A Shear Stress Relaxation Model for Continuous Fiber Reinforced Unidirectional Metal Matrix Composites with Fiber Breakages.

Abstract

A model is presented to express the relaxation of the interfacial shear stress acting on the ineffective part of a broken fiber in a unidirectional metal matrix composite reinforced with long brittle fibers. A cylindrical cell containing a broken fiber is considered, and a bilinear approximation of the fiber stress distribution in the broken fiber is employed to derive a simple differential equation for the relaxation of the interfacial shear stress. The resulting equation is applied to the cell subjected to constant or increasing strain. It is thus shown that the interfacial shear stress relaxes very slowly in comparison with the axial stress in the matrix, and that the analytical solution obtained in the case of constant strain agrees well with the numerical analysis performed by Du and McMeeking. The effect of the radial gradient of matrix shear stress on the interfacial shear stress relaxation is also discussed.