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Buckling analysis of multi-walled carbon nanotubes under combined loading considering the effect of small length scale

Abstract

The torsional and axially compressed buckling of an individual embedded multi-walled carbon nanotube (MWNTs) subjected to an internal and/or external radial pressure was investigated in this study. The emphasis is placed on new physical phenomena which are due to both the small length scale and the surrounding elastic medium. Multiwall carbon nanotubes which are considered in this study are classified into three categories based on the radius to thickness ratio, namely, thin, thick, and almost solid. Explicit formulas are derived for the van der Waals (vdW) interaction between any two layers of an MWNT based on the continuum cylindrical shell model. In most of the previous studies, the vdW interaction between two adjacent layers was considered only and the vdW interaction among other layers was neglected. Moreover, in these works, the vdW interaction coefficient was treated as a constant that was independent of the radii of the tubes. However, in the present model the vdW interaction coefficients are considered to be dependent on the change of interlayer spacing and the radii of the tubes. The effect of the small length scale is also considered in the present formulation. The results show that there is a unique buckling mode (m,n) corresponding to the critical shear stress. This result is obviously different from what is expected for the pure axially compressed buckling of an individual multi-walled carbon nanotube.

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References

  1. [1]

    S. Iijima, Helical microtubes of graphitic carbon, Nature 354 (1991) 56–58.

    Article  Google Scholar 

  2. [2]

    Y. Q. Zhang, G. R. Liu and X. Han, Effect of small length scale on elastic buckling of multi-walled carbon nanotube under radial pressure, Phys. lett. A349 (2006) 370–376.

    Google Scholar 

  3. [3]

    C. Y. Wang, C. Q. Ru and A. Mioduchowskil, Axially compressed buckling of pressured multi-walled carbon nanotubes, Int. J. Solids Struct. 40 (2003) 3893–3911.

    MATH  Article  Google Scholar 

  4. [4]

    J. Yoon, C. Q. Ru and A. Mioduchowskil, Vibration of an embedded multiwall carbon nanotube, Composite Sci. Technol. 63 (2003) 1533–1545.

    Article  Google Scholar 

  5. [5]

    S. P. Timoshenko and J. M. Gere, Theory of Elastic Stability, McGraw-Hill, New York (1961).

    Google Scholar 

  6. [6]

    Don. O. Brush and Bo. O. Almroth, Buckling of bars, plates, and shells, McGraw-Hill, New York (1975).

    MATH  Google Scholar 

  7. [7]

    L. H. Donnell, Beams, Plates, and Shells, McGraw-Hill, New York (1976).

    MATH  Google Scholar 

  8. [8]

    X. Q. He, S. Kitipornchai and K. M. Liew, Buckling analysis of multi-walled carbon nanotubes: a continuum model accounting for van der Waals interaction, Int.J. Mech. Phys. 53 (2005) 303–326.

    MATH  Google Scholar 

  9. [9]

    J. E. Lennard-Jones, The determination of molecular Fields: from the variation of the viscosity of a gas with temperature, Proc. Roy. Soc. 106A (1924) 441.

    Article  Google Scholar 

  10. [10]

    R. Saito, G. Dresselhous and M. S. Dresselhous, Physical properties of carbon nanotubes, Imperial College press, London (1988).

    Google Scholar 

  11. [11]

    C. Q. Ru, Axially compressed buckling of a double-walled carbon nanotube embedded elastic medium, J. Mech. Phys. Solids 49 (2001) 1265–1279.

    MATH  Article  Google Scholar 

  12. [12]

    X. Wang, Lu. Guoxing and Y. J. Lu, Buckling of embedded multi-walled carbon nanotubes under combined torsion and axial loading, Int.J. Solid. Struct. 44 (2007) 336–351.

    MATH  Article  Google Scholar 

  13. [13]

    X. Wang, H. K. Yang and K. Dong, Torsional buckling of multi-walled carbon nanotubes, Mater. Sci. Eng. A 404 (2005) 314–322.

    Google Scholar 

  14. [14]

    O. Gulseren, T. Yildirim and S. Ciraci, Systematic ab initio study of curvature effects in carbon nanotubes, Physical ReviewB 65 (2002)153405.

    Google Scholar 

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Correspondence to A. Ghorbanpour Arani.

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Ghorbanpour Arani, A., Rahmani, R., Arefmanesh, A. et al. Buckling analysis of multi-walled carbon nanotubes under combined loading considering the effect of small length scale. J Mech Sci Technol 22, 429–439 (2008). https://doi.org/10.1007/s12206-007-1045-2

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Keywords

  • Carbon nanotubes
  • Buckling
  • van der Waals interaction
  • Continuum shell model
  • Small length scale
  • Elastic medium