The multiple parallel cracks in an orthotropic non-homogeneous infinite plane subjected to transient in-plane loading

In this paper, the mixed mode fracture problem of multiple parallel cracks in an orthotropic functionally graded plane under transient dynamic loading is studied. The medium contains Volterra type glide and climb edge dislocations. It has been assumed that the Young's modulus and mass density of materials vary exponentially along the x-axis. The distributed dislocation technique is used to obtain a system of integral equations for the transient dynamic problem. At first, with the help of Fourier and Laplace transforms the dislocation problem is solved and the stress fields are obtained. The integral equations are of Cauchy type singularity, and are solved numerically using the Lobatto-Chebyshev integration formula in order to evaluate the dislocation densities on the face of several cracks. Several numerical examples are solved to show the effects of the orthotropy and non-homogeneity parameters on the dynamic stress intensity factors.