Studies On Mechanical Properties Of Graphene And Carbon Nanotubes

Since the carbon nanotubes (CNTs) were discovered, more and more attention has been attracted due to their outstanding properties and widely potential applications. The investigation on the basic mechanical behaviors of CNTs has become one of the current international hot issues. Studies on the properties of CNTs could be carried out with numerous methods. However, it's difficult to conduct the experiment at atomic scale and many significant problems should be overcame before the continuum mechanics is appropriately used on the CNTs. Atomic simulations are widely used to study the mechanical properties of CNTs because it is convenient to consider the defects, temperature and different loading conditions, though the simulations of large systems are hard to run. We focus on the single- and double- walled carbon nanotubes (SWCNTs and DWCNTs), carry out molecular dynamical (MD) simulations and develop a new continuum model in present work to investigate the mechanical properties and the effect of several factors on the mechanical properties of CNTs.Axially compressed buckling and post-buckling behavior and deformed shapes of some CNTs with typical size are analyzed based on the MD simulations. The effect of the length of SWCNTs and the temperature change on the mechanical properties is systematically investigated, with some useful results attained. Both the T-B potential and the Morse one can be use to describe the actions of C-C bonds in CNTs. The in-plane stiffness increases with the increase in the chiral angles (0o~30o) of CNTs. SWCNTs with larger (>16) ratios of length to diameter present a pole-like integral buckling mode and their buckling problems can be solved with the strut theory of continuum mechanics. All of the critical buckling load, the critical buckling strain and the in-plane stiffness decreased with the increase in temperature. The degree of the effect of the temperature is not only related to the chirality of the SWCNTs but also dependent on the temperature range and the length of the tube.Effects of the defects in the walls of CNTs on the mechanical properties are systematically investigated based on the MD simulations of axially compressed buckling for defective armchair and zigzag SWCNTs. The different buckling modes of the two types of defective SWCNTs and their post-buckling behavior are analyzed individually and compared with each other. Effect of temperature changing on the mechanical properties of CNTs is studied and also investigated is the reason that two types of double vacancies induce quite different in-plane stiffness of the armchair SWCNTs. It is revealed that the defects have enormous and distinct influence on the critical buckling load, critical buckling strain and the buckling mode. The buckling properties of the defective tubes are slightly affected by the temperature and appear to be similar along with the increase of the temperature, which is different to the perfect CNTs.The axially compressed buckling of the DWCNTs are investigated via MD simulations, DWCNTs with defective inner tubes and DWCNTs with the inner/outer tubes axially compressed also concerned. The critical buckling strain of the DWCNTs is between the individual constitutional inner and outer tubes. The layer distance of the DWCNTs remains stable when the tubes are uniformly compressed, even at the loacal deformed or defective area. The carrying efficiency per atom in perfect DWCNTs could be increased due to the cooperative deformation. When the outer tube of DWCNTs is compressed but the inner one is not, the buckling deformation of the entire DWCNTs stays cooperative. But the situation is different if only the inner tube is compressed. A reasonable explanation about this phenomenon is give in this work.The effect of the strain rate on the buckling properties is studies via MD simulations of axial compression of SWCNTs and DWCNTs, and the effect on the perfect tubes and the defective ones is compared. The reaserch shows that the critical buckling load of perfect SWCNTs increases first and then decreases with the increase of the strain rate, and the in-plane stiffness almost keep the same. The critical buckling load and the in-plane stiffness of defective SWCNTs increase with the increase of the strain rate. The critical buckling load of DWCNTs changes similarly as the SWCNTs with the various strain rates. However, the rules of defective DWCNTs are affected by both the defective inner tube and the perfect outer tube. When the loading rate is very high the effect of the defect in the inner tube of DWCNTs could be ignored so that the defective DWCNTs could be treated as perfect ones.A new theoretical method is presented to investigate the elastic properties of the graghite sheet, with which it is theoretically demonstrated that the graghite sheet is isotropic when it is under plane stress. The equivalent model of the graghite could be transferred to the CNTs according to their similarity of structure. Thus, the relationship between the anisotropy and the changes of the C-C-C angles of the CNTs could be deduced, based on which the scale effect of the axially compressed behavior of CNTs is studied. It is showed that the scale effect of the zigzag CNTs is more significant than the armchair ones. The SWCNTs with diameter greater than 2nm could be treated as isotropic with the elastic constants of graghite, because the scale effect could be ignored no mater what chirality they are. Smaller SWCNTs, the diameter smaller than 1nm, should be regarded as anisotropic materials and the scale effect should be considered, the elastic constants of which could be attained from the formulas in current work. The significance of the present theory is that it not only clarify some puzzlement in the basic mechanical research of CNTs, but also provide a direction for applying the mechanics of composite material to the research in the mechanical properties of CNTs. It is also lay the foundations for the application of continuum mechanics in the theoretical analysis of CNTs.