Skip to main content
Log in

A review of the mechanical properties of isolated carbon nanotubes and carbon nanotube composites

  • Published:
Mechanics of Composite Materials Aims and scope

A literature review on the prediction of Young’s modulus for carbon nanotubes, from both theoretical and experimental aspects, is presented. The discrepancies between the values of Young’s modulus reported in the literature are analyzed, and different trends of the results are discussed. The available analytical and numerical simulations for predicting the mechanical properties of carbon nanotube composites are also reviewed. A gap analysis is performed to highlight the obstacles and drawbacks of the modeling techniques and fundamental assumptions employed which should be overcome in further studies. The aspects which should be studied more accurately in modeling carbon nanotube composites are identified.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. H. Dai, “Carbon nanotubes: opportunities and challenges,” Surface Sci., 500, 218-241 (2002).

    CAS  ADS  Google Scholar 

  2. I. Kang, Y. Y. Heung, J. H. Kim, J. W. Lee, R. Gollapudi, S. Subramaniam, et al., “Introduction to carbon nanotube and nanofiber smart materials,” Composites, Pt. B, 37, 382-394 (2006).

    Google Scholar 

  3. J. P. Salvetat-Delmotte and A. Rubio, “Mechanical properties of carbon nanotubes: a fiber digest for beginners,” Carbon, 40, 1729-1734 (2002).

    CAS  Google Scholar 

  4. D. Qian, E. Dickey, R. Andrews, and T. Rantell, “Load transfer and deformation mechanisms in carbon nanotube-polystyrene composites,” Appl. Phys. Lett., 76, No. 20, 2868-2870 (2000).

    CAS  ADS  Google Scholar 

  5. E. T. Thostenson, Z. Ren, and T.-W. Chou, “Advances in the science and technology of carbon nanotubes and their composites: a review,” Compos. Sci. Technol., 61, 1899-1912 (2001).

    CAS  Google Scholar 

  6. T. Belin and F. Epron, “Characterization methods of carbon nanotubes: a review,” Mater. Sci. Eng. B, 199, 105-118 (2005).

    Google Scholar 

  7. H. Rafii-Tabar, “Computational modelling of thermo-mechanical and transport properties of carbon nanotubes,” Phys. Rep., 390, 235-452 (2004).

    CAS  ADS  Google Scholar 

  8. M. M. Treacy, T. W. Ebbesen, and J. M. Gibson, “Exceptionally high Young’s modulus observed for individual carbon nanotubes,” Nature, 38, 678-680 (1996).

    ADS  Google Scholar 

  9. A. Krishnan, E. Dujardin, T. W. Ebbesen, P. N. Yianilos, and M. M. J. Treacy, “Young’s modulus of single-walled nanotubes,” Phys. Rev. Lett. B, 58, No. 20, 14013-14019 (1998).

    CAS  ADS  Google Scholar 

  10. O. Lourie, D. M. Cox, and H. D. Wagner, “Buckling and collapse of embedded carbon nanotubes,” Phys. Rev. Lett., 81, No. 8, 1638-1641 (1998).

    CAS  ADS  Google Scholar 

  11. J. P. Salvetat, G. A. D. Briggs, J. M. Bonard, R. R. Bacsa, A. J. Kulik, T. Stockli, et al., “Elastic and shear modulus of single-walled carbon nanotube ropes,” Phys. Rev. Lett., 82, No. 5, 944-947 (1999).

    CAS  ADS  Google Scholar 

  12. M. F. Yu, O. Lourie, M. J. Dyer, K. Moloni, T. F. Kelly, and R. S. Ruo, “Strength and breaking mechanism of multiwalled carbon nanotubes under tensile load,” Science, 287, No. 5453, 637-640 (2000).

    CAS  PubMed  ADS  Google Scholar 

  13. T. W. Tombler, C. Zhou, J. Kong, H. Dai, L. Liu, C. S. Jayanthi, et al., “Reversible electromechanical characteristics of carbon nanotubes under local-probe manipulation,” Nature, 405, 769-772 (2000).

