Interplay between continuous dislocations and disclinations in elasto-plasticity

Abstract

A new elasto-plastic constitutive model is proposed to describe the behaviour of crystalline materials with microstructural defects which account for the interplay between dislocations and disclinations. The defects are defined in terms of the incompatible tensor fields and related to the anholonomic configurations. Based on the formulated free energy imbalance principle, involving the free energy which depends on the torsion of the so-called plastic connection as a measure of the interplay disclinations–dislocations, the non-local diffusion-like evolution equations describing the coupling between dislocations and disclinations are derived.In the case of small distortions, the wedge disclination and edge dislocations problems are defined. The evolution equations for the plastic distortion and disclination tensor are derived starting from the finite distortion case. The initial and boundary value problem concerning the tensile test of a rectangular sheet is solved numerically in the hypothesis that, at the initial moment, a single disclination dipole or edge dislocations describe the heterogeneity of defects.This paper aims to give a comprehensive procedure within the constitutive framework of continuous mechanics, which is able to solve problems related to the presence of defects such as dislocations and disclinations under various aspects, for initial preexisting dislocations or disclinations, as well as problems with pure dislocations or a dislocation–disclination interplay.