An extended Bueckner–Rice theory for arbitrary geometric perturbations of cracks

The aim of this paper is to define a new, simple and efficient method of solution of elasticity problems for 3D bodies containing cracks slightly perturbed out of their original plane or surface. This method extends that proposed by Rice (1985, 1989), from a re-formulation of Bueckner (1987)’s 3D weight function theory, for the treatment of coplanar crack perturbations. First, a general formula is derived for the variation of total energy of a cracked elastic body, resulting from some small but otherwise arbitrary geometric perturbation of the embedded crack(s). This formula, which involves integrals over both the front and the surface of the crack, is derived from an expression of deLorenzi (1982) and Destuynder et al. (1983) in the form of a volumic integral, originally limited to purely tangential crack perturbations but duly extended here to arbitrary perturbations having both tangential and normal components. It is then used to derive a general expression of the variation of displacement arising from a general perturbation of the crack(s), anywhere in the cracked body. The reasoning here basically follows the same lines as in the works of Rice (1985, 1989), but for the presence of an additional normal component of the crack perturbation. The possible use of the formalism developed to treat problems of out-of-plane, or out-of-surface perturbations of cracks is finally briefly evoked; the straightforwardness of the new method proposed is hoped to permit future applications to non-coplanar crack problems too complex to be accessible by more conventional methods.