Crack onset and growth at the fibre–matrix interface under a remote biaxial transverse load. Application of a coupled stress and energy criterion

Abstract

A theoretical model for prediction of the critical load generating a crack onset at the fibrematrix interface under a remote biaxial transverse load is presented. In particular, this work is focused on the tension dominated failure. After an abrupt onset the crack grows unstably up to achieving an arrest length. A simple plane strain model of a single circular inclusion surrounded by an unbounded matrix allows to obtain conclusions approximately valid for a dilute fibre packing. Linear isotropic elastic behaviour is assumed for both inclusion and matrix. Two classical elastic solutions for both perfectly bonded and partially debonded circular inclusions are used together with a coupled stress and energy criterion, proposed recently in the framework of Finite Fracture Mechanics, and a phenomenological law for fracture toughness of interface cracks growing in fracture mixed mode. The obtained analytical and semi-analytical expressions make easy to study the influence of all the dimensionless parameters governing the fibrematrix system behaviour: Dundurs elastic bimaterial constants $\alpha$ and $\beta$, the interface brittleness number $\gamma$, the load biaxiality parameter $\eta$, and the fracture mode-sensitivity parameter $\lambda$. A size effect of the inclusion radius on the critical load is predicted, smaller inclusions being stronger and less dependent on the secondary load. Finally, an experimental procedure for measurement of the fibre-matrix interface fracture and strength properties is proposed.