Effect of CNT waviness on the effective mechanical properties of long and short CNT reinforced composites

Carbon nanotubes (CNTs) possess extremely high stiffness, strength and resilience, and may provide ultimate reinforcing materials for the development of nanocomposites. CNT reinforced composite materials (CNTRC) can be effectively used in aircraft structures, due to their high strength to weight ratio. Accordingly, several experimental and analytical studies have been performed for evaluating effective mechanical properties of CNT-reinforced polymer matrix. However, several complex issues including sizes and forms of CNTs dispersed in a matrix, their distribution and orientation in the matrix make the simulations of the mechanical behaviour of these composites extremely complicated. One such issue is assessing the effect of nanotube curvature since embedded CNTs seldom remain straight inclusions. Nanotube curvature is often characterized by means of the waviness that accounts for the deviation from the straight particles assumption. In this paper, the effect of waviness of CNT is analyzed using a 3-D nanoscale representative volume element (RVE) based on continuum mechanics, and effective elastic modulus is calculated for two cases namely, a RVE with long CNT (CNT throughout the length of RVE) and a RVE with short CNT (CNT completely inside the RVE). Finite element method is used for the analysis. Further, a theoretical model based on the micromechanics of multi-phase composite and energy principles has also been developed to evaluate effective elastic constants of these RVEs. It is found that the reinforcing capacity of the CNTs reduces drastically even with a small waviness as compared to the straight CNTs. The effect of waviness is much more pronounced in case of long wavy CNT than short wavy CNT. The analysis is finally extended to predict the effective moduli of these composites embedded with completely randomly oriented CNTs of different waviness.