【作者】 辛浩；

【导师】 韩强；

【作者基本信息】 华南理工大学 ， 固体力学， 2010， 博士

【摘要】 自碳纳米管被发现以来,其优异的性能和广阔的潜在应用空间引起了人们的广泛关注,针对碳纳米管基础力学行为的研究已经成为国际上的热点问题之一。研究碳纳米管的手段多种多样,但鉴于其结构特点,进行实验研究较为困难,使用连续介质力学的相关理论仍有一些关键问题需要解决。原子尺度的数值模拟虽然难以处理大型的体系,却可以较为精确地描述碳纳米管的受力变形特性,而且可以考虑碳纳米管中的缺陷、环境温度以及加载条件等对其力学性能的影响。本文以单层和双层碳纳米管为研究对象,通过进行分子动力学模拟和建立新的连续体模型,进一步研究了碳纳米管的受力变形特性以及几种因素对其力学性能的影响规律。通过分子动力学模拟,对比分析了若干典型尺寸单层碳纳米管的轴压屈曲模态和后屈曲变形行为,系统地研究了单层碳纳米管管长和温度变化对其力学变形特性的影响。分析表明,T-B势与Morse势均可用来较好地模拟碳纳米管中“C-C”键的作用。单层碳纳米管的面内刚度随着手性角的增大(0o~30o)而增大。当碳纳米管长径比大于16时,其屈曲行为则完全表现为杆件的整体屈曲特征,可以采用连续介质力学的压杆理论研究其屈曲问题。单层碳纳米管临界荷载值、临界应变值和面内刚度均随着温度降低而显著减小,温度的影响程度不仅与单层碳纳米管手性有关,而且与温度的变化区间、纳米管管长均有关。文中还系统地研究了碳纳米管管壁缺陷对其力学变形性能的影响。对含缺陷扶手椅形和锯齿形单层碳纳米管的轴压屈曲进行了分子动力学模拟,分析和对比了两种手性的含缺陷管的屈曲模态和后屈曲变形行为,研究了温度变化对含缺陷碳纳米管力学性能和变形的影响,探讨了扶手椅形单层碳纳米管中两种双原子缺陷对其面内刚度造成不同影响的原因。研究发现,缺陷对碳纳米管的临界荷载、临界应变以及屈曲形态等轴压屈曲特性造成了显著的影响,其中,几种不同缺陷的结构产生的影响各具特点。含缺陷单层碳纳米管的屈曲性能受温度影响较小,且随着温度的升高,几种缺陷管的屈曲性能相互趋近,差别缩小。通过分子动力学模拟的方法,对双层碳纳米管的轴压屈曲变形进行了研究,还考虑了内层管含有不同缺陷的情况,以及内、外层管单独受压的情况。模拟结果表明,完善双层碳纳米管的临界屈曲应变介于组成它的两个单层碳纳米管的临界屈曲应变之间,在端部均匀轴向受压的变形过程中,双层碳纳米管层间距始终保持稳定,无论在发生局部变形的部位还是其它部位,无论是否含有缺陷,层间距均未发生改变。这种协同变形提高了完善双层碳纳米管中单位原子的承载利用效能。研究发现,当外管单独受压产生屈曲变形时,内外管的变形是协同的,而当内管单独受压产生屈曲变形时,内外管的变形并不协调,文中对此现象作了合理的解释。通过对单层和双层碳纳米管轴向压缩过程的分子动力学模拟,研究了应变率对碳纳米管轴压屈曲性能的影响,对比了应变率对含缺陷结构与完善结构的不同影响。分析显示,完善单层碳纳米管的轴压临界屈曲荷载并非随着应变率的增大而单调性地变化,而是先增大后减小,其面内刚度与应变率几乎无关。含缺陷单层碳纳米管的轴压临界屈曲荷载随着应变率的增大而增大,各含缺陷单层碳纳米管的面内刚度随应变率的增大出现不同程度的增加。完善双层碳纳米管临界荷载随应变率的变化曲线与完善单层碳纳米管的较为相似,而内管含缺陷双层碳纳米管的轴压屈曲荷载随应变率的变化规律受到内外层管共同的影响。在加载速度较高时,可以忽略缺陷的影响将含缺陷的多层碳纳米管视为一个完善理想的多层碳纳米管。提出了一种新的理论分析方法用以研究石墨片层的弹性性能,从理论上证明了石墨片层在平面受力状态下为一各向同性的弹性体。鉴于碳纳米管与石墨层结构的相互对应关系,采用石墨层等效模型及其理论,导出了碳纳米管各向异性与碳纳米管中C-C-C键角变化的相互关系,以此为基础进一步研究了单层碳纳米管的轴压变形的尺度效应。分析发现,与扶手椅形碳纳米管相比锯齿形碳纳米管的尺度效应更为明显;对于管径大于2nm的碳纳米管,无论手性如何其尺度效应均可忽略,仍可将其视为各向同性体,采用石墨层的材料常数即可,但是对于直径小于1nm的碳纳米管,应将其视为各向异性体并考虑其尺度效应,此时纳米管的材料常数可由本文给出的有关公式计算。该理论分析的重要意义在于,它不仅澄清了碳纳米管基础力学研究中至今尚存的若干困惑,还为采用复合材料力学方法进一步研究碳纳米管的力学性能指出了新的研究方向,同时为碳纳米管理论分析中连续介质力学的应用奠定了重要基础。更多还原

【Abstract】 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.更多还原