Penny-shaped crack in a fiber-reinforced matrix

Using the slender inclusion model developed earlier the elastostatic interaction problem between a penny-shaped crack and elastic fibers in an elastic matrix is formulated. For a single set and for multiple sets of fibers oriented perpendicularly to the plane of the crack and distributed symmetrically on concentric circles the problem is reduced to a system of singular integral equations. Techniques for the regularization and for the numerical solution of the system are outlined. For various fiber geometries numerical examples are given and distribution of the stress intensity factor along the crack border is obtained. Sample results showing the distribution of the fiber stress and a measure of the fiber-matrix interface shear are also included.