Prediction of the critical buckling load of multi-walled carbon nanotubes under axial compression

Abdelaziz Timesli; Bouazza Braikat; Mohammad Jamal; Noureddine Damil

doi:10.1016/j.crme.2016.12.002

Prediction of the critical buckling load of multi-walled carbon nanotubes under axial compression

Abdelaziz Timesli ¹; Bouazza Braikat ² ; Mohammad Jamal ²; Noureddine Damil ²

¹ Département de génie civil et environnement, École nationale des sciences appliquées (ENSA), Université Mohammed-Premier, BP 03, Ajdir Al Hoceima, Morocco
² Laboratoire d'Ingénierie et Matériaux LIMAT, Faculté des Sciences Ben M'Sik, Université Hassan-II de Casablanca, Sidi Othman, Casablanca, Morocco

Comptes Rendus. Mécanique, Volume 345 (2017) no. 2, pp. 158-168.

Abstract
Résumé

In this paper, we propose a new explicit analytical formula of the critical buckling load of double-walled carbon nanotubes (DWCNT) under axial compression. This formula takes into account van der Waals interactions between adjacent tubes and the effect of terms involving tube radii differences generally neglected in the derived expressions of the critical buckling load published in the literature. The elastic multiple Donnell shells continuum approach is employed for modelling the multi-walled carbon nanotubes. The validation of the proposed formula is made by comparison with a numerical solution. The influence of the neglected terms is also studied.

Cet article a pour objectif la proposition d'une formule analytique explicite de la charge critique de flambage des nantubes de carbone à double parois (DWCNT) soumis à une compression axiale. Cette formule prend en compte les interactions de van der Waals entre les tubes adjacents et l'influence des rayons, généralement negligée dans les formules donnant la charge critique de flambage publiées dans la littérature. L'approche continue des coques multiples de Donnell est utilisée pour la modélisation des nanotubes de carbone multi-parois. La validation de la formule proposée est faite par une comparaison avec une solution numérique. L'effet des termes négligés a aussi été étudié.

Received: 2016-11-16
Accepted: 2016-12-20
Published online: 2017-01-06

DOI: 10.1016/j.crme.2016.12.002

Keywords: Buckling, Multi-walled carbon nanotubes, Van der Waals interaction, Axial compression, Elastic multiple Donnell shell
Mots-clés : Flambage, Nanotubes de carbone multi-parois, Interaction de van der Waals, Compression axiale, Coque élastique multiple de Donnell

Author's affiliations:

Abdelaziz Timesli ¹; Bouazza Braikat ²; Mohammad Jamal ²; Noureddine Damil ²

¹ Département de génie civil et environnement, École nationale des sciences appliquées (ENSA), Université Mohammed-Premier, BP 03, Ajdir Al Hoceima, Morocco
² Laboratoire d'Ingénierie et Matériaux LIMAT, Faculté des Sciences Ben M'Sik, Université Hassan-II de Casablanca, Sidi Othman, Casablanca, Morocco

@article{CRMECA_2017__345_2_158_0,
     author = {Abdelaziz Timesli and Bouazza Braikat and Mohammad Jamal and Noureddine Damil},
     title = {Prediction of the critical buckling load of multi-walled carbon nanotubes under axial compression},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {158--168},
     publisher = {Elsevier},
     volume = {345},
     number = {2},
     year = {2017},
     doi = {10.1016/j.crme.2016.12.002},
     language = {en},
}

TY  - JOUR
AU  - Abdelaziz Timesli
AU  - Bouazza Braikat
AU  - Mohammad Jamal
AU  - Noureddine Damil
TI  - Prediction of the critical buckling load of multi-walled carbon nanotubes under axial compression
JO  - Comptes Rendus. Mécanique
PY  - 2017
SP  - 158
EP  - 168
VL  - 345
IS  - 2
PB  - Elsevier
DO  - 10.1016/j.crme.2016.12.002
LA  - en
ID  - CRMECA_2017__345_2_158_0
ER  -

%0 Journal Article
%A Abdelaziz Timesli
%A Bouazza Braikat
%A Mohammad Jamal
%A Noureddine Damil
%T Prediction of the critical buckling load of multi-walled carbon nanotubes under axial compression
%J Comptes Rendus. Mécanique
%D 2017
%P 158-168
%V 345
%N 2
%I Elsevier
%R 10.1016/j.crme.2016.12.002
%G en
%F CRMECA_2017__345_2_158_0

