Elastic fields in polycrystalline or composite materials with slip inclusions

Abstract

Inclusion slip induced by eigenstrains in polycrystalline or composite materials is modeled by adding Somigliana dislocations along the matrix-inclusion interface. It is shown that the elastic strain energy of a slip inclusion is in the minimum state. Therefore, a general and simple method to determine the slip represented by the Burgers vector is developed through the principle of minimum strain energy. The corresponding surface dislocation density is then obtained analytically. Following the eigenstrain formulation, the associated elastic fields inside and outside a slip spherical inclusion are presented in closed form. The results show that strains and stresses in the slip inclusion are not uniform, in contrast to the perfectly bonded inclusions where Eshelby's solution holds. The results of this work can be readily utilized in the solution of numerous problems pertaining to slip such as grain boundary sliding in polycrystals and granular media, behavior of precipitates at high temperature, and debonding of fibers in composite materials.