A shear-lag model for a broken fiber embedded in a composite with a ductile matrix

A shear-lag model has been developed for the prediction of stress recovery in a broken fiber embedded in a ductile-matrix composite. The model builds on the original shear-lag model of (Cox HL. Br J Appl Phys 1952;3:72–9) by introducing plasticity constitutive behavior into the matrix. The matrix is assumed to be an elastic/perfectly-plastic material that deforms according to J2 flow theory. The use of a flow rule to govern the matrix deformation in this model differs from previous attempts to represent plasticity in the matrix. A non-linear partial differential equation is obtained from the model. Numerical solutions to the equation are obtained and compared to simpler shear-lag models which assume sliding at the fiber/matrix interface controlled by a uniform shear stress. Axisymmetric finite-element calculations were done to assess the validity of the shear-lag model. It proves to be in good agreement with the finite-element analysis. Predictions of the shear-lag calculations suggest that the global load-sharing (GLS) strength model of (Curtin WA. J Am Ceram Soc 1991;74:2837–45) is valid for a composite with a yielding matrix that is elastically rigid.