    CAS  PubMed  ADS  Google Scholar 

  14. Q. Lu, B. Bhattacharya, “The role of atomistic simulations in probing the small-scale aspects of fracture—a case study on a single-walled carbon nanotube,” Eng. Fract. Mech., 72, 2037-2071 (2005).

    Google Scholar 

  15. Y. Omata, Y. Yamagami, K. Tadano, T. Miyake, and S. Saito, “Nanotube nanoscience: a molecular-dynamics study,” Physica E, 29, 454-468 (2005).

    CAS  ADS  Google Scholar 

  16. K. J. Bathe, Finite Element Procedures, Prentice-Hall of India Private Ltd., New Delhi — 110 001 (1997), pp. 1-14.

  17. K. Behfar and R. Naghdabadi, “Nanoscale modeling of an embedded multi-shell fullerene and its application to vibrational analysis,” Int. J. Eng. Sci., 44, 1156-1163 (2006).

    CAS  MathSciNet  Google Scholar 

  18. E. B. Tadmor, R. Phillips, and M. Ortiz, “Mixed atomistic and continuum models of deformation in solids,” Langmuir, 12, No. 19, 4529-4534 (1996).

    CAS  Google Scholar 

  19. G. M. Odegard, T. S. Gates, L. M. Nicholson, and K. E. Wise, “Equivalent-continuum modeling of nano-structured materials,” Compos. Sci. Technol., 62, 1869-1880 (2002).

    CAS  Google Scholar 

  20. T. Chang and H. Gao, “Size-dependent elastic properties of a single-walled carbon nanotube via a molecular mechanics model,” J. Mech. Phys. Solids, 51, 1059-1074 (2003).

    MATH  CAS  ADS  Google Scholar 

  21. L. Nasdala and G. Ernst, “Development of a 4-node finite element for the computation of nano-structured materials,” Comput. Mater. Sci., 33, 443-458 (2005).

    Google Scholar 

  22. D. G. Robertson, D. W. Brenner, and J. W. Mintmire, “Energies of nanoscale graphitic tubule,” Phys. Rev. B, 45, No. 21, 12592-12595 (1992).

    ADS  Google Scholar 

  23. J. M. Molina, S. S. Savinsky, and N. V. Khokhriakov, “A tight-binding model for calculations of structures and properties of graphitic nanotubes,” J. Chem. Phys., 104, No. 12, 4652-4656 (1996).

    CAS  ADS  Google Scholar 

  24. C. F. Cornwell and L. R. Wille, “Elastic properties of single-walled carbon nanotubes in compression,” Solid State Commun., 101, No. 8, 555-558 (1997).

    CAS  ADS  Google Scholar 

  25. R. S. Ruoff and D. C. Lorents, “Mechanical and thermal properties of carbon nanotubes,” Carbon, 33, 925-930 (1995).

    CAS  Google Scholar 

  26. J. P. Lu, “Elastic properties of carbon nanotubes and nanoropes,” Phys. Rev. Lett., 79, No. 7, 1297-1300 (1997).

    CAS  ADS  Google Scholar 

  27. B. I. Yakobson, C. J. Brabec, and J. Bernholc, “Nanomechanics of carbon tubes: Instabilities beyond linear response,” Phys. Rev. Lett., 76, No. 14, 2511-2514 (1996).

    CAS  PubMed  ADS  Google Scholar 

  28. T. Haliciglu, “Stress calculation for carbon nanotubes,” Thin Solid Films, 312, 11-14 (1998).

    ADS  Google Scholar 

  29. N. Yao and V. Lordi, “Young’s modulus of single-walled carbon nanotubes,” J. Appl. Phys., 84, No. 4, 1939-1943 (1998).

    CAS  ADS  Google Scholar 

  30. G. Overney, W. Zhong, and D. Z. Tomanek, “Structural rigidity and low frequency vibrational modes of long carbon tubules,” J. Phys. D, 27, 93-96 (1993).

    CAS  ADS  Google Scholar 

  31. E. Hernandez, C. Goze, P. Bernier, and A. Rubio, “Elastic properties of single-wall nanotubes,” Appl. Phys. A, 68, 287-292 (1999).

