Investigation of Vacancy Defects on the Young’s Modulus of Carbon Nanotube Reinforced Composites in Axial Direction via a Multiscale Modeling Approach

Document Type: Research Paper


1 Department of Mechanical Engineering, Semnan University

2 Department of Mechanical Engineering, University of Tehran


In this article, the influence of various vacancy defects on the Young’s modulus of carbon nanotube (CNT) - reinforcement polymer composite in the axial direction is investigated via a structural model in ANSYS software. Their high strength can be affected by the presence of defects in the nanotubes used as reinforcements in practical nanocomposites. Molecular structural mechanics (MSM)/finite element (FE) Multiscale modeling of carbon nanotube/polymer composites with linear elastic polymer matrix is used to study the effect of CNT vacancy defects on the mechanical properties. The nanotube is modeled at the atomistic scale using MSM, where as the interface we assumed to be bonded by Vander Waals interactions based on the Lennar-Jonze potential at the interface and polymer matrix. A nonlinear spring is used for modeling of interactions. It is studied for zigzag and armchair Nanotubes with various aspect ratios (Length/Diameter). Finally, results of the present structural model show good agreement between our model and the experimental work.       


[1] Iijima S., 1991, Helical microtubules of graphitic carbon, Nature 354- 568.

[2] Dresselhaus M.S., Dresselhaus G., Eklund P.C., 1996, Science of Fullerenes and Carbon Nanotubes, Academic Press, San Diego.

[3] Nardelli M.B., Fattebert J.L., Orlikowski D., Roland C., Zhao Q., Bernholc J., 2000, Mechanical properties, defects and electronic behavior of carbon nanotubes, Carbon 38: 1703–1711.

[4] Yakobson B.I., Avouris P., 2001, Mechanical properties of carbon nanotubes, Carbon Nanotubes, Topics in Applied Physics, edited by M.S. G. Dresselhaus, Dresselhaus, P. Avouris, Springer Verlag, Berlin/Heidelberg 80: 287-329.

[5] Overney G., Zhong W., Tomanek D., 1993, Structural rigidity and low-frequency vibrational modes of long carbon tubules, Zeitschrift Fur Physik D 27: 93-96.

[6] Lu J.P., 1997, Elastic properties of carbon nanotubes and nanoropes, Physical Review Letters 79: 1297-1300.

[7] Chang T., Gao H., 2003, Size-dependent elastic properties of a single-walled carbon nanotube via a molecular mechanics model nanotubes, Journal of the Mechanics and Physics of Solids 51: 1059-1074.

[8] Molina J.M., Savinsky S.S., Khokhriakov N.V., 1996, A tight-binding model for calculations of structures and properties of graphitic nanotubes, Journal of Chemical Physics 104: 4652-4656.

[9] Hernandez H., Goze C., Bernier P., Rubio A., 1998, Elastic properties of C and Bx Cy Nz composite nanotubes, Physical Review Letters 80: 4502-4505.

[10] Guzman de Villoria R.., Miravete A., 2007, Mechanical model to evaluate the effect of the dispersion in nanocomposites Acta Materialia 55 :3025-3031.

[11] Qian D., Wagner G.J., Liu W.K., Yu M.F., Rouff R.S., 2002, Mechanics of carbon nanotubes, Applied Mechanics Review 22: 495-533.

[12] Tserpes K.I., Papanikos P., 2005, Finite element modeling of single-walled carbon nanotubes, Composites Part B: Engineering 36: 468-477.

[13] Sakhaee-pour A., 2008, Vibrational analysis of single layered grapheme sheets, Nanothechnology 19: 085702.

[14] Chopra N. G., Zettl A., 1998, Measurement of the elastic modulus of a multi-wall boron nitride nanotube, Solid State Communications 105: 297-300.

[15] Krishnan A., Dujardin E., Ebbesen T.W., Yianilos P.N., Treacy M.M.J., 1998, Young’s modulus of single-walled nanotubes, Physical Review B 58: 14 013-14 019.

[16] Salvetat J.P., Bonard J.M., Thomson N.H., Kulik A.J., Forro L., Benoit W., Zuppiroli L.,1999, Mechanical properties of carbon nanotubes, Applied Physics A 69: 255-260.

[17] Popov V.N., Van Doran V.E., Balkanski M., 2000, Elastic properties of single-walled carbon nanotubes, Physical Review B 61: 3078-3084.

[18] Jin Y., Yuan F.G., 2002, Elastic properties of single-walled carbon nanotubes, in: 43rd AIA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, April 22-25, Denver, Colorado, USA.

[19] Frankland S.J.V., Caglar A., Brenner D.W., Griebel M., 2002, Molecular simulation of the influence of chemical cross-links on the shear strength of carbon nanotube-polymer interfaces, Journal of Physical Chemistry B 106: 3046-3048.

[20] Montazeri A., Naghdabadi R., 2009, Study the effect of Viscoelastic matrix model on the stability of CNT/polymer composites by Multiscale modeling, polymer composites, Journal of the Brazilian Chemical Society 20(3): 466-471.

[21] Yu M.F., Lourie O., Dyer M.J., Moloni K., Kelly T.F., Ruoff R.S., 2000, Strength and breaking mechanism of multi walled carbon nanotubes under tensile load, Science 287: 637-640.

[22] Krasheninikov A.V., Nordlund K., 2004, Irradiation effects in carbon nanotubes, Nuclear Instruments and Methods in Physics Research Section B 216: 355-366.

[23] Li C., Chou T.W., 2003, A structural mechanics approach for the analysis of carbon nanotubes, International Journal of Solids and Structures 40: 2487-2499.

[24] Sammalkorpi V.M., Krasheninnikov A.V., Kuronen A., Nordlund K., Kaski K., 2004, Mechanical properties of carbon nanotubes with vacancies and related defect, Physical Review B 1: 1-8.