Tensile Behavior of Single-Walled Zigzag Carbon Nanotubes Using Finite Element Modeling Approach

Carbon nanotubes (CNT), first reported by Iijima in 1991, possess extraordinary high stiffness and strength.The atomic structure of nanotubes can be described in terms of the tube chirality or helicity, which is defined by a pair of indices (n, m). The amount of twist in the tube is determined by the chiral angle, θ . The chiral vector, the diameter n and the chiral angle D θ of the CNT can be written as follows 1 2 r = n a + m a r r r , ]2( ) sin [ 3 2 2 1 n nm m m + + θ = − , π 3( 2 2 ) 0 r n m nm Dn + + = (1) where 0 is the C-C bond length and is equal to 0.142. r In this paper, molecular-mechanics-based finite element approach was used to approximate the tensile stiffness and strength of zigzag carbon nanotubes using step by step progressive fracture model. The concept of the model is based on the assumption that loaded carbon nanotubes can be modeled as a space-frame structure. The bonds between carbon atoms are considered as load-carrying beam elements with variable modulus of elasticity at each load step. The modified Morse interatomic potential [1] is used to describe the non-linear behavior of the C–C bonds and the FE method is utilized to analyze the spatial structure. A nonlinear behavior of the elements has been assumed at each load step. This is a modified approach in cases where continuum methods are used to analyze zigzag carbon nanotubes.