Independence of the presence of cracks or inclusions of the net interaction force acting on a dislocation by a skewed line singularity

Orlov and Indenbom [1] have shown that the net (integrated) interaction for ce F between two skew dislocations with Burgers vectors (b) over cap, b sep arated by a distance h in an infinite anisotropic elastic medium is indepen dent of h. Nix [2] computed numerically the net interaction force F between two skew dislocations that are parallel to the traction-free surface x(2) = 0 of an isotropic elastic half-space. His numerical results showed that F was independent of h; a partial result of what Barnett [3] called Nix's th eorem. The separation-independence portion of Nix's theorem has been proved to hold for a general anisotropic elastic half-space with a traction-free, rigid, or slippery surface, and for bimaterials [3-5]. In this paper, we s how that the net interaction force F(on (b) over cap) is independent of the presence of inclusions. We will consider the case in which the line disloc ation b is a more general line singularity which can include a coincident l ine force with strength f per unit length of the line singularity. An inclu sion is an infinitely long dissimilar anisotropic elastic cylinder of an ar bitrary cross-section whose axis is parallel to the line singularity (f, b) . The (skew) line dislocation (b) over cap does not intersect the inclusion . The special cases of an inclusion are a void, crack, or rigid inclusion. There can be more than one inclusion of different cross sections and differ ent materials. The line singularity (f, b) can be outside the inclusions or inside one of the inclusions. The inclusions and the matrix need not have a perfect bonding. One can have a debonding with or without friction.