Continuum theory of pasticity and dislocations

Abstract

The stress field in a perfectly plastic solid defined in continuum plasticity is the sum of the applied stress (solution of boundary value problem in elasticity) and the dislocation stress caused by dislocations created in the so-called plastic domains. The distribution of dislocations or dislocation dipoles inside the plastic domains and the distribution of surface dislocations on lines of discontinuity are determined from the shear line theory of continuum plasticity in the case of plane strain, where the material is assumed to obey von Mises' yield criterion. The theory proposed in this paper suggests a new method of stress analysis in elasto-plastically deformed bodies, since the applied stress can be obtained by solving the boundary value problem in elasticity and the dislocation stress can be found from the dislocation distribution which is determined from the shear line theory.