Theoretical model for the elastic behavior of composites reinforced with short fibers

The two simplest models that can be put forward to account for the elasticity of composite materials are the Reuss model and the Voigt model in which the constituents undergo, respectively, the same stress or the same strain. Experimental measurements always fall between the values predicted by these models. We propose correcting the Reuss model by stating\documentclass{article}\pagestyle{empty}\begin{document}$ \sigma _f = K\sigma _m $\end{document} σ f and ϵ m being the average stresses undergone, respectively, by reinforcing agent and the matrix. Similarly, we shall modify the Voigt model by supposing\documentclass{article}\pagestyle{empty}\begin{document}$ \epsilon _f = L\epsilon _f $\end{document} σ f and ϵ m being the average strain undergone, respectively, by reinforcing agent and the matrix. K and L are interrelated tensors which depend on the nature of the reinforcing agent, on its possible orientation, and on the mechanical behavior of the interface and also on the moduli of the constituents. We have developed the equations for determining the tensors with regard to fiber composite, taking into account the characteristics of the fibers (length, diameter, orientation, interface). The evaluation of K and L enables us, therefore, to calculate the modulus or the compliance. Conversly, by measuring the modules or the complience, one can determine K or L and , in this way, obtain data on the machnism of load transfer from the matrix to the reingforcing agent and thus on the behavior of their interface. The theoretical values of the Young modules calculated from our model are in good agreement with the experemental values obtained by Lees. 8