Abdelaziz Timesli; Bouazza Braikat; Mohammad Jamal; Noureddine Damil. Prediction of the critical buckling load of multi-walled carbon nanotubes under axial compression. Comptes Rendus. Mécanique, Volume 345 (2017) no. 2, pp. 158-168. doi : 10.1016/j.crme.2016.12.002. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2016.12.002/

References
Cited by

[1] S. Iijima Helical microtubes of graphitic carbon, Nature, Volume 354 (1991) no. 6348, pp. 56-58

[2] B.I. Yakobson; C.J. Brabec; J. Bernholc Nanomechanics of carbon tubes: instabilities beyond linear response, Phys. Rev. Lett., Volume 76 (1996) no. 14, pp. 2511-2514

[3] W.T. Koiter On the stability of elastic equilibrium, 1945 (Ph.D. thesis, English translation, NASA Technology Transfer Programme)

[4] N. Yamaki Elastic Stability of Circular Cylindrical Shells, North-Holland, Amsterdam, 1984

[5] W.T. Koiter The effect of axisymmetric imperfections on the buckling of cylindrical shells under axial compression, Proc. K. Ned. Akad. Wet., Ser. B, Phys. Sci., Volume 66 (1963), pp. 265-279

[6] G.W. Hunt; N. Lucena Localized buckling in long axially loaded cylindrical shells, J. Mech. Phys. Solids, Volume 39 (1991) no. 7, pp. 770-783

[7] C.Q. Ru Effective bending stiffness of carbon nanotubes, Phys. Rev. B, Volume 62 (2000) no. 15, pp. 9973-9976

[8] C.Q. Ru Effect of van der Waals forces on axial buckling of a double-walled carbon nanotube, J. Appl. Phys., Volume 87 (2000) no. 10, pp. 7227-7231

[9] L. Sudak Column buckling of multiwalled carbon nanotubes using nonlocal continuum mechanics, J. Appl. Phys., Volume 94 (2003) no. 11, pp. 7281-7287

[10] C.Y. Wang; C.Q. Ru; A. Mioduchowski Axially compressed buckling of pressured multiwall carbon nanotubes, Int. J. Solids Struct., Volume 40 (2003) no. 15, pp. 3893-3911

[11] J.T. Feng; K.Y. Xu; C.Q. Ru Curvature effect of interlayer van der Waals forces on axial buckling of a double-walled carbon nanotubes, Int. J. Struct. Stab. Dyn., Volume 4 (2004), pp. 515-526

[12] Y.Q. Zhang; G.R. Liu; J.S. Wang Small-scale effects on buckling of multiwalled carbon nanotubes under axial compression, Phys. Rev. B, Volume 70 (2004) no. 20

[13] X.Q. He; S. Kitipornchai; K.M. Liew Buckling analysis of multi-walled carbon nanotubes: a continuum model accounting for van der Waals interaction, J. Mech. Phys. Solids, Volume 53 (2005) no. 2, pp. 303-326

[14] T. Natsuki; Q.Q. Ni; M. Endo Stability analysis of double-walled carbon nanotubes as afm probes based on a continuum model, Carbon, Volume 49 (2011), pp. 2532-2537

[15] A.R. Ranjbartoreh; G.X. Wang; A. GhorbanpourArani; A. Loghman Comparative consideration of axial stability of single and double-walled carbon nanotube and its inner and outer tubes, Physica E, Volume 41 (2008), pp. 202-208

[16] T. Natsuki; T. Tsuchiya; Q.Q. Ni; M. Endo Torsional elastic instability of double-walled carbon nanotubes, Carbon, Volume 48 (2010) no. 15, pp. 4362-4368

[17] J. Wu; Q. Cheng; B. Liu; Y.W. Zhang; W.B. Lu; K.C. Hwang Study on the axial compression buckling behaviors of concentric multi-walled cylindrical shells filled with soft materials, J. Mech. Phys. Solids, Volume 60 (2012), pp. 803-826

[18] C.Q. Ru Degraded axial buckling strain of multiwalled carbon nanotubes due to interlayer slips, J. Appl. Phys., Volume 89 (2001) no. 6, pp. 3426-3433

