Crack front rotation and segmentation in mixed mode I + III or I + II + III. Part I: Calculation of stress intensity factors

This paper and its companion are devoted to the theoretical analysis, compared with experiments, of crack front rotation and segmentation in brittle solids under mixed mode I + III or I + II + III loadings. A first, indispensable task, which is the topic of the present paper, consists of evaluating the stress intensity factors along the front of a crack after rotation or segmentation of this front. The method of analysis combines three elements. The first one is 3D matched asymptotic expansions. The second one is an analogy with the related problem of a planar crack, but with a slightly wavy front. The output of these two ingredients is the reduction of the search for the quantities of interest to the solution of some 2D, plane strain or antiplane elasticity problems. The third element consists of the use of Muskhelishvili's complex potentials formalism and conformal mapping to solve these problems.