave with propagation distance is characterized by two different regimes; a fast one that corresponds to plastic strain rates above ∼105 s−1 and a slower one at lower strain rates. Since the shear stress at which the change-over takes place is very close to the Peierls stress of iron, we assume that above this stress the decay is governed by the phonon-damped over-barrier dislocation motion, while below it, the thermally activated generation and motion of the dislocation kinks is the governing mechanism. Based on the parameters of the P1 and P2 waves, both the initial and the maximum rates of the α→ε transformation in iron have been estimated. The results indicate that the approach to the Curie point is associated with a substantial, by 2–3 times, increase of the transformation rate.

Attenuation of the dynamic yield point of shocked aluminum using elastodynamic simulations of dislocation dynamics.

When a metal is subjected to extremely rapid compression, a shock wave is launched that generates dislocations as it propagates. The shock wave evolves into a characteristic two-wave structure, with an elastic wave preceding a plastic front. It has been known for more than six decades that the amplitude of the elastic wave decays the farther it travels into the metal: this is known as "the decay of the elastic precursor." The amplitude of the elastic precursor is a dynamic yield point because it marks the transition from elastic to plastic behavior. In this Letter we provide a full explanation of this attenuation using the first method of dislocation dynamics to treat the time dependence of the elastic fields of dislocations explicitly. We show that the decay of the elastic precursor is a result of the interference of the elastic shock wave with elastic waves emanating from dislocations nucleated in the shock front. Our simulations reproduce quantitatively recent experiments on the decay of the elastic precursor in aluminum and its dependence on strain rate.

Dynamic behavior of zirconium alloy E110 under submicrosecond shock-wave loading

Stress waves have been measured under shock wave loading of zirconium alloy E110 samples with the 0.5 – 8 mm thickness at normal and elevated temperatures. Duration of shock loading pulses varied from ∼0.05 up to 1μs with the amplitude varying from 3.4 up to 23 GPa. Free-surface velocity profiles have been registered using VISAR and PDV interferometers with nanosecond resolution. Attenuation of the elastic precursor has been measured to determine plastic strain rate behind the elastic precursor front. The plastic strain rate was observed to decrease with propagation from 10 6 s −1 at the 0.46-mm distance down to 2 ⋅ 10 4 s −1 at the 8-mm distance. Spall strength has been measured under normal and elevated temperatures. Spall strength versus strain rate relationships have been constructed in the 10 5 s −1 – 10 6 s −1 range. Under shock compression higher than 10.6 GPa, the three-wave configuration of the shock wave has been registered and the polymorphous α → ω transition is considered to be the reason of this phenomenon. This work was supported by State Atomic Energy Corporation “Rosatom” within State Contract # H.4x.44.90.13.1111

Deformation of zirconium – niobium alloy E635 in sub-microsecond shock waves

Strength characteristics of zirconium - niobium alloy E635 were measured under shock - wave loading conditions at normal and elevated temperatures and results of these measurements are presented. Measurements were taken in conditions when samples were impacted by plane shock waves with the pressure up to 13 GPa and duration from ∼0.05 μs up to 1 μs. Free-surface velocity profiles were recorded with the help of VISAR and PDV laser Doppler velocimeters having nanosecond time resolution. Evolution of elastic precursors with samples thickness varying from 0.5 up to 8 mm is also considered. Measured attenuation of the elastic precursor was used to determine plastic strain rate behind the precursor front. Temperature effect on the value of dynamic elastic limit and spall strength at normal and elevated temperatures is studied. This work is implemented with the support of the State Atomic Energy Corporation “Rosatom” under State Contract H.4x.44.90.13.1111.

Overstress and flowstress approaches to dynamic viscoplasticity

Viscoplasticity is mostly modelled by the flowstress approach, where the flowstress (Y) is a function of pressure, temperature, plastic strain and strain rate Y(P,T, e p , e). For dynamic Viscoplasticity the flowstress approach is used in hydrocodes together with the radial return algorithm, to determine deviatoric stress components in each computational cell and for each time step. The flowstress approach assumes that during plastic loading, the flowstress in stress space follows the current stress point (current Y). Unloading of a computational cell is therefore always elastic. The overstress approach to dynamic viscoplasticity was used in various versions in the 1950s and early 1960s, before the advent of hydrocodes. By the overstress approach a state point may move out of the quasistatic flow surface upon loading, and hence the term overstress. When this happens, the state point tends to fall back (or relax) onto the quasistatic flow surface through plastic flow, and the rate of this relaxation is an increasing function of the amount of overstress. In the paper we first outline in detail how these two approaches to dynamic viscoplasticity work, and then show an example for which the overstress approach has an advantage over the flowstress approach. The example has to do with elastic precursor decay in planar impact, and with the phenomenon of anomalous thermal strengthening, revealed recently in planar impact tests. The overstress approach has an advantage whenever plastic flow during unloading is of importance.

