Advances in materials Research

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Thermal buckling properties of zigzag single-walled carbon nanotubes using a refined nonlocal model

  • Semmah, Abdelwahed (Faculte des Sciences Exactes, Departement de Physique, Universite de Sidi Bel Abbes) ;
  • Beg, O. Anwar (Gort Engovation-Propulsion, Nanomechanics and Biophysics, Southmere Avenue) ;
  • Mahmoud, S.R. (Department of Mathematics, Faculty of Science, King Abdulaziz University) ;
  • Heireche, Houari (Faculte des Sciences Exactes, Departement de Physique, Universite de Sidi Bel Abbes) ;
  • Tounsi, Abdelouahed (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department)
  • Received : 2014.05.11
  • Accepted : 2014.06.29
  • Published : 2014.06.25
⟨ Previous Next ⟩

Abstract

In the present article, the thermal buckling of zigzag single-walled carbon nanotubes (SWCNTs) is studied using a nonlocal refined shear deformation beam theory and Von-Karman geometric nonlinearity. The model developed simulates both small scale effects and higher-order variation of transverse shear strain through the depth of the nanobeam. Furthermore the present formulation also accommodates stress-free boundary conditions on the top and bottom surfaces of the nanobeam. A shear correction factor, therefore, is not required. The equivalent Young's modulus and shear modulus for zigzag SWCNTs are derived using an energy-equivalent model. The present study illustrates that the thermal buckling properties of SWCNTs are strongly dependent on the scale effect and additionally on the chirality of zigzag carbon nanotube. Some illustrative examples are also presented to verify the present formulation and solutions. Good agreement is observed.

