The tensile strength of hybrid fibre composites: A probabilistic analysis of the hybrid effects

A hybrid composite formed by brittle and less brittle fibres embedded into a ductile matrix is taken as the model for study. The breaking strains of distinct fibre types in the hybrid composite are considered in this paper as statistical variables so that the stress-strain relationship of the composite is treated as a typical stochastic process indexed with the composite strain. Also the mechanism reflecting the interactions between the constituents revealed by the fragmentation process during composite extension, and the effect of breaking strain variation between individual fibres of the same type have been included in the stochastic formula. Based on this theoretical model, the prediction of the entire stress-strain curve of a hybrid composite is provided in this study. A comprehensive parametric study is then carried out to illustrate the inter-relationships between the composite breaking behaviour and the fibre and composite interfacial properties. Next, as the hybrid effect is defined by comparing the hybrid composite either with the rule of mixtures using single fibre properties or fibre bundle properties, or with a non-hybrid composite, the differences in these cases are discussed in detail. Various sources causing the hybrid effect are revealed, studied and summarized. These sources are found due partly to the property variations of the fibres which affect the interactions in the hybrid composite between fibres and matrix, and partly to the cross coupling interactions between the fibres of different types in the hybrid composite. The impacts of these sources on the composite behaviour as well as the associated hybrid effects are demonstrated and the important factors are detected and examined. It is then stressed in this paper that since most of the mechanisms responsible for causing the so-called hybrid effects have been proved effective in nonhybrid composites as well, we need to be more cautious concerning the definition for the hybrid effects in a hybrid composite. Finally, the relationships between the hybrid effects and the important variables such as the relative hybrid ratio, a(LE), the relative fibre-matrix interface shear strength tau(y)/E(f), and the relative fibre tensile modulus F-fHE/E(fLE) are investigated and illustrated.