Dislocation structure of plastic relaxation waves in polycrystals and alloys under intense shock wave loading

The influence of the structure factors (sizes of grains and precipitates) on the dislocation structure formed in polycrystals and alloys behind the shock wave front (elastic precursor) has been theoretically discussed in terms of the dislocation kinetic relationships and kinetic equation for the dislocation density. The critical conditions of the transition from the cellular dislocation structure to a uniform dislocation distribution have been formulated. These conditions are used to determine the dependences of the critical pressure, above which the dislocation distribution becomes uniform, on the grain size and precipitate volume density.

Metal behavior near theoretical ultimate strength in experiments with femtosecond laser pulses

An interferometric method is used in the picosecond range to study the evolution of shock-compression waves generated in metallic film specimens by a powerful femtosecond laser. Shock waves with compression stress behind the elastic precursor front up to 27.5 GPa and 12.6 GPa, respectively, were registered in the case of submicron propagation length in iron and aluminum. The obtained values of the shear and bulk strength are comparable with computed values of the theoretical ultimate shear and tensile strength.

Dynamic properties of zirconium alloy E110 under shock-wave loading of submicrosecond duration

The results of stress wave measurements under shock-wave loading of specimens of zirconium alloy W110 of thickness from 0.5 to 8 mm at normal and elevated temperatures are presented. The duration of shock loading pulses varied from ∼0.05 to 1 µs with amplitude from 3.4 to 23 GPa. The free surface velocity profiles were registered by interferometric velocimeters VISAR and PDV with nanosecond time resolution. The results of measurement of the elastic precursor decay were used to determine the plastic strain rate behind its front, which decreases from 106 s−1 at a distance of 0.46 mm to 2 × 104 s−1 at a distance of 8 mm in the course of propagation. The spall strength values at normal and elevated temperatures were obtained, and its dependencies on the strain rate in the range from 105 to 106 s−1 were constructed. The three-wave configuration of the shock wave caused by the polymorphic transformation as α → ω was registered under a shock compression pressure of 10.6 GPa.

Shock response of magnesium single crystals at normal and elevated temperatures

A series of magnesium single crystals, from 0.2 to 3 mm thick, were shock loaded in directions parallel and perpendicular to the c-axis of the hexagonal closed packed (hcp) structure and at 45° to the c-axis. Shock compression along the c-axis is associated with the largest Hugoniot elastic limit (HEL) for this material. Microscopic observation of recovered c-cut samples demonstrated intense twinning with a greater density of twins near the impact surface. The low-energy basal slip was activated by shock loading along the inclined direction and has the smallest HEL. In all cases, we observe the decay of the elastic precursor wave and growth of the HEL with increasing temperature. For the inclined shock compression after the HEL, two plastic waves were found where the stress level of the first plastic wave depends on the peak shock stress. Finally, the largest spall strength was along the transversal direction and the smallest in the off-axis direction. The fracture surface of the sample of transversal orientation contains numerous groves oriented along the base planes of the crystals.

Deformation resistance and fracture of iron over a wide strain rate range

The results of measurements of the decay of an elastic precursor in iron at the distances from 0.13 to 10 mm and the spall strength of the samples with such thicknesses have been compared with similar data for the nanometer-scale samples. The decay has been described by a unique dependence whose differentiation gives the relationship between the initial plastic strain rate in the range from 103 to 109 s−1 and the compression stress in the elastic shock wave from 1.5 to 27.5 GPa. The dynamic breaking strength (spall strength) varies in this range of shock-wave load time from 1.5 to 20 GPa.

Determining the refractive index of shocked [100] lithium fluoride to the limit of transmissibility

Lithium fluoride (LiF) is a common window material used in shock- and ramp-compression experiments because it displays a host of positive attributes in these applications. Most commonly, it is used to maintain stress at an interface and velocimetry techniques are used to record the particle velocity at that interface. In this application, LiF remains transparent to stresses up to 200 GPa. In this stress range, LiF has an elastic-plastic response with a very low (<0.5 GPa) elastic precursor and exhibits no known solid-solid phase transformations. However, because the density dependence of the refractive index of LiF does not follow the Gladstone-Dale relation, the measured particle velocity at this interface is not the true particle velocity and must be corrected. For that reason, the measured velocity is often referred to as the apparent velocity in these types of experiments. In this article, we describe a series of shock-compression experiments that have been performed to determine the refractive index of LiF at the two most commonly used wavelengths (532 nm and 1550 nm) between 35 and 200 GPa to high precision. A modified form of the Gladstone-Dale relation was found to work best to fit the determined values of refractive index. In addition, we provide a direct relationship between the apparent and true particle velocity to correct experimentally obtained wave profiles by others using these velocimetry techniques.

