Description of plane strain deformation of FCC crystals by a gradient theory of crystal plasticity

Abstract

A higher-order gradient crystal plasticity theory applicable to three-dimensional problems is reduced to a plane strain version to be used for the analysis of the deformation of face-centered cubic (FCC) crystals at a particular orientation that the out-of-plane plastic deformation cancels out. Plane strain conditions have been frequently quoted in the literature on theoretical crack problems and experimental studies on FCC crystals since effective information on the fundamental deformation behavior of such materials under multiaxial states of stress and strain is obtained. The present plane strain theory is formulated with planar pseudo slip systems that are contractions of the crystallographic slip systems 111110 of FCC crystals. The resultant theory is purely two-dimensional, but it involves the nature of FCC crystal deformation, i.e., effects of latent hardening, cross slip, and backstresses (equivalently, internal stresses with the opposite sign) associated with the distribution of the edge and screw components of the geometrically necessary dislocations.