Influence of particle-size distribution on effective properties of nanocomposites

Classical micromechanics methods in predicting the effective properties of particle-filled composites do not admit the size dependence of particles. However, when particle sizes are in the nanometer range, the surface/interface energy effect will become prominent, which renders the effective properties of composites to be size-dependent. In this paper, the influence of particle-size distribution on the effective properties of nanocomposites is studied. First, equations for the constitutive relation of the interface expressed in terms of the first kind Piola-Kirchhoff interface stress, and the Lagrangian description of the Young-Laplace equations are re-derived. Second, the Mori-Tanaka method is extended to take into account the effect of particle-size distribution. Finally, closed-form solutions are obtained for the effective bulk and shear moduli of nanocomposites, which are shown to be dependent on interface energy, average radius of particles, and particle-size dispersion. It is found that the effect of particle-size distribution can significantly influence the mechanical properties of composite materials containing second phase nano-particles.