Dislocations

Abstract

Plastic deformation involves planes of atoms sliding over each other. The sliding happens through the movement of linear defects called dislocations. The phenomenology of dislocations and their characterisation by the Burgers circuit and line direction are described. The Green’s function plays a central role in Volterra’s formula for the displacement field of a dislocation and Mura’s formula for the strain and stress fields. The isotropic elastic fields of edge and screw dislocations are derived. The field of an infinitesimal dislocation loop and its dipole tensor are also derived. The elastic energy of interaction between a dislocation and another source of stress is derived, and leads to force on a dislocation. The elastic energy of a dislocation and the Frank-Read source of dislocations are also discussed. Problem set 6 extends the content of the chapter in several directions including grain boundaries and faults.