CRACK PATHS IN PLANE SITUATIONS .2. DETAILED FORM OF THE EXPANSION OF THE STRESS INTENSITY FACTORS

In a previous paper, we established the general form of the expansion of the stress intensity factors in powers of the crack extension length, for a crack propagating in a two-dimensional body along an arbitrary kinked and curved path. The aim of the present paper is to calculate precisely the various functions of the geometric and mechanical parameters which appear in this expansion. The functions involved in the case of a straight extension are identified by considering the special case of a crack composed of two straight branches, placed in an infinite body loaded by uniform forces at infinity; the problem is solved with the aid of Muskhelishvili's formalism and conformal mapping. The functions describing the effect of the curvature of the crack extension are determined by studying another special case, identical to the first one except that the crack extension is curved; the method of solution consists of using a perturbative procedure with respect to the curvature parameters to reduce the original problem to a simpler one involving a crack with two straight branches, and solving again the latter problem by conformal mapping. A numerical strategy using these results for the prediction of crack paths over arbitrary long distances is discussed in conclusion.