Plastic behavior of aluminum in high strain rate regime

The aim of this experiment was to study the plastic response of Al to dynamic loading at high strain rates. Dynamic loading was applied by direct laser ablation of the sample with pulse width of 3 ns long. The free surface velocity histories of shock loaded samples, 60-310 μm thick at room temperature, and 150 μm thick with initial temperature from 293 to 893 K, have been recorded using a line velocity interferometer for any reflections (VISAR) system. The line VISAR could measure free surface velocity profile with high temporal resolution (∼100 ps). The measured amplitudes of the elastic precursor waves have been approximated by power functions of the propagation distance with the power index of 0.581, and these data have been converted into relationships between the shear stress at Hugoniot elastic limit and the initial plastic strain rate. The peak longitudinal elastic stress and the strain rate meet a power law dependency with the power index of 0.44. Samples were recovered for post-shot metallographic analysis. The metallographic analysis leads to the conclusion that the spall strength of preheated aluminum is determined more by the rate of void nucleation rather than its growth.

Dynamic compressive and tensile strengths of spark plasma sintered alumina

Fully dense submicron grain size alumina samples were manufactured from alumina nano-powder using Spark Plasma Sintering and tested in two kinds of VISAR-instrumented planar impact tests. In the first kind, samples were loaded by 1-mm tungsten impactors, accelerated to a velocity of about 1 km/s. These tests were aimed at studying the Hugoniot elastic limit (HEL) of Spark Plasma Sintering (SPS)-processed alumina and the decay, with propagation distance, of the elastic precursor wave. In the tests of the second kind, alumina samples of 3-mm thickness were loaded by 1-mm copper impactors accelerated to 100–1000 m/s. These tests were aimed at studying the dynamic tensile (spall) strength of the alumina specimens. The tensile fracture of the un-alloyed alumina shows a monotonic decline of the spall strength with the amplitude of the loading stress pulse. Analysis of the decay of the elastic precursor wave allowed determining the rate of the irreversible (inelastic) strains in the SPS-processed alumina at the initial stages of the shock-induced inelastic deformation and to clarify the mechanisms responsible for the deformation. The 1-% addition of Cr2O3 decreases the HEL of the SPS-processed alumina by 5-% and its spall strength by 50% but barely affects its static properties.

Tantalum and vanadium response to shock-wave loading at normal and elevated temperatures. Non-monotonous decay of the elastic wave in vanadium

The evolution of the elastic precursor waves in pure tantalum and vanadium is presented at normal and elevated temperatures over propagation distances that ranged from 0.125 to 3 mm. Measurements were performed in order to obtain experimental data about the temperature-rate dependence of the yield stress of the two metals. With increasing propagation distance, the rate of the decay of elastic precursor decreases, as the shear stress in the elastic precursor wave approaches the Peierls stresses. It has been found that the decay, with propagation distance, of the post-spike minimum of the spike-like elastic precursor wave in vanadium is essentially non-monotonous. The experiments also revealed that annealing of tantalum and vanadium increases their Hugoniot elastic limit. The anomalous increase of the high strain rate yield stress with temperature, as observed earlier for some FCC and HCP metals, has not been detected in these measurements.

Mechanism of formation of cellular dislocation structures during propagation of intense shock waves in crystals

The mechanism of formation of a cellular dislocation structure in face-centered cubic (fcc) metal crystals subjected to shock compression at strain rates \(\dot \varepsilon \) > 106 s−1 has been considered theoretically within the dislocation kinetic approach based on the kinetic equation for the dislocation density (dislocation constitutive equation). A dislocation structure of the cellular type is formed in the case of a two-wave structure of the compression wave behind its shock front (elastic precursor). It has been found that, at pressures σ > 10 GPa, the dislocation cell size Λc depends on the pressure σ and the density ρG of geometrically necessary dislocations generated at the shock front according to the relationship Λc ∼ ρG−n ∼ σ−m, where n = 1/4–1/2, m = 3/4–3/2, and m = 1, for different pressures and orientations of the crystal. It has been shown that, in copper and nickel crystals with the shock loading axis oriented along the [001] direction, the cellular structure is not formed after reaching the critical pressures σc equal to 31 and 45 GPa, respectively.

Elastic-plastic collapse of super-elastic shock waves in face-centered-cubic solids

Shock waves in the [110] and [111] directions of single-crystal Al samples were studied using molecular dynamics (MD) simulations. Piston-driven simulations were performed to investigate the split shock-wave regime. At low piston velocities, the material is compressed initially to a metastable over-compressed elastic state leading to a super-elastic single shock wave. This metastable elastic state later collapses to a plastic state resulting in the formation of a two-wave structure consisting of an elastic precursor followed by a slower plastic wave. The single two-zone elastic-plastic shock-wave regime appearing at higher piston velocities was studied using moving window MD. The plastic wave attains the same average speed as the elastic precursor to form a single two-zone shock wave. In this case, repeated collapse of the highly over-compressed elastic state near the plastic shock front produces ultrashort triangle pulses that provide the pressure support for the leading elastic precursor.