    CAS  ADS  Google Scholar 

  32. E. W. Wong, P. E. Sheehan, and C. M. Lieber, “Nanobeam mechanics: elasticity, strength, and toughness of nanorods and nanotubes,” Science, 227, 1971-1975 (1997).

    Google Scholar 

  33. S. B. Sinnott, O. A. Shenderova, C. T. White, and D. W. Brenner, “Mechanical properties of nanotube fibers and composites determined from theoretical calculations and simulations,” Carbon, 36, Nos. 1/2, 1-9 (1998).

    CAS  Google Scholar 

  34. C. Goze, L. Vaccarini, L. Henard, P. Bernier, E. Hernandez, and A. Rubio, “Elastic and mechanical properties of carbon nanotubes,” Synth. Met., 103, 2500-2501 (1999).

    CAS  Google Scholar 

  35. D. Sanchez-Portal, E. Artacho, J. M. Soler, A. Rubio, and P. Ordejon, “Ab initio structural, elastic, and vibrational properties of carbon nanotubes,” Phys. Rev. B, 59, No. 19, 12678-12688 (1999).

    CAS  ADS  Google Scholar 

  36. Y. I. Prylutskyy, S. S. Durov, O. V. Ogloblya, E. V. Buzaneva, and P. Scharff, “Molecular dynamics simulation of mechanical, vibrational and electronic properties of carbon nanotubes,” Comp. Mater. Sci., 17, Nos. 2/4, 352-355 (2000).

    CAS  Google Scholar 

  37. G. V. Lier, C. V. Alsenoy, V. V. Doren, and P. Geerlings, “Ab initio study of the elastic properties of single-walled carbon nanotubes and grapheme,” Chem. Phys. Lett., 326, 181-185 (2000).

    Google Scholar 

  38. L. Vaccarini, C. Goze, L. Henrard, E. Hernandez, P. Bernier, and A. Rubio, “Mechanical and electronic properties of carbon and boron–nitride nanotubes,” Carbon, 38, 1681-1690 (2000).

    CAS  Google Scholar 

  39. Z. Xin, Z. Jianjun, and O. Y. Zhong-can, “Strain energy and Young’s modulus of single-wall carbon nanotubes calculated from electronic energy-band theory,” Phys. Rev. B, 62, No. 20, 13692-13696 (2000).

    CAS  ADS  Google Scholar 

  40. G. Zhou, W. Duan, and B. Gu, “First-principles study on morphology and mechanical properties of single-walled carbon nanotube,” Chem. Phys. Lett., 333, 344-349 (2001).

    CAS  ADS  Google Scholar 

  41. K. N. Kudin, G. E. Scuseria, and B. I. Yakobson, “C2F, BN, and C nanoshell elasticity from ab initio computations,” Phys. Rev. B, 64, No. 23, Art. No. 235406 (2001).

  42. Y. Jin and F. G. Yuan, “Simulation of elastic properties of single-walled carbon nanotubes,” Compos. Sci. Technol., 63, 1507-1515 (2003).

    CAS  Google Scholar 

  43. V. N. Popov, V. E. Van Doren, and M. Balkanski, “Elastic properties of crystals of single-walled carbon nanotubes,” Solid State Commun., 114, 395-399 (2000).

    CAS  ADS  Google Scholar 

  44. K. M. Liew, X. Q. He, and C. W. Wong, “On the study of elastic and plastic properties of multi-walled carbon nanotubes under axial tension using molecular dynamics simulation,” Acta Mater., 52, 2521-2527 (2004).

    CAS  Google Scholar 

  45. H. W. Zhang, J. B. Wang, and X. Guo, “Predicting the elastic properties of single-walled carbon nanotubes,” J. Mech. Phys. Solids, 53, 1929-1950 (2005).

    MATH  CAS  ADS  Google Scholar 

  46. T. Natsuki, K. Tantrakarn, and M. Endo, “Prediction of elastic properties for single-walled carbon nanotubes,” Carbon, 42, 39-45 (2004).