Keywords

References

  1. Anwar Beg, O. and Islam, M.N. (2011), HPM Simulation of Double-Walled Carbon Nanotubes in Bending, Technical Report, Aero-786, Dept. Engineering and Mathematics, Sheffield Hallam University.
  2. Benguediab, S., Tounsi, A., Zidour, M. and Semmah, A. (2014), "Chirality and scale effects on mechanical buckling properties of zizag double-walled carbon nanotubes", Compos. Part B: Eng, 57, 21-24. https://doi.org/10.1016/j.compositesb.2013.08.020
  3. Dirote, E.V. (2004), "Trends in Nanotechnology research", Nova Science Publishers, New York.
  4. Cornell, W.D., Cieplak, P., Bayly, C.I., Gould, I.R., Merz, K.M., Feguson, D.M., Spellmeyer, D.C., Fox, T., Caldwell, J.W. and Kollman, P.A. (1995), "A second generation force field for the simulation of proteins, nucleic acids, and organic molecules", J. Am. Chem. Soc., 117, 5179. https://doi.org/10.1021/ja00124a002
  5. Cowper, C.R. (1996), "The shear coefficient in Timoshenko's beam theory",J. Appl. Mech., 33, 335-340.
  6. Eringen, A.C. and Edelen, D.G.B. (1972), "On nonlocal elasticity", Int. J. Eng. Sci., 10, 233-248. https://doi.org/10.1016/0020-7225(72)90039-0
  7. Eringen, A.C. (1983), "On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves", J. Appl. Phys., 54, 4703-4710. https://doi.org/10.1063/1.332803
  8. Eringen, A.C. (2002), "Nonlocal continuum field theories", Springer, New York.
  9. Heireche, H., Tounsi, A., Benzair, A., Maachou, M. and Adda Bedia, E.A. (2008a), "Sound wave propagation in single- walled carbon nanotubes using nonlocal elasticity", Physica E., 40, 2791-2799 https://doi.org/10.1016/j.physe.2007.12.021
  10. Heireche, H., Tounsi, A., Benzair, A. and Mechab, I. (2008b), "Sound wave propagation in single - Carbon nanotubes with initial axial stress", J. Appl. Phys., 104, 014301. https://doi.org/10.1063/1.2949274
  11. Heireche, H., Tounsi, A. and Benzair, A. (2008c), "Scale effect on wave propagation of double-walled carbon nanotubes with initial axial loading", Nanotech., 19, 185703. https://doi.org/10.1088/0957-4484/19/18/185703
  12. Hernandez, E., Goze, C., Bernier, P. and Rubio, A. (1998), "Elastic Properties of C and BxCyNz Composite Nanotubes", Phys. Rev. Lett., 80, 4502. https://doi.org/10.1103/PhysRevLett.80.4502
  13. Iijima, S. (1991), "Helical microtubules of graphitic carbon", Nature, 354, 56-58. https://doi.org/10.1038/354056a0
  14. Iijima, S., Brabec, C., Maiti, A. and Bernholc, J. (1996), "Structural flexibility of carbon nanotubes", J. Chem. Phys., 104, 2089-2092. https://doi.org/10.1063/1.470966
  15. Kiani, K. (2013a), "Longitudinal, transverse, and torsional vibrations and stabilities of axially moving single-walled carbon nanotubes", Current Appl. Phys., 13(8), 1651-1660. https://doi.org/10.1016/j.cap.2013.05.008
  16. Kiani, K. (2013b), "Vibration behavior of simply supported inclined single-walled carbon nanotubes conveying viscous fluids flow using nonlocal Rayleigh beam model", Appl. Math. Model., 37(4), 1836-1850. https://doi.org/10.1016/j.apm.2012.04.027
  17. Kiani, K. (2014a), "Vibration and instability of a single-walled carbon nanotube in a three-dimensional magnetic field", J. Phys. Chem. Solids, 75(1), 15-22. https://doi.org/10.1016/j.jpcs.2013.07.022
  18. Kiani, K. (2014b), "Nonlocal continuous models for forced vibration analysis of two- and three-dimensional ensembles of single-walled carbon nanotubes", Phys. E., 60, 229-245. https://doi.org/10.1016/j.physe.2014.01.033
  19. Lu, P., Lee, H.P., Lu, C. and Zhang, P.Q. (2006), "Dynamic properties of flexural beams using a nonlocal elasticity model", J. Appl. Phys., 99, 073510. https://doi.org/10.1063/1.2189213
  20. Lu, P., Lee, H.P., Lu, C. and Zhang, P.Q. (2007), "Application of nonlocal beam models for carbon nanotubes", Int. J. Solids Struct., 44, 5289-5300. https://doi.org/10.1016/j.ijsolstr.2006.12.034
  21. Ottenhouse, A.P. (2009), "Carbon nanotubes: new research", New York, NY: Nova Science Publishers.
  22. O'Connell, M.J. (2006), "Carbon Nanotubes: Properties and Applications", CRC Press, Boca Raton.
  23. Peddieson, J., Buchanan, G.R. and McNitt, R.P. (2003), "Application of nonlocal continuum models to nanotechnology", Int. J. Eng. Sci., 41, 305-312. https://doi.org/10.1016/S0020-7225(02)00210-0
  24. Reddy, J.N. and Pang, S.D. (2008), "Nonlocal continuum theories of beams for the analysis of carbon nanotubes", J. Appl. Phys., 103, 023511. https://doi.org/10.1063/1.2833431
  25. Sanchez-Portal, D., Artacho, E., Soler, J.M., Rubio, A. and Ordejon, P. (1999), "Ab-initio structural, elastic, and vibrational properties of carbon nanotubes", Phys. Rev. B., 59, 12678. https://doi.org/10.1103/PhysRevB.59.12678
  26. Semmah, A., Tounsi, A., Zidour, M.,Heireche, H. and Naceri, M. (2014), "Effect of chirality on critical buckling temperature of a zigzag single-walled carbon nanotubes using nonlocal continuum theory", Fullerenes, Nanotubes and Carbon Nanostructures, (In press).
  27. Sudak, L.J. (2003), "Column buckling of multiwalled carbon nanotubes using nonlocal continuum mechanics", J. Appl.Phys., 94, 7281. https://doi.org/10.1063/1.1625437
