Branched Cracks in Anisotropic Elastic Solids

Abstract

Branched crack problems are analyzed in two-dimensional, anisotropically elastic homogeneous solids. The method of analysis is based on the complex variable approach of Savin and Lekhnitskii. The Hilbert problem in an anisotropic body is defined, and a pair of singular integral equations are derived for dislocation density functions associated with a branched crack. For both symmetric and nonsymmetric geometries, and under symmetric and antisymmetric loads, the stress intensity factors and the energy release rate are computed numerically by extrapolation for infinitesimally small lengths of branched cracks. The results are compared with those of the isotropic case given in the literature and the effects of anisotropy are discussed.