The annular crack surrounding an elastic fiber in a tension field

Matrix cracking in brittle-matrix fiber-reinforced composites is investigated when the fracture strain of the fiber is greater than that of the matrix. The axisymmetric problem of an infinitely long elastic fiber perfectly bonded to an elastic matrix which contains an annular crack surrounding the fiber is considered for the case of uniform longitudinal strain. The problem is formulated in terms of a singular integral equation with a Cauchy type kernel. When the inner crack tip terminates at the interface, it is shown that the characteristic equation is the same as that for the case of plane strain. Stress intensity factors at the crack tips are given when (a) the inner crack tip is away from the interface and (b) the inner crack tip is at the interface.