A Model for Shear Stress Relaxation around a Fiber Break in Unidirectional Metal Matrix Composites

Abstract

A model is presented to have insights into the shear stress relaxation around a fiber break in unidirectional metal matrix composites 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 shear stress relaxation. The resulting relaxation equation is applied to the cell subjected to either constant or increasing strain. It is thus shown that the shear stress relaxes very slowly in comparison with the axial normal 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. It is also shown that the relaxation equation under constant strain is almost derivable on the basis of the overall balance of energy in the cell. In addition effect of the radial gradient of shear stress in the matrix is discussed.