The mechanics of deformation-induced subgrain-dislocation structures in metallic crystals at large strains
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.
© 2003 Royal Society. Received 14 February 2002; accepted 14 April 2003; published online 7 October 2003. We are grateful for support provided by the US Department of Energy through Caltech's ASCI/ASAP Center for the Simulation of the Dynamic Behaviour of Solids. We are also indebted to Darcy Hughes for many useful discussions and suggestions, and for making her data available to us.