Analysis of the fiber-matrix cylindrical model with a circumferential crack

An axisymmetrical fiber-matrix cylindrical model with a circumferential crack in the matrix of finite diameter 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, stress intensity factors associated with the crack length and the material properties are calculated and discussed. The solutions presented in this study are found to be general, including the solutions as special cases of the present formulation for a homogeneous solid cylindrical bar and a thick-walled shell with an outer circumferential crack.