A bridging law for creeping fibres Original Research Article

The problem of a creeping fibre being pulled out of a semi-infinite elastic matrix to which it is coupled by Coulomb friction is considered. Analytical approximations based on shear lag theory and the assumption of Lamé-like elastic fields lead to simple relations between the relative displacement of the end of the fibre and the surface of the matrix. The existence of a steady state configuration for the frictional contact zone between the fibre and the matrix is demonstrated, which propagates invariantly away from the surface of the matrix under constant applied loads. With trivial extensions, this relation yields a bridging traction law that would describe the relation between the crack opening displacement and the bridging tractions supplied by the fibres in the wake of a matrix crack in a composite. A useful, general result applicable to any traction history is obtained from the steady state results via a quasi-static approximation, which is valid if the tractions do not change too rapidly.