    CAS  Google Scholar 

  47. K. Chandraseker and S. Mukherjee, “Atomistic-continuum and ab initio estimation of the elastic moduli of single-walled carbon nanotubes,” Comput. Mater. Sci., 40, 147-158 (2007).

    CAS  Google Scholar 

  48. H. Jiang, P. Zhang, B. Liu, Y. Huang, P. H. Geubelle, H. Gao, et al., “The effect of nanotube radius on the constitutive model for carbon nanotubes,” Comput. Mater. Sci., 28, 429-442 (2003).

    CAS  Google Scholar 

  49. J. Despres, E. Daguerre, and K. Lafdi, “Flexibility of graphene layers in carbon nanotubes,” Carbon, 33, 87-92 (1995).

    CAS  Google Scholar 

  50. S. Iijima, C. J. Brabec, A. Maiti, and J. Bernholc, “Structural flexibility of carbon nanotubes,” J. Chem. Phys., 104, 2089-2092 (1996).

    CAS  ADS  Google Scholar 

  51. N. Chopra, L. Benedict, V. Crespi, M. Cohen, S. Louie, and A. Zettl, “Fully collapsed carbon nanotubes,” Nature (London), 377, 135-138 (1995).

    CAS  ADS  Google Scholar 

  52. S. Govindjee and J. L. Sackman, “On the use of continuum mechanics to estimate the properties of nanotubes,” Solid State Commun., 110, 227-230 (1999).

    CAS  ADS  Google Scholar 

  53. V. M. Harik, “Mechanics of carbon nanotubes: applicability of the continuum-beam models,” Comput. Mater. Sci., 24, 328-342 (2002).

    CAS  Google Scholar 

  54. C. Q. Ru, “Degraded axial buckling strain of multiwalled carbon nanotubes due to interlayer slip,” J. Appl. Phys., 89, No. 6, 3426-3433 (2001).

    CAS  ADS  Google Scholar 

  55. J. Tersoff and R. S. Ruoff, “Structural properties of a carbon-nanotube crystal,” Phys. Rev. Lett., 73, 676-679 (1994).

    CAS  PubMed  ADS  Google Scholar 

  56. H. Gao, Y. Huang, and F. A. Abharam, “Continuum and atomistic studies of intersonic crack propagation,” J. Mech. Phys. Solids, 49, 2113-2132 (2001).

    MATH  ADS  Google Scholar 

  57. Z. Tu and Z. Ou-Yang, “Single-walled and multiwalled carbon nanotubes viewed as elastic tubes with the effective Young’s moduli dependent on layer number,” Phys. Rev. B, 65, No. 23, Art. No. 233407 (2002).

  58. P. Zhang, Y. Huang, P. H. Geubelle, P. A. Klein, and K. C. Hwang, “The elastic modulus of single-wall carbon nanotubes: a continuum analysis incorporating interatomic potentials,” Int. J. Solids Struct., 39, 3893-3906 (2002).

    MATH  Google Scholar 

  59. E. Saether, S. J. V. Frankland, and R. B. Pipes, “Transverse mechanical properties of single-walled carbon nanotube crystals. Pt. I: Determination of elastic moduli,” Compos. Sci. Technol., 63, 1543-1550 (2003).

    CAS  Google Scholar 

  60. X. L. Gao and K. Li, “Finite deformation continuum model for single-walled carbon nanotubes,” Int. J. Solids Struct., 40, 7329-7337 (2003).

    MATH  MathSciNet  Google Scholar 

  61. Q. Wang, “Effective in-plane stiffness and bending rigidity of armchair and zigzag carbon nanotubes,” Int. J. Solids Struct., 41, 5451-5461 (2004).

    MATH  Google Scholar 

  62. J. R. Xiao, B. A. Gama, and J. W. Gillespie Jr., “An analytical molecular structural mechanics model for the mechanical properties of carbon nanotubes,” Int. J. Solids Struct., 42, 3075-3092 (2005).

    MATH  Google Scholar 

  63. C. Li and T. W. Chou, “A structural mechanics approach for the analysis of carbon nanotubes,” Int. J. Solids Struct., 40, 2487-2499 (2003).

