A DOUBLY PERIODIC RECTANGULAR ARRAY OF FIBER-MATRIX INTERFACIAL CRACKS UNDER LONGITUDINAL SHEARING

The antiplane strain problem of a unidirectional fiber composite consi sting of a doubly periodic rectangular array of fibers containing inte rfacial cracks in an infinite matrix is considered. The interfacial cr acks are assumed to exhibit the same periodicity as the fibers. The pe riodicity of the geometry allows the use of a unit cell in the formula tion of the problem. The governing weakly singular integral equation o f the mixed boundary value problem permits an explicit solution which contains a set of unknown constants. The unknown constants are then de termined by satisfying the boundary conditions on the external surface s of the unit cell through the method of least squares. The stress int ensity factor is calculated for various crack lengths, fiber volume fr actions, and fiber spacings. Unlike the plane strain or plane stress d eformation, the oscillations in stress and displacement around the int erface crack tip are absent in the current antiplane strain problem.