Considering a crack that lies in one solid, but has a tip that touches an interface with a second solid, Bogy found that the assumption of a traction-free crack tip leads to oscillating singularities for certain combinations of materials. Such oscillating singularities lead to overlapping of the crack faces, and the purpose of this article is to eliminate the oscillating singularities by allowing the crack tip to be closed. Using an asymptotic analysis and incorporating the effect of friction, the nature of the singularity at the closed crack tip is established and the various consequences explored.

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