A fiber-reinforced matrix containing a penny-shaped crack under mode III loading condition

One of the fundamental problems related to the fracture of composite materials, that is, a penny-shaped crack in a fiber-reinforced matrix is solved under the Mode III loading condition, where the fibers are perpendicular to the crack plane and located along the crack border. An elastic fiber model is developed to the above torsional problem, yielding a Fredholm-type integral equation of the second kind for a set of fibers distributed symmetrically on a circle concentric with the crack. The integral equation is numerically evaluated, and the stress intensity factors are presented with the parameter of the fiber to matrix Young's modulus ratio for various geometries.