Discontinuous constitutive response of brittle matrix fibrous composites

Abstract

A bridged-crack model is proposed in order to explain and reproduce the constitutive flexural response of brittle matrix fibrous composites. This response is often discontinuous owing to the presence of virtual catastrophic branches; i.e. snap-through with load-control and snap-back with deflection-control. The bridging tractions are assumed as constant plastic forces, whereas the cracks run in an elastic brittle matrix. The bridged-crack model accounts very well for small-scale microstructural studies of fibre-reinforced materials, or in the case of a rather small number of reinforcements, rivets or patches. The bridged-crack model results approach those of the cohesive-crack model of the Dugdale type when the density of the bridging elements tends to infinity. The role of size scale is fundamental for the global structural behaviour, which can range from ductile to catastrophic simply with the variation of a dimensionless brittleness number, which is a function of matrix toughness, reinforcement yielding or slippage limit, reinforcement volume fraction and characteristic structural size. When the matrix is over-reinforced, the case of brittle crack propagation across the specimen is predicted, while, at the same time, intact bridging ligaments remain over most of the crack wake.