Upper bounds for the stress intensity factors along the boundaries of interacting coplanar cracks in three-dimensional elasticity

An elementary method for obtaining upper bounds for the stress intensity factors along the boundaries of interacting coplanar cracks inside an infinite isotropic elastic medium is presented. This method is based on the singular integral equation of the aforementioned elasticity problem and on the solutions of this equation for each particular crack problem, assumed known. The method is applied to the simple problem of interaction of two circular cracks, as well as to the similar problem of two cracks having the shape of a straight strip. The present results constitute a generalization of the corresponding method for crack problems in two-dimensional elasticity and can easily be further generalized to apply to more complicated crack problems in three-dimensional elasticity.