  28. Tokio, Y. (1995), "Recent development of carbon nanotube", Synth Met., 70, 1511-1518. https://doi.org/10.1016/0379-6779(94)02939-V
  29. Tounsi, A., Heireche, H., Berrabah, H.M., Benzair, A. and Boumia, L. (2008), "Effect of small size on wave propagation in double-walled carbon nanotubes under temperature field", J. Appl. Phys.104, 104301. https://doi.org/10.1063/1.3018330
  30. Tounsi, A., Heireche, H., Berrabah, H.M. and Mechab, I. (2009a), "Comment on [Vibration analysis of fluid-conveying double-walled carbon nanotubes based on nonlocal elastic theory]", J. Phys.-Condens. Matter., 21, 448001. https://doi.org/10.1088/0953-8984/21/44/448001
  31. Tounsi, A., Heireche, H. and Adda Bedia, E.A. (2009b), "Comment on "Free transverse vibration of the fluid-conveying single-walled carbon nanotube using nonlocal elastic theory" [J. Appl. Phys. 103, 024302 2008]", J. Appl. Phys., 105, 126105. https://doi.org/10.1063/1.3153960
  32. Tounsi, A., Benguediab, S., Adda Bedia, E.A., Semmah, A. and Zidour, M. (2013a), "Nonlocal effects on thermal buckling properties of double-walled carbon nanotubes", Adv. Nano Res., 1(1), 1-11. https://doi.org/10.12989/anr.2013.1.1.001
  33. Tounsi, A., Benguediab, S., Houari, M.S.A. and Semmah, A. (2013b), "A new nonlocal beam theory with thickness stretching effect for nanobeams", Int. J. Nanosci., 12, 1350025. https://doi.org/10.1142/S0219581X13500257
  34. Tounsi, A., Semmah, A. and Bousahla, A.A. (2013c)," Thermal buckling behavior of nanobeam using an efficient higher-order nonlocal beam theory", J. Nanomech. Micromech. (ASCE), 3, 37-42. https://doi.org/10.1061/(ASCE)NM.2153-5477.0000057
  35. Wang, Y.Z., Li, F.M. and Kishimoto, K. (2010a), "Wave propagation characteristics in fluid-conveying double-walled nanotubes with scale effects",Comput. Mater. Sci., 48, 413-418. https://doi.org/10.1016/j.commatsci.2010.01.034
  36. Wang, Y.Z., Li, F.M. and Kishimoto, K. (2010b), "Flexural wave propagation in double-layered nanoplates with small scale effects", J. Appl. Phys., 108, 064519. https://doi.org/10.1063/1.3481438
  37. Wang, Y.Z., Li, F.M. and Kishimoto, K. (2010c), "Scale effects on the longitudinal wave propagation in nanoplates", Phys. E., 42, 1356-1360. https://doi.org/10.1016/j.physe.2009.11.036
  38. Wang, Q. and Varadan, V.K. (2006), "Vibration of carbon nanotubes studied using nonlocal continuum mechanics", Smart Mater. Struct., 15, 659. https://doi.org/10.1088/0964-1726/15/2/050
  39. Wang, Q. (2005), "Wave propagation in carbon nanotubes via nonlocal continuum mechanics", J. Appl. Phys., 98, 124301. https://doi.org/10.1063/1.2141648
  40. Wang, L.F. and Hu, H.Y. (2005), "Flexural wave propagation in single-walled carbon nanotubes",Phys. Rev. B., 71, 195412. https://doi.org/10.1103/PhysRevB.71.195412
  41. Wang, C.M., Zhang, Y.Y., Ramesh, S.S. and Kitipornchai, S. (2006), "Buckling analysis of micro-and nano-rods/tubes based on nonlocal Timoshenko beam theory", J. Phys. D: Appl. Phys., 39, 3904-3909. https://doi.org/10.1088/0022-3727/39/17/029
  42. Wang, C.M., Zhang, Y.Y. and He, X.Q. (2007), "Vibration of nonlocal Timoshenko beams", Nanatechnology, 18, 105401. https://doi.org/10.1088/0957-4484/18/10/105401
  43. Wu, Y., Zhang, X., Leung, A.Y.T. and Zhong, W. (2006), "An energy-equivalent model on studying the mechanical properties of single-walled carbon nanotubes",Thin-Walled Struct., 44, 667-676. https://doi.org/10.1016/j.tws.2006.05.003
  44. Yakobson, B.I., Campbell, M.P., Brabec, C.J. and Bernholc, J. (1997), "High strain rate fracture and C-chain unraveling in carbon nanotubes", Comput. Mater. Sci., 8, 341-348. https://doi.org/10.1016/S0927-0256(97)00047-5
  45. Yao, X. and Han, Q. (2006), "Buckling analysis of multiwalled carbon nanotubes under torsional loadcoupling with temperature change", J. Eng. Mater. Technol., 128, 419-424. https://doi.org/10.1115/1.2203102
  46. Zidour, M., Benrahou, K.H., Semmah, A., Naceri, M., Belhadj, H.A., Bakhti, K. and Tounsi, A. (2012), "The thermal effect on vibration of zigzag single walled carbon nanotubes using nonlocal Timoshenko beam theory", Comput. Mater. Sci., 51, 252-260. https://doi.org/10.1016/j.commatsci.2011.07.021
  47. Zidour, M., Daouadji, T.H., Benrahou, K.H., Tounsi, A., Adda Bedia, E.A. and Hadji, L. (2014), "Buckling analysis of chiral single-walled carbon nanotubes by using the nonlocal Timoshenko beam theory", Mech. Compos. Mater., 50(1), 95-104. https://doi.org/10.1007/s11029-014-9396-0

Cited by

  1. Numerical simulation of self-similar thermal convection from a spinning cone in anisotropic porous medium vol.28, pp.2, 2016, https://doi.org/10.1016/S1001-6058(16)60620-0
  2. Nonlinear ultrasonic waves in a magneto-flexo-thermally actuated single walled armchair carbon nanotube embedded on polymer matrix vol.18, pp.1, 2014, https://doi.org/10.1108/wje-02-2020-0066
  3. Ultrasonic waves in a single walled armchair carbon nanotube resting on nonlinear foundation subjected to thermal and in plane magnetic fields vol.10, pp.1, 2021, https://doi.org/10.12989/csm.2021.10.1.039