Laminate analogy approach for the effective elastic properties of metal matrix nanocomposites filled with randomly dispersed graphene nanoplatelets

Abstract

In this study, the laminate analogy technique is utilized to calculate the elastic properties of metal matrix nanocomposites filled with graphene nanoplatelets. The graphene nanoscale fillers are the most commonly used form of graphene inclusions, which are mostly considered to be disk-shaped. With the help of the Eshelby tensor, the effects of three different shapes of graphene inclusions on the mechanical response are examined. Combining layers of metal matrix composite lamina reinforced by uniformly dispersed graphene inclusions, which are aligned differently in each layer, the metal matrix nanocomposite is simulated. In each lamina, the Mori–Tanaka micromechanical method is employed to calculate the effective elastic properties. Given the fact that the inclusions are aligned, the change in the principal axis of each laminate from the global axis does not affect the Mori–Tanaka results thus resulting in an equivalent laminate composite. Then, classical laminate theory is implemented to obtain the elastic modulus of the equivalent laminate composite. The results obtained from this analytical model are compared with experimental data and a good agreement can be found between them. Two factors are observed to play a critical role in the final results; (i) the number of layers and (ii) the geometrical features of the graphene inclusions. An equivalent laminate composite with few layers acts as a composite material with anisotropic properties, and the increase of the number of layers will cause the isotropic behavior in the equivalent laminate composite. By increasing the aspect ratio, the effective elastic modulus of the nanocomposite exhibits a near-linear growth.