Time-harmonic analysis of multiple interface cracks in two dissimilar FGM half-planes: In-plane problem

Abstract

In this study, the dynamic stress intensity factors (DSIFs) at the tip of several cracks located at the interface between two half-planes made of functionally graded materials (FGMs) are calculated using the Distributed Dislocation technique (DDT). In this paper, the in-plane time-harmonic loading is considered and it is assumed that the properties of the FGMs follow the law of exponential function. First, the problem of two dissimilar half-planes that are weakened by an interface Volterra type climb and glide edge dislocation is solved using the Fourier transform, and then, using the DDT, singular integral equations with a singularity of the Cauchy type are extracted. To calculate the DSIFs at the cracks tips, the resulting singular integral equations are numerically discretized and the dislocation densities on the crack surfaces are obtained. Second, the graphs are presented in the numerical results section to show the effects of change in the parameters such as non-homogeneous constant, Poisson ratio, crack length, frequency and interaction between the cracks on DSIFs.