Abstract
In this paper, the problem of a penny-shaped crack in the center of multiple concentric cylinders is considered. By making appropriate choices for the stress functions in each of the constituents and making the standard assumptions of linear elasticity, it is possible to reduce the problem to the solution of a Fredholm integral equation of the second kind which may be solved numerically. This solution is used in conjunction with a geometry approximation to model the stress concentrations due to a broken fiber in a unidirectional composite material. The results suggest that models of such a shear lag may be missing important features of the stress state including surrounding broken fibers in composite materials.
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