Elastic interactions of point defects in a semi-infinite medium

Abstract

Two problems involving the elastic interactions of point defects in a semi-infinite, isotropic elastic medium, bounded by a planar, stress-free surface, have been solved. The first is the determination of the energy of interaction of a point defect with the surface. The point defect is represented by the superposition of three, mutually perpendicular, double forces without moment, of unequal strength, one of which is perpendicular to the plane of the surface. The interaction energy is negative and decreases as the inverse third power of the distance of the defect from the surface. The second problem solved is the determination of the energy of interaction of two such defects. In the case that both defects are isotropic (the three double forces without moments have equal strengths) there is no interaction at a distance between these two defects in an infinitely extended medium. In the presence of a surface, however, they interact with an energy that varies as the inverse cube of the function [(x ∥ (1) − x ∥ (2)) 2 + (x 3 (1) + x 3 (2)) 2] 1 2 , where (x ∥ (1), x 3 (1)) and (x ∥ (2), x 3 (2)) are the positions of the two defects, and which can be attractive or repulsive depending on the relative orientation of the two defects. In both cases the results are obtained analytically, in closed form, by a Green function approach.