Stress field analysis near the semi-infinite crack tip terminating perpendicular to the interface between two orthotropic materials

Abstract eng:
The study of the stress and displacement field near the semi-infinite crack tip terminating perpendicular to the interface between two orthotropic materials is considered in this paper. Using an anisotropic complex method, the present analysis gives singularity exponents and − as the solution of an eigenvalue problem and as the root of some nonlinear equation. This leads to a closed-form expression for stresses and displacements. The matrix of the eigenvalue problem depends on the number of layers at the singular point, their relative elastic properties and the boundary conditions such as free surface or bonded interface close to the crack tip. While the is associated to the singular solution of the semi-infinite crack problem, the − is associated to the auxiliary solution. The auxiliary solution features stronger singularity and can be used to determination of the generalized intensity factor by the ψ-integral.

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