An analysis of edge dislocation pileups against a circular inhomogeneity or a bimetallic interface

Equilibrium configurations of edge dislocation pileups against a circular inhomogeneity or a bimetallic interface are determined numerically for a given number N of dislocations, the applied shear stress τ, the size of the inhomogeneity, and the degree of material disparity. The increase of applied stress moves a pileup closer to the inhomogeneity and increases the density of dislocations within a pileup, which is more pronounced for smaller and softer inhomogeneities due to their weaker repulsion of dislocations. The configurational force exerted by the pileup on a circular inhomogeneity is equal to Nτbx, where bx is a Burgers vector of dislocations, plus a term dependent on dislocation positions and material properties. The configurational force on a bimetallic plane interface is equal to Nτbx, independently of dislocation positions and material properties. The stress concentration caused by dislocation pileups against different interfaces is evaluated and discussed, which is of importance for the study of interface cracking. In general, the increase of the shear modulus and the Poisson ratio disparities (G2/G1 and ν2/ν1, where the subscript 1 specifies the material in which dislocations reside) diminishes the interface stresses.