Abstract
Prior to determining the conditions of brittle and quasi-brittle fracture of elastic solids with cracks, it is necessary to solve the corresponding three-dimensional elasticity problem. Since analytical solutions are known only for certain simple configurations such as an infinite space containing a plane, penny-shaped, or elliptical crack, and a half-plane or a strip crack [1–3], numerical procedure may have to be used.This paper is concerned with a tensile crack (or Mode I crack) on a plane domain in infinite elastic medium. A technique is proposed for constructing exact solutions for crack configurations that are obtainable by inversion transformation from the canonical contours such as a circle, ellipse or half-plane, for which exact solutions are known. Simple formulae are derived which yield the stress intensity factor distribution over the transformed crack boundary with loads appropriately adjusted according to the initial crack region. Hence, it is not necessary to find the complete solution. Solutions obtained by this method are presented for cracks bounded by convex as well as nonconvex contour, i.e., oval and sickle-shape contours.
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