A Three Dimensional Unit Cell Model for the Analysis of Thermal Residual Stresses in Polymer Composites Reinforced with Wavy Carbon Nanotubes

This paper presents a numerical approach to predict the thermal residual stresses in polymer nanocomposites reinforced with a periodic array of wavy carbon nanotubes. A three dimensional unit cell model is established to accurately account for the waviness of the nanotube. Periodic boundary conditions are determined for the unit cell with a pair of curved surfaces. Appropriate methods to evaluate the macroscopic stresses and strains are also determined for the unit cell model in which the interior pores of the nanotubes are explicitly included. It is demonstrated that the macroscopic behavior of the nanocomposites is orthotropic due to the symmetries manifested. By employing material properties of the two constituents, the thermal residual stresses and strains induced by high temperature curing and cooling-down are predicted for an epoxy/wavy-nanotube composite. It is also demonstrated that the curing process tends to increase the waviness of the nanotube and the waviness has a significant influence on the distribution of the microscopic residual stresses.