Plasticity of Crystals with Interacting Slip Systems

A new, non-conventional approach to the analysis of crystalline lattice rotations caused by large plastic strains of crystals is presented. Only rigid-ideally plastic crystals are considered. Contrary to the theory based on the Schmid law, the proposed model assumes that a yield initiation depends on stress states of all slip systems, i.e. interactions between slip systems are taken into account. In the paper an interaction rule, founded on microscopic observations, is governed by one integer constant n. For n = 1, the crystals satisfy the Mises criterion with a quadratic yield surface. For n → ∞ , the crystals are described by smooth (with rounded-off corners) yield surfaces tending to those generated by the Schmid law. For a fixed n, the interaction rule determines constitutive relations in terms of the strain rate tensor, the plastic spin tensor and the stress tensor. Three additional constitutive equations for the plastic spin components lead to an explicit descriptions of lattice reorientations. A generalized plastic potential for the strain rate and the plastic spin is introduced. A smooth yield condition generated by this potential enables to for­mulate a complete system of equations for the model, what considerably simplifies the numerical analysis. The f.c.c, crystals in tension and compression are examined in detail. The presented strain paths demonstrate a predominant influence of interactions between slip systems on the lattice reorientations.