Analysis of a fiber-matrix axisymmetrical model with a circumferential crack

A fiber-matrix cylinder with a circumferential crack in the matrix is formulated within elastostatic scope. The problem is considered by means of integral transforms and a singular integral equation with a dominant generalized Cauchy kernel is obtained. Following the numerical solution technique developed by Erdogan, Gupta and Cook, the singular integral equation is reduced to a system of linear equations. By solving the linear equations, the stress intensity factor associated with the depth of the crack length and the material properties is calculated and discussed. The solutions presented in this study are found to be general, including those obtained as special cases of the present formulation for a homogeneous solid cylindrical bar and a thick-walled shell with an outer circumferential crack.