Evolution of elastic precursor and plastic shock wave in copper via molecular dynamics simulations

Large-scale molecular dynamics (MD) simulations are performed to investigate shock propagation in single crystal copper. It is shown that the P-V plastic Hugoniot is unique regardless of the sample's orientation, its microstructure, or its length. However, the P-V pathway to the final state is not, and depends on many factors. Specifically, it is shown that the pressure in the elastic precursor (the Hugoniot elastic limit (HEL)) decreases as the shock wave propagates in a micron-sized sample. The attenuation of the HEL in sufficiently-long samples is the main source of disagreement between previous MD simulations and experiment: while single crystal experiments showed that the plastic shock speed is orientation-independent, the simulated plastic shock speed was observed to be orientation-dependent in relatively short single-crystal samples. Such orientation dependence gradually disappears for relatively long, micrometer-sized, samples for all three low-index crystallographic directions ⟨100⟩, ⟨110⟩, and ⟨111⟩, and the plastic shock velocities for all three directions approach the one measured in experiment. The MD simulations also demonstrate the existence of subsonic plastic shock waves generated by relatively weak supporting pressures.

On the residual yield stress of shocked metals

Precise measurement of the free-surface velocity can be a rich source of information on the effects of time and strain on material strength. With this objective, we performed a careful comparative measurement of the free-surface velocity of shock loaded aluminium AD1 and magnesium alloy Ma2 samples of various thicknesses in the range 0.2 mm to 5 mm. We observed the expected decay in the elastic precursor state with increasing sample thickness for both aluminium and magnesium alloy. However, we also observed a small change in the magnitude of hysteresis in the elastic-plastic compression-unloading cycle; where qualitatively the peak free-surface velocity also increased with increasing specimen thickness. Interestingly, the observed change in hysteresis as function of specimen thickness for the Ma2 alloy was relatively smaller than the AD1, in contrast with the larger change in precursor magnitude observed for the magnesium. We propose that softening due to multiplication of dislocations is relatively large in Ma2 and results in a smaller hysteresis in the elastic-plastic cycle.

Response of magnesium single crystals to shock-wave loading at room and elevated temperatures

A series of magnesium single crystals, from 0.2 to 3 mm thick, were shock loaded along specific axes, a and c, of the hexagonal closed packed (hcp) structure. Other experiments involved loading at 45 degrees to these principal axes. Shock compression along the c-axis causes inelastic deformation by means of pyramidal slip and twinning and is associated with the largest Hugoniot elastic limit (HEL) for this material. The low-energy basal slip was activated by shock loading along the inclined direction and has he smallest HEL. In all cases, we observe the decay of the elastic precursor wave and growth of the HEL with increasing temperature. For the c-orientation this change is caused by a decrease of elastic constants, not an increase of shear stress along the pyramidal slip planes. For the other orientations the shear stress on the slip planes increased with temperature. For the inclined shock compression, after the HEL, two plastic waves were found: the stress level of the first plastic wave depends on the ultimate shock stress. Finally, the largest spall strength was along the a-axis and the smallest in the off-axis direction.

Improved understanding of the dynamic response in anisotropic directional composite materials through the combination of experiments and modeling

Recently there has been renewed interest in the dynamic response of composite materials; specifically low density epoxy matrix binders strengthened with continuous reinforcing fibers. This is in part due to the widespread use of carbon fiber composites in military, commercial, industrial, and aerospace applications. The design community requires better understanding of these materials in order to make full use of their unique properties. Planar impact testing was performed resulting in pressures up to 15 GPa on a unidirectional carbon fiber - epoxy composite, engineered to have high uniformity and low porosity. Results illustrate the anisotropic nature of the response under shock loading. Along the fiber direction, a two-wave structure similar to typical elastic-plastic response is observed, however, when shocked transverse to the fibers, only a single bulk shock wave is detected. At higher pressures, the epoxy matrix dissociates resulting in a loss of anisotropy. Greater understanding of the mechanisms responsible for the observed response has been achieved through numerical modeling of the system at the micromechanical level using the CTH hydrocode. From the simulation results it is evident that the observed two-wave structure in the longitudinal fiber direction is the result of a fast moving elastic precursor wave traveling in the carbon fibers ahead of the bulk response in the epoxy resin. Similarly, in the transverse direction, results show a collapse of the resin component consistent with the experimental observation of a single shock wave traveling at speeds associated with bulk carbon. Experimental and simulation results will be discussed and used to show where additional mechanisms, not fully described by the currently used models, are present.