Latent hardening in single crystals. II. Analytical characterization and predictions

Abstract

Constitutive equations are developed that characterize the multiple-slip behaviour of crystalline materials at low temperature. A matrix of instantaneous hardening moduli that relate the rate of hardening on each slip system to all slip-rates is proposed based upon well-known observations and the latent hardening experiments reported in Part I. In general, these moduli depend on the history of slips. Simulations of various behaviours are presented for FCC single crystals (copper) that are in good agreement with observations. These include, for example, stress-strain curves in a uniaxial loading test, hardening rate variations with respect to initial orientation, latent hardening, tensile overshoot and secondary slips. Numerical calculations are facilitated using an extremum principle and a modified quadratic programming algorithm.