Dynamic response of a crack in a functionally graded material between two dissimilar half planes under anti-plane shear impact load

摘要

This article provides a theoretical and numerical treatment of a finite crack subjected to an anti-plane shear impact load in a media with spatially varying elastic properties. This variation is in a direction perpendicular to the crack surfaces.The elastic properties of the interfacial aver are assumed to vary continuously between that of two dissimilar homogeneous bonding layers. Laplace and Fourier transforms are applied to reduce this mixed boundary value problem to a system of dual integralequations which in turn will be reduced to a standard Fredholm integral equation of the second kind The Fredholm integral equation is solved in the Laplace transform plane numerically. The time inversion is accomplished by a numerical scheme. The dynamicstress intensity factor is found to either increase or decrease with the crack length to the layer thickness depending on the relative magnitudes of the material properties of the adjoining layer.