Elastic Wave Scattering From an Interface Crack in a Layered Half Space

Abstract

Many applications in industry utilize a layered elastic structure in which a relatively thin layer of one material is bonded to a much thicker substrate. Often the fabrication process is imperfect and cracks occur at the interface. This paper is concerned with the plane strain, time-harmonic problem of a single elastic layer of one material on a half space of a different material with a single crack at the interface. Green’s functions for the uncracked medium are used with the appropriate form of Green’s integral theorem to derive the scattered field potentials for arbitrary incident fields in the cracked layered half space. These potentials are used in turn to reduce the problem to a system of singular integral equations for determining the gradients of the crack opening displacements in the scattered field. The integral equations are analyzed to determine the crack tip singularity, which is found, in general, to be oscillatory, as it is in the corresponding static problem of an interface crack. For many material combinations of interest, however, the crack tip singularity in the stress field is one-half power, as in the case of homogeneous materials. In the numerical work presented here attention is restricted to this class of composites and the integral equations are solved numerically to determine the Mode I and Mode II stress intensity factors as a function of a dimensionless wave number for various ratios of crack length to layer depth. The results are presented in graphical form and are compared with previously published analyses for the special cases where such results are available.