Analysis of a mode III crack problem in a functionally graded coating-substrate system with finite thickness

摘要

This paper presents an analysis of the static problem of model III crack of a functionally graded coating-substrate system with an internal crack perpendicular to the interface under anti-plane shear loading when the coating layer and substrate have finite thickness. After the Fourier transform method is employed, the expressions of the displacement components can be obtained. Integral transforms are employed to reduce the problem to a singular integral equation that can be solved numerically. The influences of the non-homogeneity constant, relative crack length and thickness ratio are quantitatively studied.