Analysis of the interfacial stresses produced by a pile-up of discrete edge dislocations in two phase materials

Abstract

The local stresses associated with a pile-up of discrete edge dislocations against a welded interface at a second phase have been calculated using the elasticity solution of Dundurs. The calculations permit a study of the effects of applied stress, pile-up length, and the elastic properties of the two phases on the distribution of dislocations in the pile-up and on the stresses at the interface. The equilibrium positions of the dislocations and their discrete contributions to the stresses at the interface have been investigated for cases in which the shear modulus of the second phase is greater than and less than (or equal to) that of the matrix. For the latter case, the leading dislocation is assumed to be locked at the interface. The local stress is found to increase with applied stress and pile-up length, as expected. For a given applied stress and pile-up length, the stresses at the interface increase with decreasing shear modulus of the second phase and also depend on the Poisson's ratios of the two phases. The analysis is used to study the effects of microstructure on the plastic deformation of two phase alloys.