Elastostatic interaction of cracks in the infinite plane

The stress boundary value problem of an infinite, planar region with embedded rectilinear cracks is investigated from the viewpoint of two-dimensional, static, linear elasticity theory (plane strain or generalized stress). Any finite number of cracks may be considered. Their orientation may be arbitrary, so long as they do not intersect. Boundary loadings may take the form of quite general in-plane tractions along the crack surfaces, together with a bounded in-plane stress field at infinity. Using Muskhelishvili’s solution for colinear cracks, the problem is reduced to a set of one-dimensional Fredholm integral equations. A simple numerical technique is presented for the approximate solution of these equations. The method is established to possess an extremely high rate of convergence. Results are presented for a number of two-crack interaction problems. As expected, the interaction of the cracks generally tends to reduce the fracture strength of a material, relative to the strength that would exist with either crack acting independently. However, for certain orientations, it is found that the interaction phenomenon can actually increase the resistance to fracture