Effect of CNT waviness on the effective mechanical properties of long and short CNT reinforced composites Shweta Paunikar a , Surendra Kumar b,⇑ a Academy of Scientific & Innovative Research, CSIR – Central Mechanical Engineering Research Institute, Durgapur 713209, India b Mechanics & Stress Analysis Department, CSIR – Central Mechanical Engineering Research Institute, Duragapur 713209, India article info Article history: Received 31 March 2014 Received in revised form 27 May 2014 Accepted 10 June 2014 Keywords: Carbon nanotubes (CNTs) Nanocomposites Micromechanics Mechanical properties Finite element method abstract Carbon nanotubes (CNTs) possess extremely high stiffness, strength and resilience, and may provide ultimate reinforcing materials for the development of nanocomposites. CNT reinforced composite mate- rials (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 anal- ysis. 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. Ó 2014 Elsevier B.V. All rights reserved. 1. Introduction Carbon nanotubes (CNTs) accidently discovered by Iijima in the year 1991, have shown great potential to be the ultimate reinforce- ment for nanocomposites based on nanotubes or nanoparticles because of their exceptional mechanical properties. The high mechanical properties are directly attributed to the fact that CNTs are cylindrically rolled graphene. Graphene is a single atom thick hexagonal honeycomb lattice structure of sp 2 hybridized carbon atoms. The C–C covalent bond and the almost defect free structure is the main reason for the CNTs to have axial Young’s modulus in the range of 1 to 5 TPa, strength up to 63 GPa, and density in the range 1.3–1.5 g/cm 3 . The diameter and length of CNTs lie in the range 1–25 nm and 0.1–100 lm respectively. The CNTs possess high strength to weight ratio due to unique combination of size, geometry and density. The CNTs also have high thermal, electrical, magnetic and optical properties [1]. The excellent mechanical properties have fuelled the interests of many scientists and engineers for the development of CNT rein- forced polymer composites as the ultimate new age material. Many experimental and theoretical studies have been done to analyze the nature of CNT reinforced polymer composite. Qian et al. [2] showed that addition of only 1% by weight of miltiwalled CNTs to polystyrene matrix increased the stiffness between 36% and 42% and the tensile strength by 25% of the composite. Liu et al. [3,4] demonstrated analytically that addition of about 2% and 5% of volume fractions of CNTs in a polymer matrix increased the overall stiffness of nanocomposite with short and long CNT by 0.7 and 9.7 times respectively. Qian et al., Schadler et al., Wagner et al., Bower et al. [2,5–7] performed experimental work to show the mechanical load carrying capacities of CNTs in nanocompos- ites. This indicates that there is a strong interface and effective load http://dx.doi.org/10.1016/j.commatsci.2014.06.034 0927-0256/Ó 2014 Elsevier B.V. All rights reserved. ⇑ Corresponding author. E-mail addresses: shweta.paunikar@yahoo.com (S. Paunikar), surendra_ kumar@cmeri.res.in (S. Kumar). Computational Materials Science 95 (2014) 21–28 Contents lists available at ScienceDirect Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci