The mechanics of deformation–induced subgrain–dislocation structures in metallic crystals at large strains

Abstract

We present a streamlined limiting case of the theory of Oritz & Repetto for crystals with microstructure in which the crystals are assumed to exhibit infinitely strong latent hardening. We take this property to signify that the crystal must necessarily deform in single slip at all material points. This requirement introduces a non–convex constraint that renders the incremental problem non–convex. We have assessed the ability of the theory to predict salient aspects of the body of experimental data compiled by Hansen et al. regarding lamellar dislocation structures in crystals deformed to large strains. Although the comparisons with experiment are somewhat indirect, the theory appears to correctly predict salient aspects of the statistics of misorientation angles and lamellar–boundary spacings, and the scaling of the average misorientation and spacing with increasing macroscopic strain.