Micromechanical analysis of the effective elastic properties of carbon nanotube reinforced composites

Effective elastic properties for carbon nanotube reinforced composites are obtained through a variety of micromechanics techniques. Using the in-plane elastic properties of graphene, the effective properties of carbon nanotubes are calculated utilizing a composite cylinders micromechanics technique as a first step in a two-step process. These effective properties are then used in the self-consistent and Mori-Tanaka methods to obtain effective elastic properties of composites consisting of aligned single or multi-walled carbon nanotubes embedded in a polymer matrix. Effective composite properties from these averaging methods are compared to a direct composite cylinders approach extended from the work of Z. Hashin and B. Rosen [1964. The elastic moduli of fiber-reinforced materials. Journal of Applied Mechanics 31, 223-232]and R. Christensen and K. Lo [1979. Solutions for effective shear properties in three phase sphere and cylinder models. Journal of the Mechanics and Physics of Solids 27, 315-330]. Comparisons with finite element simulations are also performed. The effects of an interphase layer between the nanotubes and the polymer matrix as result of functionalization is also investigated using a multi-layer composite cylinders approach. Finally, the modeling of the clustering of nanotubes into bundles due to interatomic forces is accomplished herein using a tessellation method in conjunction with a multi-phase Mori-Tanaka technique. In addition to aligned nanotube composites, modeling of the effective elastic properties of randomly dispersed nanotubes into a matrix is performed using the Mori-Tanaka method, and omparisons with experimental data are made.