An elasto-plastic theory of dislocation and disclination fields

Abstract

A linear theory of the elasto-plasticity of crystalline solids based on a continuous representation of crystal defects – dislocations and disclinations – is presented. The model accounts for the translational and rotational aspects of lattice incompatibility, respectively associated with the presence of dislocations and disclinations. The defects content relates to the incompatible plastic strain and curvature tensors. The stress state is described by using the conjugate variables to strain and curvature, i.e., the stress and couple-stress tensors. Defect motion is described by two transport equations. A dynamic interplay between dislocations and disclinations results from a disclination-induced source term in the transport of dislocations. Thermodynamic guidance provides the driving forces conjugate to dislocation and disclination velocity in a continuous context, as well as admissible constitutive relations for the latter. When dislocation and disclination velocity vanish, the model reduces to deWit’s elasto-static theory of crystal defects. It also reduces to Acharya’s linear elasto-plastic theory for dislocation fields when the disclination density is ignored. The theory is intended for use in instances where rotational defects matter, such as grain boundaries. To illustrate its applicability, a finite high-angle tilt boundary is modeled using a disclination dipole and its behavior under tensile loading normal to the boundary is shown.