[19] C.Q. Ru Axially compressed buckling of a double-walled carbon nanotube embedded in an elastic medium, J. Mech. Phys. Solids, Volume 49 (2001) no. 6, pp. 1265-1279

[20] C.Q. Ru Elastic models for carbon nanotubes (H.S. Nalwa, ed.), Encyclopedia of Nanoscience and Nanotechnology, vol. 2, American Scientific, Stevenson Ranch, CA, USA, 2004, pp. 731-744

[21] E.W. Wong; P.E. Sheehan; C.M. Lieber Nanobeam mechanics elasticity, strength, and toughness of nanorods and nanotubes, Science, Volume 277 (1977), pp. 1971-1975

[22] B.I. Yacobson; C.J. Brabec; J. Bernhole Nanomechanics of carbon nanotubes: instabilities beyond linear response, Phys. Rev. Lett., Volume 76 (1996), pp. 2511-2514

[23] M.M.J. Treacy; T. Ebbesen; J.M. Gibson Exceptionally high Young's modulus observed for individual carbon nanotubes, Nature, Volume 381 (1996), pp. 678-680

[24] M.R. Falvo; G.J. Clary; R.M. Taylor; V. Chi; F.P. Brooks; S. Washburn; R. Superfine Bending and buckling of carbon nanotubes under large strain, Nature, Volume 389 (1997), pp. 582-584

[25] P. Poncharal; Z.L. Wang; D. Ugarte; W.A. De Heer Electrostatic deflexions and electromechanical resonances of carbon nanotubes, Science, Volume 283 (1999), pp. 1513-1516

[26] L.H. Donnell A new theory of the buckling of thin cylindrical shells under compression and bending, ASME Trans., Volume 56 (1934), pp. 795-806

[27] S.P. Timoshenko; J.M. Gere Theory of Elastic Stability, McGraw-Hill, New York, 1961

[28] C. Calladine Theory of Shell Structures, Cambridge University Press, Cambridge, UK, 1983

[29] D. Brush; B. Almroth Buckling of Bars, Plates and Shells, McGraw-Hill, New York, 1975

[30] R. Abdelmoula; N. Damil; M. Potier-Ferry Influence of distributed and localized imperfections on the buckling of cylindrical-shells under external-pressure, Int. J. Solids Struct., Volume 29 (1992), pp. 1-25

[31] N. Damil; M. Potier-Ferry Amplitude equation for cellular instability, Dyn. Stab. Syst., Volume 7 (1992), pp. 1-34

[32] M. Jamal; M. Midani; N. Damil; M. Potier-Ferry Influence of localized imperfections on the buckling of cylindrical shells under axial compression, Int. J. Solids Struct., Volume 36 (1999) no. 3, pp. 441-464

[33] M. Jamal; L. Lahlou; M. Midani; H. Zahrouni; A. Limam; N. Damil; M. Potier-Ferry A semi-analytical buckling analysis of imperfect cylindrical shells under axial compression, Int. J. Solids Struct., Volume 40 (2003), pp. 1311-1327

[34] R. Saito; R. Matsuo; T. Kimura; G. Desselhaus; M.S. Dresselhaus Anomalous potential barrier of double-wall carbon nanotube, Chem. Phys. Lett., Volume 348 (2001) no. 3–4, pp. 187-193

[35] N. Damil; M. Potier-Ferry A new method to compute perturbed bifurcations: application to the buckling of imperfect elastic structures, Int. J. Eng. Sci., Volume 28 (1990), pp. 943-957

[36] M. Jamal; M. Midani; N. Damil; M. Potier-Ferry Influence of localized imperfections on the buckling of cylindrical shells under axial compression, Int. J. Solids Struct., Volume 25 (1999), pp. 330-353

[37] M. Endo; H. Muramatsu; T. Hayashi; Y.A. Kim; M. Terrones; M.S. Dresselhaus Nanotechnology: ‘buckypaper’ from coaxial nanotubes, Nature, Volume 433 (2005) no. 7025, p. 476

[38] Y.G. Sun; X.H. Yao; Q. Han Combined torsional buckling of double-walled carbon nanotubes with axial load in the multi-field coupled condition, Sci. China, Ser. G, Phys. Mech. Astron., Volume 54 (2011) no. 9, pp. 1659-1665

Cited by Sources:

Comments - Policy