Bimaterial comers

Mohammed, H. and Leichti, K.M., Cohesive zone modeling of eracknncleation at bimaterial comers, Journal of the Mechanics and Physics of Solids, 2000,48,735-764. 

The main emphasis of this chapter will be on the basic fracture mechanics concepts for cohesive and adhesive fracture with some extension to crack branching and crack nucleation from bimaterial comers. Most of the current fracture mechanics practice in testing adhesives and designing of adhesively bonded joints is limited to linear elastic fracture mechanics concepts. The development of the background material presented here will therefore be similarly constrained, except for the last section. Historically, fracture mechanics developed from energy balance concepts and examinations of stresses around crack tips. The adhesive fracture community has tended to favor the former, but both have useful features and will be carried forward in the discussions that follow. 

Adhesively bonded joints abound with bimaterial comers. These can be sources of crack nucleation due to the stress concentrations that can be associated with them. The simplest situation arises when one of the materials is comparatively rigid. In that case, we have a plate, which is clamped along one boundary and free on the other (Fig. 16). This is one of several combinations of boundary conditions at a corner that Williams [61] considered. With a polar coordinate system originating at the comer, it can be shown that the stresses have the form... 

When both materials are compliant, singular stresses can also occur. The situation is more complicated because now there may be multiple singularities and they depend on the elastic properties of each material in addition to the corner angles in each material (Fig. 18). There are several ways to present the state of stress near a bimaterial comer. One common approach is given below. 

Elastoplastic analyses of bimaterial comers have also been conducted, albeit more recently. A singularity analysis based on 72-deformation theory was devel-... 

Labossiere, P.E.W., Dunn, M.L., and Cunningham, S.J., Application of bimaterial interface comer failure mechanics to silicon/glass anodic bonds, Jourruil of the Mechanics and Physics of Solids 2002, 50,405-433. 

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