Multiple interacting arbitrary shaped cracks in an FGM plane

In this paper, modes I and II stress intensity factors for the multiple curved cracks in a nonhomogeneous plane base on the dislocation technique are formulated. It is assumed that the Young's modulus of the medium varies exponentially along the x-axis. Stress analysis is carried out in a nonhomogeneous plane weakened by climb and glide of an edge dislocation. These solutions are used to derive a system of Cauchy singular integral equations for analyzing multiple curved cracks. The integral equations can be solved numerically to obtain dislocation densities on a crack face which are employed to calculate the mixed mode stress intensity factors. Several examples are presented to study the interaction of multiple arbitrary shaped cracks.