Prediction of the overall moduli of layered silicate-reinforced nanocomposites - part I: basic theory and formulas

This part of the two-part paper presents the basic theory and formulas for the prediction of the overall moduli of layered silicate-reinforced polymeric nanocomposites. In view of the morphology of the composites and the anisotropic nature of layered silicate, formulas for the overall moduli of composite materials reinforced with transversely isotropic spheroids are derived in this part using the Mori-Tanaka method. These formulas are then used to examine the influences of the anisotropy and aspect ratio of the transversely isotropic spheroids on the overall moduli of the composite materials. It is found that the overall moduli of the composite materials reinforced with transversely isotropic spheroids are predominated by the stiffness of the spheroids in the direction of their major axis, especially for the cases of small and large aspect ratios. The predictions based upon the Mori-Tanaka method are also compared with approximate formulas in the literature for isotropic thin oblate spheroids. It is found that these approximate formulas agree well with the Mori-Tanaka predictions at low volume fractions of the reinforcement. (C) 2004 Elsevier Ltd. All rights reserved.