Dynamic mode III stress intensity factors of multiple axisymmetric interfacial cracks in an FGM coated orthotropic layer

In the present study, mode III dynamic stress intensity factors (DSIFs) for the multiple axisymmetric interfacial cracks in an orthotropic layer with FGM orthotropic coating under transient torsional loading are formulated. It is assumed that the mass density and the shear modulus of the FGM orthotropic coating vary exponentially and power-law form along the thickness of the layer. At first, the solution for Somigliana-type dynamic rotational ring dislocation in the layer and its coating is obtained by using the Laplace and Hankel transforms. Then, the dislocation solution is used to derive a set of singular integral equations for a system of coaxial axisymmetric interfacial cracks, including penny-shaped and annular cracks. 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 DSIFs for axisymmetric interfacial cracks. Finally, several examples are provided to study 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 DSIFs.