Kinked crack in anisotropic bodies

Solutions are presented for a crack kinking out of the crack plane in a generally anisotropic elastic body under two-dimensional deformation. Based on Stroh formalism, a system of singular integral equations governing the kinking crack with small kink length is given in a simple, straightforward form. The explicit expressions of the stress intensity factors, T-stresses, and energy release rates at the kinked crack tip are presented in terms of some nondimensional coecients together with the stress intensity factors, T-stresses, and the coecients of the third term acting on the main crack tip prior to crack kinking. The nondimensional coecients depend on kink angle and material constants, but not on kink length. The energy release rate ratio which may characterize the competition along di€erent crack growth directions is provided. The role of T-stresses and the third-term applied at the main crack ®eld are determined which can be signi®cant in the kinking and the stability of the kinked crack. Based on the energy release rate fracture criterion, the stability condition of the kinked crack is derived. The in¯uences of anisotropy and loading mixity on the implications of crack kinking behavior is also given. The results for monoclinic materials with symmetry plane at x3 ˆ 0 are derived from general results. Numerical results for the stress intensity factors, T-stresses at the kinked acrack tip and the energy release rate ratio for some special cases are provided. The dimensionless coecients for crack kinking of orthotropic materials at the right angle to the main crack plane are tabulated