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

Mechanics of Materials
Volume 38, Issues 8-10, August-October 2006, Pages 884-907
Advances in Disordered Materials

Gary D. Seidel and Dimitris C. Lagoudas,
Department of Aerospace Engineering, Texas A&M University, College Station, TX 77843-3141, USA
Received 10 December 2004. Available online 15 December 2005.

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 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 comparisons with experimental data are made.

Keywords: Micromechanics; Nanotubes; Clustering; Interphase; Composite cylinders; Mori–Tanaka; Self-consistent; Effective properties