Effect of modulus and cohesive energy on critical fibre length in fibre-reinforced composites

Abstract

The effect of fibre modulus and cohesive energy on critical fibre length and radius in ceramic-fibre-reinforced brittle composites has been investigated employing both analytical theory and computer simulation. The theory consists of a shear-lag analysis in which an energy failure criterion is incorporated. The simulation consists of a two-dimensional computer model based upon a discrete network of grid points. Failure is also defined in terms of an energy criterion, where the energy is calculated on the basis of a two- and three-body interaction between the grid points. Both theory and simulation show that a minimum critical aspect ratio is found as a function of the elastic moduli ratio, Ef/Em, with a divergence occurring at both low- and high-modulus values. As the modulus ratio is increased, there is a transition in failure mechanism from tensile-dominated failure in the matrix to shear-dominated failure at the fibre-matrix interface. In addition, families of critical aspect ratio curves are obtained as a function of the cohesive energy ratio, Uf/Um. Larger cohesive energy ratios shift the critical aspect ratio curve to larger values. These features potentially explain trends in the experimental results reported by Asloun et al., where the critical fibre aspect ratio was measured for fibre/matrix systems having different modulus and toughness ratios.