Material instability in the tensile response of short-fibre-reinforced quasi-brittle composites

Abstract

This paper gives the conditions for the onset of instability in the tensile response of short-fibre-reinforced quasi-brittle composites whose deformation is characterised by multiple cracking and localisation. First, the tensile stress-strain relation is established analytically for a body containing multiple bridged microcracks. The material instability is examined using the classical bifurcation criterion, with an emphasis on the role played by fibre bridging in the macroscopic instability. It is found that while the microscopic instability in the bridging traction plays a major role in the macroscopic instability of the composite, it is the level of damage in the matrix that determines when the macroscopic instability is induced by the bridging instability. The satisfaction of the classical bifurcation criterion is identified with several failure modes, depending on the degree of damage in the matrix.