Anti-plane stress analysis of cracked circular regions with outer coating

First, using the finite Fourier sine transform, the stress solution of a coated circular plane with a screw dislocation is achieved. In special case of study, namely an isotropic circular plane with a screw dislocation, the solution is validated using the method of images. After that, anti-plane deformation analysis of an intact coated circular plane under self-equilibrating traction is accomplished and the resulting stress field is computed. Also, via dislocation solution and the stress field of the intact coated circular plane under traction, integral equations are formulated for the same circular plane weakened by several cracks. The resulting singular integral equations, which are of Cauchy types, are solved numerically with the aim of finding the dislocation density functions on crack surfaces. The dislocation density functions on crack surfaces are used to determine the stress intensity factors (SIFs) of the tips of the cracks. The paper is furnished with several examples of a single crack and multiple cracks. For isotropic cases, the solution is validated by the published results in the literature. Effect of material properties of circular plane and its coating, thickness of coating as well as the crack location on the ensuing stress intensity factors at crack tips are studied.