Determination of effective thermal expansion coefficients of unidirectional fibrous nanocomposites

Abstract

We present an efficient numerical scheme (based on complex variable techniques) to calculate the effective thermal expansion coefficients of a composite containing unidirectional periodic fibers. Moreover, the mechanical behavior of the fibers incorporates interface effects allowing the ensuing analytical model of the composite to accommodate deformations at the nanoscale. The resulting ‘nanocomposite’ is subjected to a uniform temperature variation which leads to periodic deformations within the plane perpendicular to the fibers and uniform deformations along the direction of the fibers. These deformation fields are determined by analyzing a representative unit cell of the composite subsequently leading to the corresponding effective thermal expansion coefficients. Numerical results are illustrated via several physical examples. We find that the influence of interface effects on the effective thermal expansion coefficients (in particular that corresponding to the transverse direction in the plane perpendicular to the fibers) decays rapidly as the fibers become harder. In addition, by comparing the results obtained here with those from effective medium theories, we show that the latter may induce significant errors in the determination of the effective transverse thermal expansion coefficient when the fibers are much softer than the matrix and the fiber volume fraction is relatively high.