High strain-rate shear-strain localization in f.c.c. crystalline materials: a perturbation analysis

A new perturbation formulation has been developed that is based on a rate-dependent crystalline plasticity constitutive formulation to investigate planar high strain-rate instabilities and shear-strain localization in face- centered cubic (f.c.c.) crystalline materials. This new formulation can account for strain-rate sensitivity values that range from rate-independent to highly rate-dependent values. Hence, accurate and detailed predictions of material instabilities and shear-strain localization can be obtained for high strain-rate deformations of crystalline materials that are rate-sensitive, such as f.c.c. materials. Critical instability parameters are obtained for deformation modes that account for the e€ects of strain-rate history, inertia, strain-hardening, wave number, and thermal and geometrical softening for applied strain-rates that range from 100 to 5000 s ÿ1. Post-instability behavior and localization modes are monitored by tracking the rate of growth of stability parameters beyond the initial instability point. Results from these perturbation analyses are in good agreement with rate-independent limiting cases and high strain-rate experimental observations. The present study underscores the importance of characterizing material instabilities and shear-strain localization in terms of the competing softening and hardening mechanisms of the lattice structure. 7