Fiber waviness in nanotube-reinforced polymer composites—I: Modulus predictions using effective nanotube properties

Results in the literature demonstrate that substantial improvements in the mechanical behavior of polymers have been attained through the addition of small amounts of carbon nanotubes as a reinforcing phase. This suggests the possibility of new, extremely lightweight carbon nanotube-reinforced polymers with mechanical properties comparable to those of traditional carbon-fiber composites. Motivated by micrographs showing that embedded nanotubes often exhibit significant curvature within the polymer, we have developed a model combining finite element results and micromechanical methods to determine the effective reinforcing modulus of a wavy embedded nanotube. This effective reinforcing modulus (ERM) is then used within a multiphase micromechanics model to predict the effective modulus of a polymer reinforced with a distribution of wavy nanotubes. We found that even slight nanotube curvature significantly reduces the effective reinforcement when compared to straight nanotubes. These results suggest that nanotube waviness may be an additional mechanism limiting the modulus enhancement of nanotube-reinforced polymers. # 2003 Elsevier Ltd. All rights reserved.