Threading Screw Dislocations in a Two-Phase Plate and a Two-Phase Sphere

Abstract

Abstract A screw dislocation perpendicular to free surfaces and an interface in a two-phase plate, and a screw dislocation piercing a two-phase hollow sphere are considered. The analytical solutions of the boundary-value problems have been found for the first time with the help of the virtual defects technique. Elastic fields of the screw dislocation in the plate are presented in the form of integrals with Bessel functions. Elastic fields of the screw dislocation in the hollow sphere have the form of series with Legendre polynomials. Stress distributions in both of the considered geometries are plotted. The influence of the geometric parameters of the considered solids and the ratio of the shear moduli on the stresses is analyzed. The interaction of a screw dislocation with a parallel edge dislocation is discussed.