Effects of the weak/micro-discontinuity of interface on the fracture behavior of a functionally graded coating with an inclined crack

The mechanical model was established for the anti-plane fracture problem of a functionally graded coating–substrate system with a coating crack inclined to the weak/micro-discontinuous interface. The Cauchy singular integral equation for the crack was derived using Fourier integral transform, and the Lobatto–Chebyshev collocation method put up by Erdogan and Gupta was used to get its numerical solution. Finally, the effects of the weak/micro-discontinuity of the interface on SIFs were analyzed, the “affected regions” corresponding to the two crack tips have been obtained and their engineering significance was discussed. It was indicated that, for the crack tip in the corresponding “affected region”, to reduce the weak-discontinuity of the interface and to make the interface micro-discontinuous are the two effective ways to reduce the SIF, and the latter way always has more remarkable SIF-reduction effect. For the crack tip outside the “affected region”, its SIF is mainly influenced by material stiffness, and to prevent such a tip from growing toward the interface “softer coating and stiffer substrate” is a more advantageous combination than “stiffer coating and softer substrate”.