Atomistic Simulations of Fracture of 2d Graphene Systems and the Elastic Properties of Carbon Nanotubes

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Title: Atomistic Simulations of Fracture of 2d Graphene Systems and the Elastic Properties of Carbon Nanotubes
Author: Jin, Yun
Advisors: Dr. Kara Peters, Committee Member
Dr. Eric C. Klang, Committee Member
Dr. Jeffrey W. Eischen, Committee Member
Dr. Fuh-Gwo Yuan, Committee Chair
Abstract: The essential feature of all the macroscopic mechanical properties of a material are governed by constitutive atoms and the basic laws of physics. The traditional descriptions of fracture phenomena in solids have been developed almost exclusively from continuum concepts. These continuum approaches have successfully described many fracture mechanism in solid materials and continue to be of great use. Nevertheless, they still have some shortcomings, such as the spurious singularity of the stress field at crack tip. Hence, atomistic predictions may open new avenues in the studies of microscopic origins of material failure behavior. Also the highly active researches on the lightweight nano-structured materials in the past decade revealed the emergence of interests in predicting the properties of materials in the atomic level before they are synthesized. 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. There is a very good agreement between atomistic simulation and theoretical results from LEFM for the energy release rate in a semi-infinite graphene sheet containing cracks. The atomic description of the stress field in this case is also obtained and matches very well with the linear elastic solutions. Then another case in which a center-cracked graphene sheet with finite width is proposed. The energy release rates are obtained in both global energy approach and local force approach. These simulations show 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, the method to calculate J integral in the atomic system is successfully developed. The numerical results of J integral agree very well with the energy release rate in the same systems. Then after a necessary modification on the Tersoff-Brenner potential, the critical value of J integral, denoted by , is eventually reached as the measure of the fracture toughness of graphene sheet. The mechanical properties of single-walled carbon nanotube (SWNT) have also been evaluated in this dissertation. Several elastic moduli of SWNTs using the MD simulations were obtained at the atomic scale. 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. It has been shown from simulations that overall 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 was confirmed by numerical calculations. Besides the conventional energy approach, a new method, which denoted as force approach in the dissertation, has been developed to analysis 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.
Date: 2004-11-15
Degree: PhD
Discipline: Mechanical Engineering

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