The current paper describes an anti-plane problem for an internal crack and an edge crack perpendicular to the interface of a functionally graded coating-homogeneous substrate structure for the material whose properties are one-dimensionally dependent. Integral transform and dislocation density functions are employed to reduce the problem to a solution of a system of singular integral equations. Numerical results show the effect of the material gradient parameter and crack configuration on the stress intensity factors of the functionally graded coating-homogeneous substrate structure.
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