Crack paths in plane situations—I. General form of the expansion of the stress intensity factors

Abstract

The aim of this series of papers is to provide formulas for the geometrical parameters (branching angle, curvature) of a crack propagating in the most general plane situation. These formulas can be used for numerical predictions of crack paths.The first paper addresses the problem of establishing the general form of the first three terms of the expansion of the stress intensity factors in powers of the crack extension length, i.e. of specifying the geometrical and mechanical parameters they depend upon. The treatment is bused on two main elements: dimensional analysis (scale changes) and regularity properties (continuity, differentiability) of the stresses with respect to the crack extension length. It is shown that most terms have universal expressions in the sense that they depend only on the parameters characterizing the local geometry of the crack and its extension and the stress field near the initial crack tip. whatever the geometry of the body under consideration and the prescribed forces or displacements.