Analytic and computational micromechanics of clustering and interphase effects in carbon nanotube composites.

Abstract

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 Hashin and Rosen (1964) and Christensen and Lo (1979). 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 comparisons with experimental data are made.Computational micromechanical analysis of high-stiffness hollow fiber nanocomposites is performed using the finite element method. The high-stiffness hollow fibers are modeled either directly as isotropic hollow tubes or equivalent transversely isotropic effective solid cylinders with properties computed using a micromechanics based composite cylinders method. Using a representative volume element for clustered high-stiffness hollow fibers embedded in a compliant matrix with the appropriate periodic boundary conditions, the effective elastic properties are obtained from the finite element results. These effective elastic properties are compared to approximate analytical results found using micromechanics methods. The effects of an interphase layer between the high-stiffness hollow fibers and matrix to simulate imperfect load transfer and/or functionalization of the hollow fibers is also investigated and compared to a multi-layer composite cylinders approach. Finally the combined effects of clustering with fiber-matrix interphase regions are studied. The parametric studies performed herein were motivated by and used properties for single-walled carbon nanotubes embedded in an epoxy matrix, and as such are intended to serve as a guide for continuum level representations of such nanocomposites in a multi-scale modeling approach.