Shock compression of metal single crystals modeled via Finsler-geometric continuum theory

Abstract

A continuum theory of nonlinear crystal mechanics based on principles from Finsler differential geometry and phase field dynamics is used to model shock compression of metal single crystals. A director component of pseudo-Finsler space is treated as an order parameter, with the metric and derived quantities such as material volume dependent on this parameter. For the present application to shock of magnesium along the c-axis, the order parameter quantifies pyramidal slip and dislocation density, with internal energy depending in part on the latter. Constitutive equations and jump conditions for planar shocks are solved simultaneously. Results for stress, particle velocity, and shock velocity accurately match experimental data, where adjustment of only one parameter scaling the six-fold slip contribution from pyramidal systems is sufficient. Predictions suggest strength improvement should occur upon processing steps that would increase this parameter, and to a lesser extent, those that would increase energy stored per unit dislocation line length in defect substructure.