Three dimensional micromechanical analysis of the CNT waviness influence on the mechanical properties of polymer nanocomposites
The effects of carbon nanotube (CNT) waviness on the elastic characterizations of polymer nanocomposites are investigated using a three dimensional unit cell based micromechanical model. The most important advantages of this model are its accuracy, simplicity, and efficiency. Both random and regular CNT arrangements can be included in the modeling. The wavy CNTs are modeled as sinusoidal solid CNT fibers while at any location along the length of CNT, the CNT is considered as transversely isotropic material. The polymer and interphase formed due to non bonded interaction between a CNT and the polymer are assumed to be homogeneous and isotropic as well. Results show that the effect of CNT waviness is not important for the effective coefficients $C_{11}$C11, $C_{12}$C12, and $C_{13}$C13 of the nanocomposites. CNT waviness plays a critical role in determining the effective coefficients $C_{22}$C22, $C_{23}$C23, $C_{33}$C33, and $C_{44}$C44 of the nanocomposites. Also, it is found that the CNT waviness slightly affects the effective values of $C_{55}$C55 and $C_{66}$C66. The effects of volume fraction of CNT and interphase on the mechanical properties of the nanocomposite are examined. Comparison of the present model results shows very good agreement with other available micromechanical analysis and experiment. As comparing with the finite element method, the present model requires much less computational time for obtaining the effective properties of the nanocomposites. Consequently, the results emphasize that all four important parameters, i.e. CNT behavior and waviness, CNT random arrangement, and interphase contributions, should be precisely included in the modeling to predict a more realistic outcome.