A shear-lag model with a cohesive fibre–matrix interface for analysis of fibre pull-out

A shear-lag model with a cohesive fibre–matrix interface has been developed for the analysis of stress transfer between the fibre and the matrix in fibre-reinforced composites in this paper. A bilinear cohesive damage evolution law is used to describe the fibre–matrix interface behaviour. The governing equations for the interfacial shear stress and the axial stress in the fibre are derived. Accurate analytical solutions are obtained when the fibre– matrix interface is in the initial linear elastic deformation regime. When debonding occurs, interfacial damage and softening are modelled by superposing two elastic stress systems and satisfying the damage evolution law at both ends of the damage process zone, and approximate analytical solutions are obtained. The stress distribution and evolution during the fibre pull-out, the maximum pull-out force and the pull-out curve have been analysed using a shear strength-based debonding criterion. Analytical expressions for the maximum fibre pull-out force and its limit as the embedded fibre length approaches infinity are obtained. In addition, the new function proposed for describing the radial distribution of the shear stress in the matrix fixes the problem of zero shear-lag parameter when b=a approaches infinity, enabling the shear-lag analysis to deal with low fibre volume fractions. Generally, the analytical solutions compare satisfactorily well to the cohesive finite element calculations and experimental data in the literature. 2015 Elsevier Ltd. All rights reserved.