The influence of reinforcing fibres on the growth of cracks in brittle matrix composites

Abstract

The use of fibres to improve the work-of-fracture and strength of brittle matrices has gained interest in a number of fields, especially in the cement and plaster industry, and also in h igh-temperatu re applications of ceramics and glasses. Here a theoretical analysis is presented to account for the enhanced strain-to-failure values of a brittle matrix containing microcracks and reinforced with fibres. The theory assumes that the Griffith energy criterion for failure applies when a crack is present in the matrix. It predicts the stabilizing effect of a unidirectional uniform distribution of fibres which bridge a matrix crack by computing the rates of release of strain energy and of absorption energy with increasing length of a matrix crack. Published experimental data on the carbon fibre reinforced glass system is used to compare the predictions of the theory here with a version given by Aveston, Cooper and Kelly. Descriptions of the boundary conditions of single and multiple fracture are given. The theory is shown to further indicate the possible existence of an upper limit to the fibre volume fraction at which multiple fracture occurs, i.e. when the fibres stabilizing the crack cannot support the load. Applications of the analysis to the design of composite systems of technological importance are suggested.