Very high stresses develop near the intersection of a planar interfacial crack with the free surface of joined materials with large mismatch of elastic moduli. The socalled corner singularity is more singular than the $1/distance$ singularity of the interior fields. The eigenvalues corresponding to the most singular state, and for which the strain energy of a finite cone is bounded, are in general complex. For a wide selection of material pairs, our calculations show that the eigenvalue of the dominant singularity, 0(r−s), is real and s increases from 0.5 to about 0.75 as the moduli mismatch increases. Values of s are reported for a broad range of material combinations. A class of anisotropic materials and bicrystals is also investigated.

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