A semi-implicit integration scheme for rate independent finite crystal plasticity

Abstract

An efficient new numerical integration scheme is presented for rate independent crystal plasticity theory. A key feature of this approach is the ability to identify active slip systems prior to determining their shearing rate. Options are described for various cases of slip system hardening, including self hardening and latent hardening. Alternatives for the constitutive update are explored, including hyperelasticity based on the multiplicative decomposition of the deformation gradient as well as application of the consistency condition in a much more efficient hypoelastic formulation. Several conclusions are drawn concerning the influences of elastic and plastic properties on the activation of slip systems and their subsequent shearing rates. Key among these is the fact that, once activated, shearing rates are independent of the levels of shear flow resistance on the slip systems, provided that the plastic hardening moduli are much less in magnitude than the elastic moduli, as is usually the case. Determination of active slip systems and their shearing rates depend on the degree of elastic anisotropy of the crystal, but not on the magnitude of elastic stiffness.