A model of crystal plasticity based on the theory of continuously distributed dislocations

This work represents an attempt at developing a continuum theory of the elastic-plastic response of single crystals with structural dimensions of similar to 100 mum or less, based on ideas rooted in the theory of continuously distributed dislocations. The constitutive inputs of the theory relate explicitly to dislocation velocity, dislocation generation and crystal elasticity. Constitutive nonlocality is a natural consequence of the physical considerations of the model. The theory reduces to the nonlinear elastic theory of continuously distributed dislocations in the case of a nonevolving dislocation distribution in the material and the nonlinear theory of elasticity in the absence of dislocations. A geometrically linear version of the theory is also developed. The work presented in this paper is intended to be of use in the prediction of time-dependent mechanical response of bodies containing a single, a few, or a distribution of dislocations. A few examples are solved to illustrate the recovery of conventional results and physically expected ones within the theory. Based on the theory of exterior differential equations, a nonsingular solution for stress/strain fields of a screw dislocation in an infinite, isotropic, linear elastic solid is derived. A solution for an infinite, neo-Hookean nonlinear elastic continuum is also derived. Both solutions match with existing results outside the core region. Bounded solutions are predicted within the core in both cases. The edge dislocation in the isotropic, linear theory is also discussed in the context of this work. Assuming a constant dislocation velocity for simplifying the analysis, an evolutionary solution resulting in a slip-step on the boundary of a stress-free crystal produced due to the passage and exit of an edge dislocation is also described. (C) 2001 Elsevier Science Ltd. All rights reserved.