Fracture analysis of multiple axisymmetric interfacial cracks in an FGM coated orthotropic layer

Based on the distributed dislocation technique, an analytical solution for the orthotropic layer with functionally graded material (FGM) orthotropic coating containing multiple axisymmetric interfacial cracks subjected to torsional loading is investigated. It is assumed that the material properties of the FGM orthotropic coating vary power-law form along the thickness of the layer. At first, by using the Hankel transform, the solution for Somigliana-type rotational ring dislocation in the layer and its coating is obtained. Then, the dislocation solution is used to derive a set of singular integral equations for a system of coaxial axisymmetric interface cracks, including penny-shaped and annular cracks. cracks with Cauchy type kernel. The integral equations are of Cauchy singular type, which are solved by Erdogan’s collocation method for dislocation density on the surface of interfacial crack and the results are used to determine stress intensity factors (SIFs) for axisymmetric interface cracks. Finally, several examples are provided to study the effects of the non-homogeneity constant, orthotropy parameter and thickness of FGM coating on the SIFs for interfacial cracks. The effects of the non-homogeneity constant, orthotropy parameter and thickness of FGM coating as well as the interaction of multiple interfacial cracks on the SIFs are investigated. The results reveal that the value of the SIFs decreases with increasing the non-homogeneity parameter, orthotropy and thickness of FGM coating. The SIFs for inner tips of annular interface crack are larger than the outer tips.