A Doubly Periodic Rectangular Array of Fiber-Matrix Interfacial Cracks Under Longitudinal Shearing

Abstract

The antiplane strain problem of a unidirectional fiber composite consisting of a doubly periodic rectangular array of fibers containing interfacial cracks in an infinite matrix is considered. The interfacial cracks are assumed to exhibit the same periodicity as the fibers. The periodicity of the geometry allows the use of a unit cell in the formulation of the problem. The governing weakly singular integral equation of the mixed boundary value problem permits an explicit solution which contains a set of unknown constants. The unknown constants are then determined by satisfying the boundary conditions on the external surfaces of the unit cell through the method of least squares. The stress intensity factor is calculated for various crack lengths, fiber volume fractions, and fiber spacings. Unlike the plane strain or plane stress deformation, the oscillations in stress and displacement around the interface crack tip are absent in the current antiplane strain problem.