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

TLDR: In this article, rate-dependent constitutive relations for single crystals are derived in terms of dislocation dynamics, where contributions from slip on the individual glide planes are assumed to superpose linearly to give the total plastic strain.

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.