A theory of subgrain dislocation structures

We develop a micromechanical theory of dislocation structures and finite de formation single crystal plasticity based on the direct generation of defor mation microstructures and the computation of the attendant effective behav ior. Specifically, we aim at describing the lamellar dislocation structures which develop at large strains under monotonic loading. These microstructu res are regarded as instances of sequential lamination and treated accordin gly. The present approach is based on the explicit construction of microstr uctures by recursive lamination and their subsequent equilibration in order to relax the incremental constitutive description of the material. The mic rostructures are permitted to evolve in complexity and fineness with increa sing macroscopic deformation. The dislocation structures are deduced from t he plastic deformation gradient field by recourse to Kroner's formula for t he dislocation density tensor. The theory is rendered nonlocal by the consi deration of the self-energy of the dislocations. Selected examples demonstr ate the ability of the theory to generate complex microstructures, determin e the softening effect which those microstructures have on the effective be havior of the crystal, and account for the dependence of the effective beha vior on the size of the crystalline sample, or size effect.. In this last r egard, the theory predicts the effective behavior of the crystal to stiffen with decreasing sample size, in keeping with experiment. Tn contrast to st rain-gradient theories of plasticity, the size effect occurs for nominally uniform macroscopic deformations. Also in contrast to strain-gradient theor ies, the dimensions of the microstructure depend sensitively on the loading geometry, the extent of macroscopic deformation and the size of the sample . (C) 2000 Elsevier Science Ltd. All rights reserved.