On the Changing Order of Singularity at a Crack Tip

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Abstract
The nature of the transition in the crack tip stress singularity from an inverse square root to an inverse fractional power as a crack tip reaches a phase boundary or a geometrical discontinuity for interface cracks is examined. This is done by analyzing the simple closed-form solution to the problem of a rigid line inclusion with one side partially debonded for the case of antiplane deformation. For this example, the crack tip stress singularity changes from an inverse square root to an inverse three-quarters power as the crack tips approach the inclusion tips (i.e., when one face of the rigid line inclusion is completely debonded). A detailed analysis, based on series expansions of the closed-form solution, is used to show how the singularity transition occurs. Moreover, the expansions indicate difficulties that may be encountered when solving such problems by approximate methods.

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