Fracture analysis on the arc-shaped interfacial crack between a homogeneous cylinder and its coating

The mechanical model is established for a mode I arc-shaped crack along the interface between a functionally graded layer and a homogeneous cylinder. The displacement and stress fields are expressed in the form of infinite series by the method of variable separation. By introducing two dislocation density functions, the mixed boundary conditions of the crack are recast into a system of Cauchy singular integral equations, which are then solved numerically. Parametric studies on the stress intensity factors (SIFs) yield two aspects of guidelines for engineering designs. (a) The SIFs depend on the ratio between the outer and inner radii rather than their respective values, and 1.5 seems to be an optimal value for this ratio. (b) The outer graded layer should be stiffer than the inner homogeneous cylinder and large non-homogeneity parameter is beneficial to SIF reduction.