SynopsisThe 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 u, = Ka, uf and urn being the average stresses undergone, respectively, by the reinforcing agent and the matrix. Similarly, we shall modify the Voigt model by supposing 6, = 0, tf and ern being the average strains undergone, respectively, by the 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. Conversely, by measuring the modulus or the compliance, one can determine K or L and, in this way, obtain data on the mechanism of load transfer from the matrix to the reinforcing agent and thus on the behavior of their interface. The theoretical values of the Young modulus calculated from our model are in good agreement with the experimental values obtained by Lees.8
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