Computation of mixed mode stress intensity factors for multiple axisymmetric cracks in an FGM medium under transient loading

Abstract

In the present study, mixed-mode dynamic stress intensity factors (DSIFs) for the multiple axisymmetric cracks in an FGM medium under transient in-plane loading are formulated. It is assumed that the mass density and the shear modulus of the medium vary exponentially along the z-axis. The solution to the problem weakened by prismatic and radial dynamic dislocations is first obtained with the aid of the Laplace and Hankel transforms. This solution is used to construct integral equations in the Laplace domain for a system of coaxial axisymmetric cracks, including annular and penny-shaped cracks. The integral equations are of Cauchy singular type, which are solved numerically to obtain the dislocation density on the faces of the cracks and the results are used to determine DSIFs for cracks. Numerical examples are provided to study the effects of nonhomogeneity parameter and axisymmetric crack type as well as the interaction of multiple cracks on the DSIFs.