Atomistic simulations of fracture of two-dimensional graphene systems and the elastic properties of carbon nanotubes.

摘要

This dissertation has two main parts. The first part is the atomistic simulations of fracture of 2d graphene systems. In principle the macroscopic mechanical properties of materials are determined by the atoms and the basic laws of physics. For the fracture of materials, atomistic simulations can provide basic understanding of the origins of fracture due to the bond rupture. In this dissertation the fracture mechanism of a nanostructure material has been investigated by atomistic simulations. Macroscopic fracture parameters have been examined from both atomistic simulation and continuum models. Methods of calculating energy release rates in atomic systems have been successfully developed. The atomic descriptions of the stress field in front of crack tips were also obtained. These simulations showed that, in macroscopic fracture mechanics under small deformation, linear elastic fracture mechanics is sufficient for the description of cracking behavior for this covalently bonded material. The results merge the discrete (atomistic) and continuum (macroscopic) description of facture. Meanwhile, a method to calculate J-integral in the atomic system has been developed. The numerical results of J-integral agreed very well with the energy release rate in the linear elastic condition. After a necessary modification on the Tersoff-Brenner potential, the critical values of J-integral, denoted by Jc, have been obtained as the measure of the fracture toughness of graphene sheets.; In the second part of this dissertation the mechanical properties of single-walled carbon nanotube (SWNT) have been evaluated. The values of the in-plane Young's modulus, rotational shear modulus, and in-plane Poisson's ratio are in the range of existing theoretical and experimental results. Several elastic moduli of SWNTs have been obtained using molecular dynamic simulations. It has been shown from the simulations that the elastic constants of SWNTs are insensitive to the morphology pattern such as nanotube radius and thus the effect of curvature on the elastic constants can be neglected. Assumption of the transversely isotropic properties on the cylinder surface of the single-walled nanotube has been confirmed by numerical calculations. Besides the conventional energy approach, a new method, which denoted as force approach in the dissertation, has been developed to analyze the elastic properties of carbon nanotubes. The results from two approaches matched very well. The advantage of the force approach is that it can provide more accurate prediction than the energy approach. Furthermore, the force approach can predict the nonlinear behavior without assumption of assumed total potential energy in quadratic form described for small-strain deformation in the energy approach.