The Effect of a Layer on a 3-D Crack within the Substrate of a Layer/Substrate System

Abstract

A new numerical scheme is described for calculating the elastic field in an elastic layer/half-space caused by an embedded crack subjected to a general internal pressure and shear traction in the substrate. This scheme is based on the body force method associated with Green's functions for two perfectly bonded half-spaces, and the free surface of the coating layer is modeled by a much larger crack than the substrate crack. Thus, the surface displacement of the coating layer, which is useful for many applications, can be easily estimated from the crack opening displacements of the larger crack. Although the method can be applied generally, for simplicity, only a penny-shaped crack in a substrate subjected to a uniform tension at infinity is considered in this analysis. The effects of layering on stress intensity factors and surface displacements were also investigated.

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