Effect of interphase modulus and cohesive energy on the critical aspect ratio in short-fibre composites

Abstract

The effect of interphase modulus and cohesive energy on critical fibre length in short-fibre reinforced brittle composites has been investigated employing computer simulation. The simulation consists of a two-dimensional computer model based upon a discrete network of grid points. Failure is 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. Simulation results show that for a whisker-type fibre, a thick interphase (i.e. A _i>A_f where A represents the cross sectional area) with an elastic modulus less than that of the matrix in combination with an increased interphase toughness greatly reduce the critical aspect ratio, for both metal-matrix and ceramic-reinforced brittle polymer composites. The results also show a variation in the failure mode from tensile failure in the matrix to tensile and shear failure in the interphase as a function of the fibre-interphase modulus ratio. In particular, a significant increase in the load transfer efficiency in metal-matrix composites is found, for an interphase modulus E _i less than the matrix modulus E _m. Better load transfer properties in metal-matrix composites cause the yield point to occur at higher values of applied strain, and hence may significantly increase the toughness (area under the stress-strain curve) for certain metal-matrix composites. The computer results are compared with the predictions of Cox's shear-lag theory as well as with a new theoretical development presented in this work. The new theory is found to provide a better description of the fibre and matrix stress distribution.