The effect of nanotube waviness and agglomeration on the elastic property of carbon nanotube-reinforced composites

Owing to their superior mechanical and physical properties, carbon nanotubes seem to hold a great promise as an ideal reinforcing material for composites of high-strength and low-density. In most of the experimental results up to date, however, only modest improvements in the strength and stiffness have been achieved by incorporating carbon nanotubes in polymers. In the present paper, the stiffening effect of carbon nanotubes is quantitatively investigated by micromechanics methods. Especially, the effects of the extensively observed waviness and agglomeration of carbon nanotubes are examined theoretically. The Mori-Tanaka effective-field method is first employed to calculate the effective elastic moduli of composites with aligned or randomly oriented straight nanotubes. Then, a novel micromechanics model is developed to consider the waviness or curviness effect of nanotubes, which are assumed to have a helical shape. Finally, the influence of nanotube agglomeration on the effective stiffness is analyzed. Analytical expressions are derived for the effective elastic stiffness of carbon nanotube-reinforced composites with the effects of waviness and agglomeration. It is found that these two mechanisms may reduce the stiffening effect of nanotubes significantly. The present study not only provides the relationship between the effective properties and the morphology of carbon nanotube-reinforced composites, but also may be useful for improving and tailoring the mechanical properties of nanotube composites.