A Crack Very Close to a Bimaterial Interface

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Abstract
This paper presents the plane elastostatics analysis of a semi-infinite crack perpendicular to a perfectly bonded bimaterial interface. Both cases of the crack approaching the interface and penetrating the interface are addressed. The distance from the tip of the crack to the interface is δ. A singular integral equation approach is used to calculate the stress intensity factor, K I , and the crack-opening displacement at the interface, η, as functions of δ, the Dundurs parameters α and β, and the stress intensity factor k I associated with the same crack terminating at the interface (the case δ = 0). The results are presented as KI = kIδ1/2−λf(α, β) and η = CkIδ1−λη̃(α, β) where λ is the strength of the stress singularity associated with δ = 0, f and η̃ are functions calculated numerically and C is a material constant. These results can be used to determine the stress intensity factor and crack opening displacement of cracks of finite length 2a with one tip at a distance δ from the interface for δ/a ≪ 1. The selected results presented for a crack loaded by a uniform far-field tension in each half-plane show that the stress intensity factors approach their limits at a relatively slow rate.