Disclination based model of grain boundary in crystalline materials with microstructural defects

Abstract

This paper deals with continuous description of elasto-plastic materials with lattice defects such as dislocations and disclinations, and grain boundaries. The behaviour of crystalline solids containing defects is described by non-local fields that are smooth over an interatomic length scale and at times of micro-seconds. The dislocation and disclination densities are appropriate measures of incompatibilities of the plastic distortion and of the plastic connection relative to plastic distortion, respectively. The grain boundaries will be simulated in terms of an array of disclination dipoles. The heterogeneous initial disclinations are a source of dislocations. These lattice defects, stress, strain and the displacement vector will be provided by solving initial and boundary value problems in elasto-plastic bodies, which involve dissipative evolution equations for plastic distortion and disclination tensor. The numerical procedure and corresponding algorithms to solve the variational formulation of the initial and boundary value problems are provided. The results of numerical simulations are analyzed and a number of graphs illustrate the elasto-plastic behaviour of the sheet when a shear stress is applied on one of its edge.