Small scale geometric and material features at geometric discontinuities and their role in fracture analysis

We consider the role of small scale geometric and material features at geom etric discontinuities other than a crack and study their relevance to fract ure analysis. We are motivated by relatively recent experiments that show t hat under certain circumstances fracture initiation from geometric (sharp n otches) and material (bimaterial interface corners) discontinuities can be successfully correlated with critical values of stress intensities that ari se from a linear elastic analysis of the corresponding singular stress stat e. Implicit to such an approach is the idea that perturbations of the elast ic fields near the discontinuity, which of course destroy the singular stre sses, occur over a scale that is sufficiently small so that the complex beh avior in this region is correlated by the elastic stress intensity. While t he fracture mechanician will recognize these ideas as extensions of classic al linear elastic fracture mechanics, significant differences exist and the se are discussed in detail. We motivate the ideas through the use of a seri es of model problems in antiplane shear that are mostly amenable to exact a nalyses. We expect that the ideas carry through, albeit at the expense of f ar more complicated analysis, to planar and even three-dimensional situatio ns.