Application of a linear elastic - brittle interface model to the crack initiation and propagation at fibre-matrix interface under biaxial transverse loads

Abstract

The crack onset and propagation at the fibre-matrix interface in a composite under tensile/compressive remote biaxial transverse loads is studied by a new linear elastic - (perfectly) brittle interface model. In this model the interface is represented by a continuous distribution of springs which simulates the presence of a thin elastic layer. The constitutive law for the continuous distribution of normal and tangential of initially linear elastic springs takes into account possible frictionless elastic contact between fibre and matrix once a portion of the interface is broken. A brittle failure criterion is employed for the distribution of springs, which enables the study of crack onset and propagation. This interface failure criterion takes into account the variation of the interface fracture toughness with the fracture mode mixity. The main advantages of the present interface model are its simplicity, robustness and its computational efficiency when the so-called sequentially linear analysis is applied. Moreover, in the present plane strain problem of a single fibre embedded in a matrix subjected to uniform remote transverse loads, this model can be used to obtain analytic predictions of interface crack onset. The numerical results provided by a 2D boundary element analysis show that a fibre-matrix interface failure initiates by onset of a finite debond in the neighbourhood of an interface point where the failure criterion is reached first (under increasing proportional load), this debond further propagating along the interface in mixed mode or even, in some configurations, with the crack tip under compression. The analytical predictions of the debond onset position and associated critical load are used for checking the computational procedure implemented, an excellent agreement being obtained.