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On the mechanics of deformation instabilities in carbon nanotubes

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Abstract.

This paper reviews some of the main mechanical properties of carbon nanotubes (CNT), including nonlinear elastic instabilities and buckling, as well as defect generation, dynamics and plasticity. A multiscale modeling approach of CNT dynamics is proposed. It considers CNT as cylindrical shells and describes their dynamics through the corresponding elasticity equations. This description may also incorporate defects such as vacancies, adatoms, dislocations, Stone–Wales defects and the coupling between film elasticity and defect dynamics. Elastic constants, defect formation and interaction energies may be obtained from direct comparison with experimental results or numerical simulations at the atomic level. It is then shown how the apparition and properties of deformation instabilities may be discussed in this framework.

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References

  • B.I. Yakobson, R.E. Smalley, Amer. Sci. 85, 324 (1997)

    Google Scholar 

  • S. Iijima, Nature 354, 56 (1991)

  • B.I. Yakobson, Ph. Avouris, Topics Appl. Phys. 80 287 (2001)

    Google Scholar 

  • D. Qian, G.J. Wagner, W.K. Liu, M.-F. Yu, R.S. Ruoff, Appl. Mech. Rev. 55, 495 (2002)

    Google Scholar 

  • R.S. Ruoff, D. Qian, W.K. Liu, C. R. Phys. 4, 993 (2003)

    Google Scholar 

  • X. Zhou, J.-J. Zhou, Z.-C. Ou-Yang, Phys. Rev. B 62, 13692 (2000)

    Google Scholar 

  • Y. Jin, F.G. Yuan, Compos. Sci. Technol. 63, 1507 (2003)

    Google Scholar 

  • C.Y. Li, T.-W. Chou, Compos. Sci. Techol. 63, 1517 (2003)

    Google Scholar 

  • E. Hernandez, C. Goze, P. Bernier, A. Rubio, Phys. Rev. Lett. 80, 4502 (1998)

    Google Scholar 

  • L. Chico, R. Parez-Alvarez, C. Cabrillo, Phys. Rev. B 73, 075425 (2006)

    Google Scholar 

  • T. Vodenitcharova, L.C. Zhang, Phys. Rev. B 68, 165401 (2003)

    Google Scholar 

  • A. Sears, R.C. Batra, Phys. Rev. B 69, 235406 (2004)

    Google Scholar 

  • K. Enomoto, S. Kitakata, T. Yasuhara, N. Ohtake, Appl. Phys. Lett. 88, 153115 (2006)

    Google Scholar 

  • Y. Huang, J. Wu, K.C. Hwang, Phys. Rev. B 74, 245413 (2006)

    Google Scholar 

  • P. Poncharal, Z.L. Wang, D. Ugarte, W.A. de Heer, Science 283, 1513 (1999)

    Google Scholar 

  • C. Bower, R. Rosen, L. Jin, J. Han, O. Zhoua, Appl. Phys. Lett. 74, 3317 (1999)

    Google Scholar 

  • D. Srivastava, M. Menon, K. Cho, Phys. Rev. Lett. 83, 2973 (1999)

    Google Scholar 

  • O. Lourie, D.M. Cox, H.D. Wagner, Phys. Rev. Lett. 81, 1638 (1998)

    Google Scholar 

  • A. Rochefort, Ph. Avouris, F. Lesage, D.R. Salahub, Phys. Rev. B 60, 13824 (1999)

  • M.J. Buehler, Y. Kong, H. Gao, J. Eng. Mater. Tech. 126, 245 (2004)

    Google Scholar 

  • M.B. Nardelli, B. Yakobson, J. Bernholc, Phys. Rev. B 57, R4277 (1998)

  • M.B. Nardelli, B. Yakobson, J. Bernholc, Phys. Rev. Lett. 81, 4656 (1998)

    Google Scholar 

  • J. Pieper, J. Goree, R.A. Quinn, J. Vac. Sci. Tech. A 14, 511 (1996)

    Google Scholar 

  • M. Kosterlitz, D.J. Thouless, J. Phys. C 6, 1181 (1973)

    Google Scholar 

  • D.R. Nelson, B.I. Halperin, Phys. Rev. B 19, 2457 (1979)

    Google Scholar 

  • A.P. Young, Phys. Rev. B 19, 1855 (1979)

    Google Scholar 

  • D. Srivastava, C. Wei, K. Cho, Appl. Mech. Rev. 56, 215 (2003)

    Google Scholar 

  • M. Sammalkorpi, A. Krasheninnikov, A. Kuronen, K. Nordlund, K. Kaski, Phys. Rev. B 70, 245416 (2004)

    Google Scholar 

  • B.C. Pan, W.S. Yang, J. Yang, Phys. Rev. B 62, 12 652 (2000)

    Google Scholar 

  • C. Shet, N. Chandra, S. Namilae, Defect-defect Interaction in Carbon Nanotubes Under Mechanical Loading, in Mech. Adv. Mater. Struc. (to appear)

  • N.M. Ghoniem, H. Heinisch, H. Huang, S. Yip, S.J. Yu, J. Comp. Mater. Design, Special Issue for Multiscale Materials Modeling Symposium of the 5th IUMRS (Kluwer Academic Publishers, Dordrecht, 1999)

  • E.H. Donnell, Trans. ASME 56, 795-806 (1934)

    Google Scholar 

  • T. von Kármán, H.S. Tsien, J. Aeronaut. Sci. 8, 303-312 (1941)

    Google Scholar 

  • I.I. Vorovich, L.P. Lebedev, Nonlinear Theory of Shallow Shells (Springer Verlag, Berlin, 1999)

  • V.I. Emel'yanov, Laser Phys. 2, 389 (1992)

  • D. Walgraef, N.M. Ghoniem, J. Lauzeral, Phys. Rev. B 56, 15361 (1997)

    Google Scholar 

  • J. Lauzeral, D. Walgraef, N.M. Ghoniem, Phys. Rev. Lett. 79, 2706-9 (1997)

    Google Scholar 

  • D. Walgraef, Proceedings of the 2nd International Conference on Multiscale Materials Modeling, edited by N.M. Ghoniem (UCLA, 2004), p. 604

  • A.V. Krasheninnikov, K. Nordlund, J. Keinonen, Phys. Rev. B 65, 165423 (2002)

    Google Scholar 

  • D. Walgraef, Spatio-Temporal Pattern Formation (Springer Verlag, New York, 1996)

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Walgraef, D. On the mechanics of deformation instabilities in carbon nanotubes. Eur. Phys. J. Spec. Top. 146, 443–457 (2007). https://doi.org/10.1140/epjst/e2007-00198-3

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