Analysis For Finite Temperature Model & Thermo Mechanical Properties Of Carbon Nanotubes

Since the carbon nanotubes(CNTs) have been found, more and more attentions have been paid to them by scholars and specialists all over the world due to their extremely excellent mechanical properties. At present, there are many efforts done by the scholars about the CNTs. However, there are very limit researches about the thermo-mechanical properties of CNTs. The knowledge of thermo-mechanical properties of CNTs is very important for the efficient and lasting engineering application of CNTs. In this paper, the main purpose is to investigate the thermo-mechanical properties of CNTs.Today, four theories have been adopted to study the mechanical properties of CNTs. They are the experiment analysis, molecular dynamics, molecular mechanics, and the continuum mechanics, respectively. The molecular mechanics is the most accurate one of them, but the amount of its calculation is so complicated and significant that it is difficult for its engineering application widely. Therefore, this could be the largest bottleneck of this method. The continuum mechanics is a theory to study the microcosmic properties by the macroscopic method, and this method holds for the engineering application best.For engineering applications, this paper mainly adopts the molecular mechanics and continuum mechanics to study the relationship of the elastic properties of CNTs changed with temperature. Based on the molecular mechanics, a thickness-independent temperature-dependent model of single-walled carbon nanotube(SWNT) in the thermal environment is established to study the elastic properties of SWNT at different environment temperatures. A linear coefficient of thermal(LCTE), which changes continuously with the temperature, is also adopted. The Young’s modulus and the Poisson’s ratio of SWNTs for different temperatures are analyzed. It is found that the Young’s moduli of both armchair and zigzag SWNTs decrease with the increase of the temperature, but the Poisson’s ratio is not dependent on the temperature. Moreover, it is noted that for a given nanotube diameter, the Young’s moduli of armchair nanotubes are larger than those for zigzag nanotubes slightly. However, for a given temperature the Young’s moduli of both armchair and zigzag nanotubes increase with increasing nanotube diameters.Based on the continuum theory, a new theory incorporating interatomic potentials and finite temperatures based on the Cauchy–Born rule is developed to study critical strains of tension and compress at finite temperatures. For a better engineering application, in this article, a nonlocal model incorporating interatomic potentials and finite temperatures based on the Euler–Bernoulli beam theory is also developed to study the buckling behavior of axially loaded multi-walled carbon nanotubes in a thermal environment, and an explicit expression for the critical axial strain of a double-walled carbon nanotube is represented with a large aspect ratio.