The purpose of this study is to investigate the cause of the precursor decay anomaly in LiF single crystals, based on the stress-time profiles measured by Asay et al. [J. Appl. Phys. 43, 2132 (1972)] which suggest that the decay is caused by an evolving follower wave overtaking the precursor. It is initially inferred using the profiles that this follower wave consists in turn of a contraction wave C, two degenerate contraction waves I, II, a subrarefaction wave R′, and a rarefaction wave Rb, which appear consecutively. An exact equation for the relaxation function, which can be applied to all five followers, is then derived. Next, inequalities for the dislocation density at the front of each follower are derived by incorporating their various properties into the equations; these are then evaluated using the experimental data of Gupta, Duvall, and Fowles [J. Appl. Phys. 46, 532 (1975)]. The validity of the approach is confirmed by showing that their predicted densities satisfy the inequalities, although both the evaluations and the predictions are still too large to be true in the early stage of the decay process. Finally, this anomaly is traced to the common use of an illusive precursor decay curve of unrealistically large slope.
Submitted for the SHOCK07 Meeting of The American Physical Society Precursor decay anomaly in single-crystal lithium fluoride YUKIO SANO 1 , TOMOKAZU SANO, Osaka University-The purpose of this study is to demonstrate that the precursor decay anomaly in single-crystal lithium fluoride (LiF) can be reduced using a macroscopic approach. To this end, a method of analyzing the evolving unsteady plane wave fronts created in the crystal upon impact is developed. The values of the parameters included in modeled strain waves in the wave fronts are determined such that the time variation of particle velocity predicted at the impact surface fits the detector current at the surface measured by Asay et al. [J. Appl. Phys. 43, 2132 (1972)]. Another condition is also used that the particle velocity-time histories at and near the surface are initially parallel. It is assumed that when the amplitude of a near-steady precursor in the predicted unsteady wave front, which increases from a static yield stress, becomes a maximum, a kink occurs at the rear of the precursor and then it begins to decay. The precursor decay curves estimated, based on this assumption, are much lower than Asay's decay curve. These lower curves are expected to reduce significantly the precursor decay anomaly in this crystal.
The purpose of this study is to reduce the precursor decay anomaly in single-crystal lithium fluoride (LiF) using a macroscopic approach. To this end, a method of predicting the evolving unsteady plane wave fronts created in the crystal upon impact is developed. Parameters included in modeled strain waves in the fronts are determined such that the predicted particle velocity-time history at the impact surface fits the detector current at the LiF-quartz interface measured by Asay et al. [J. Appl. Phys. 43, 2132 (1972)]. Another condition used is that the particle velocity-time histories at and near the surface are initially parallel. It is assumed that when the amplitude of a near-steady precursor in the predicted unsteady wave front, which increases from a static yield stress, becomes a maximum, a kink occurs at the rear of the precursor and then it begins to decay. The precursor decay curves estimated, based on this assumption, are much lower than Asay’s decay curve. These lower curves are expected to reduce significantly the precursor decay anomaly in this crystal.
First, the Rankine–Hugoniot (R–H) relations are generalized for unsteady shock wave fronts of infinitesimal risetime. The equation for particle velocity has a term of strain rate, while that for stress contains terms of strain rate and acceleration. Next, shock jump equations of general form for particle velocity, stress, and specific internal energy are derived. They involve the combined effect of strain wave form, its change with time, and the path in time of strain. The effect, as well as the terms of strain rate and acceleration in the generalized R–H equations, indicates uncertainty about the applicability of familiar R–H equations to the shock fronts. Finally, jump equations for specific strain waves are evaluated: Jumps in the three quantities are influenced greatly by the effect. If both the wave form and the path are linear, then the equations are of the same form as the R–H equations.
Underdetermined system theory applied to quantitative analysis of responses caused by unsteady smoothplane waves Qualitative analysis of response caused by growing plane waves by underdetermined system theory Qualitative analysis of degradation processes of attenuating plane waves by underdetermined system theory A qualitative analysis of the mechanical response of rate-dependent media caused by a onedimensional plane smooth wave front and by a continuous wave front attenuating in the media is performed by an underdetermined system of nonlinear partial differential equations. The analysis reveals that smooth strain, particle velocity, and stress profiles, which the smooth wave front has, are not similar and that the wave front is composed of some partial waves having different properties. The property is represented by a set of strain rate, acceleration, and stress rate. The wave front derived here from the analysis is composed offour different partial waves. The front of the wave front is necessarily a contraction wave in which strain, particle velocity, and stress increase with time, while the rear is a rarefaction wave where they all decrease with time. Between these two wave fronts there are two remaining wave fronts. We call these wave fronts mesocontraction waves I and II. Wave front I is a wave in which stress decreases notwithstanding the increase in strain and particle velocity with time, which is followed by the other, i.e., wave front II, where with time, particle velocity, and stress decrease in spite of the increase in strain. The continuous wave front having continuous and nonsmooth profiles of strain, particle velocity, and stress canalso be composed offour waves. These waves possess the same property as the corresponding waves in the smooth wave front mentioned above. The velocities at three boundaries that the waves have are discontinuous. Therefore, these four wave fronts are independent waves, just as a shock wave and a rarefraction wa~e. Specifically, the front wave, i.e., a contraction wave front is being outrun by a second wave front, the second one is being outrun by a third wave front, and the third is being outrun by a fourth wave front, i.e., a rarefaction wave. We call the second wave front degenerate contraction wave I. We also call the third one degenerate contraction wave II. The stress-strain path and the stress-particle velocity path at a position in a rate-dependent medium which is passed by the continuous wave front are schematically shown. 3857
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