DEVELOPMENT OF GENERALIZED PLANE-STRAIN TENSORS FOR THE CONCENTRIC CYLINDER

A pair of two new tensors called GPS tensors S and D is proposed for t he concentric cylindrical inclusion problem. GPS tensor S relates the strain in the inclusion constrained by the matrix of finite radius to the uniform transformation strain (eigen strain), whereas tensor D rel ates the strain in the matrix to the same eigenstrain. When the cylind rical matrix is of infinite radius, censor S reduces to the appropriat e Eshelby's tenser. Explicit expressions to evaluate thermal residual stresses sigma(tau), sigma(theta) and sigma(z) in the matrix and the f iber using tensor D and tensor S, respectively, are developed. Since t he geometry of the present problem is of finite radius, the effect of fiber volume fraction on the stress distribution can be easily studied . Results for the thermal residual stress distributions are compared w ith Eshelby's infinite domain solution and finite element results for a specified fiber volume fraction.