The problem of two aligned orthotropic materials bonded perfectly along the interface with cracks embedded in either one or both of the materials while their directions being perpendicular to the interface is considered. A system of singular integral equations for general anisotropic materials is derived. Employing four effective material parameters proposed by Krenk and introducing four generalized Dundurs’ constants, the kernel functions appearing in the integrals are converted into real forms for the present problem which are keys to the present study. The kernel functions for isotropic dissimilar materials can be deduced from the present results directly, no any limiting process is needed. These kernel functions are then employed to investigate the singular behaviors for stresses at the point on the interface. Characteristic equation which determines the power of singularity for stresses is given in real forms for the case of cracks that are going through the interface. Studies of the characteristic equation reveal that the singular nature for the stresses could vanish for some material combinations and the singular nature for the stresses is found to be independent of the replacement of the material parameter Δ by Δ-1. The kernel functions developed are further used to explore analytically some interesting phenomena for the stress intensity factors, which are discussed in detail in the present context. Some numerical results for the stress intensity factors for a typical dissimilar materials are also given.

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