The method of continuously distributed dislocations is used to obtain the exact solution for the distribution of screw dislocations in a linear array of length L piled up against a circular inclusion of radius R and finite shear modulus. The solution presented is valid for 0 < G2/G1 < ∞, where G2 is the shear modulus of the inclusion and G1 is the matrix shear modulus.The solution enables one to study simultaneously the effects of second-phase size and rigidity upon N, the number of dislocations in the pileup, and upon the local stresses induced in the second phase. In the second phase close to the pileup tip it is shown that the local stresses vary as: (1) (2L/ρ)g, when the inclusion diameter is much greater than the slip line length; [Formula: see text], when the particle diameter is much less than the slip line length, ρ is the radial distance from the pileup tip, and g is a function only of the shear moduli ratio, G2/G1, with 0 < g < 1. The effects of varying second-phase size and rigidity upon the magnitude of the local stresses is explained in terms of image dislocation forces generated by the presence of the inhomogeneity ahead of the pileup.
