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The problem of an arc crack lying within the interface between a rigid elliptic inclusion and an unbounded matrix is considered under the assumption of plane deformation, and a general solution method, valid for other inclusion geometries, is presented. The particular example of a single arc crack debonding one end of the inclusion under uniaxial and equal biaxial loading at infinity is considered in detail. It is shown that, unless the matrix is incompressible in the plane of deformation, there is an oscillating square-root stress singularity at the crack tips. The strength of this singularity, referred to as the crack tip stress intensity factor, is analyzed for different ellipse shapes and applied loads. In particular, it is shown that (i) a crack debonding a slender inclusion will arrest when load is applied parallel to the inclusion, and (ii) the crack tip stress intensity factors become unbounded as the crack tip reaches a sharp geometrical discontinuity. This is shown to be a consequence of the change in the nature of the crack tip stress singularity in this case. Finally, the results are applied to a discussion of the debonding phenomenon observed in composite materials.
fracture properties, crack propagation, deformation, interfaces, cracks, crack interactions, composite materials, mechanical properties
Aerospace engineer, Air Force Flight Dynamics Laboratory, Dayton, Ohio