Dislocation Dynamics and Single-Crystal Constitutive Relations: Shock-Wave Propagation and Precursor Decay

Abstract

Rate-dependent constitutive relations for single crystals are derived in terms of dislocation dynamics. Contributions from slip on the individual glide planes are assumed to superpose linearly to give the total plastic strain. As an application of the theory, equations describing elastic precursor decay are developed for longitudinal plane-wave propagation in fcc, bcc, and rocksalt structures with wave propagation in the [100], [110], and [111] directions. In addition, expressions for precursor decay in zinc (hcp structure) are derived for wave propagation both parallel and perpendicular to the c-axis. Calculated theoretical results are compared with experimental data on precursor amplitudes for single-crystal copper (fcc), tungsten (bcc), NaCl (rocksalt), and LiF (rocksalt). Dislocation mobilities determined from direct observation of dislocations are used in these calculations. In general the theory predicts the proper relative order of the precursor amplitudes for different propagation directions. The comparisons show that in order for theoretically determined amplitudes to agree with experimental data, initial mobile dislocation densities must be two or three orders-of-magnitude greater than initial total densities which are measured in the material prior to shock loading. Possible explanations for this discrepancy are discussed.

Orientation and rate dependence in high strain-rate compression of single-crystal silicon

“…Similar analysis on high-deformation of single crystal Cu, 37 other than homogeneous dislocation flow must cause the u fs precursor peak and subsequent stress relaxation. Some possibilities are twinning, shear localization and fracture, or an unconventional dislocation nucleation mechanism to seed the initial density.…”

Shock Wave Compression of NaCl Single Crystals observed by Flash-X-Ray Diffraction

“…The intensity however is clearly higher than in the case of powder patterns. An explanation for the broaden ing may be the great increase in dislocation density in the elastic wave [18] and the appearance of mosaic structure in the crystal [5]. The increase in tem perature during shock and the corresponding broadening of the reflex can be neglected in the pressure range considered.…”

Frontiers in Anisotropic Shock-Wave Modeling

“…Johnson et al (31) proposed constitutive equations describing elastic precursor decay for longitudinal plane-wave propagation in fcc, bcc, and rocksalt structures with the wave propagation in the 100 , 110 , and 111 directions. Calculated theoretical results (Johnson et al [31]) are compared with the experimental data on precursor amplitudes for single-crystal copper (fcc), tungsten (bcc), sodium chloride (NaCl) (rocksalt), and lithium fluoride (LiF) (rocksalt). Asay et al (73) performed experimental studies on shock propagation along a 100 direction in single-crystal LiF and showed that elastic precursor decay is critically dependent on the origin of the sample.…”

“…In the early 1970s, Johnson et al (31)(32)(33) developed a continuum framework for describing the rate dependent elastic-plastic response of single crystals to shock-wave loading. Their tensor formulation coupled linear elastic response to a dislocation dynamics model that incorporated the appropriate slip system in the shocked crystals.…”