Mechanics of matrix cracking in brittle-matrix fibre-reinforced composites

Abstract

Energy-balance calculations for a continuum model of cracking in a uniaxially fibre-reinforced composite having a brittle matrix are presen­ted. It is assumed that the fibres are strong enough to remain intact when the matrix cracks across the entire cross section of the composite. By equating the energy availability for the cracking of continuum and discrete fibre models it is shown how the crack boundary condition relating fibre stress to crack opening must be selected. It is confirmed that the Griffith fracture criterion is valid for matrix cracking in composites. By considering the energy balance of long cracks it is shown that the limiting value of the stress intensity factor is independent of crack length and that it predicts a matrix-cracking strain that is consistent with the known result. An improved numerical method is described for solving a crack problem arising from the study of the cracking of brittle-matrix composites. Numerical results of high accuracy are obtained, which show how the cracking stress is related to the size of a pre-existing defect. Of special significance is the prediction of the correct threshold stress (i.e. matrix­-cracking stress) below which matrix cracking is impossible no matter how large the pre-existing defect.