    MATH  Google Scholar 

  64. Y. Wu, X. Zhang, A. Y. T. Leung, and W. Zhong, “An energy-equivalent model on studying the mechanical properties of single-walled carbon nanotubes,” Thin-Walled Struct., 44, 667-676 (2006).

    Google Scholar 

  65. A. L. Kalamkarov, A. V. Georgiades, S. K. Rokkam, V. P. Veedu, and M. N. Ghasemi-Nejhad, “Analytical and numerical techniques to predict carbon nanotubes properties,” Int. J. Solids Struct., 43, 6832-6854 (2006).

    MATH  CAS  Google Scholar 

  66. G. D. Seidel and D. C. Lagoudas, “Micromechanical analysis of the effective elastic properties of carbon nanotube reinforced composites,” Mech. Mater., 38, 884-907 (2006).

    Google Scholar 

  67. A. Selmi, C. Friebel, I. Doghri, and H. Hassis, “Prediction of the elastic properties of single walled carbon nanotube reinforced polymers: a comparative study of several micromechanical models,” Compos. Sci. Technol., 67, 2071-2084 (2007).

    CAS  Google Scholar 

  68. M. M. Shokrieh and R. Rafiee, “On the effective stiffness of graphene sheets and carbon nanotubes,” in: Extended Abstracts, 15th Int. Conf. Compos. Struct., Porto (Portugal) (2009).

  69. A. Pantano, D. M. Parks, and M. C. Boyce, “Mechanics of deformation of single- and multi-wall carbon nanotubes,” J. Mech. Phys. Solids, 52, 789-821 (2004).

    MATH  CAS  ADS  Google Scholar 

  70. X. Y. Wang and X. Wang, “Numerical simulation for bending modulus of carbon nanotubes and some explanations for experiment,” Composites, Pt. B, 35, 79-86 (2004).

    Google Scholar 

  71. C. W. S. To, “Bending and shear moduli of single-walled carbon nanotubes,” Finite Elem. Anal. Des., 42, 404-413 (2006).

    Google Scholar 

  72. B. Liu, H. Jiang, Y. Huang, S. Qu, M. F. Yu, and K. C. Hwang, “Atomic-scale finite element method in multiscale computation with applications to carbon nanotubes,” Phys. Rev. B, 72, Art. No. 035435 (2005).

    Google Scholar 

  73. X. Sun and W. Zhao, “Prediction of stiffness and strength of single-walled carbon nanotubes by molecular-mechanics based finite element approach,” Mater. Sci. Eng. A, 390, 366-371 (2005).

    Google Scholar 

  74. K. I. Tserpes and P. Papanikos, “Finite element modeling of single-walled carbon nanotubes,” Composites, Pt. B, 36, 468-477 (2005).

    Google Scholar 

  75. M. Meo and M. Rossi, “Prediction of Young’s modulus of single wall carbon nanotubes by molecular-mechanics based finite element modeling,” Compos. Sci. Technol., 66, 1597-1605 (2006).

    CAS  Google Scholar 

  76. X. Guo, A. Y. T. Leung, X. Q. He, H. Jiang, and Y. Huang, “Bending buckling of single-walled carbon nanotubes by atomic-scale finite element,” Composites, Pt. B, 39, 202-208 (2008).

    Google Scholar 

  77. P. Papanikos, D. D. Nikolopoulos, and K. I. Tserpes, “Equivalent beams for carbon nanotubes,” Comput. Mater. Sci., 43 (2008); doi:10.1016/j.commatsci.2007.12.010

  78. G. I. Giannopoulos, P. A. Kakavas, and N. K. Anifantis, “Evaluation of the effective mechanical properties of single walled carbon nanotubes using a spring based finite element approach,” Comput. Mater. Sci., 41, No. 4, 561-569 (2008).

    CAS  Google Scholar 

  79. R. S. Ruoff, D. Qian, and W. K. Liu, “Mechanical properties of carbon nanotubes: theoretical predictions and experimental measurement,” C. R. Physique, 4, 993-1008 (2003).

    CAS  ADS  Google Scholar 

  80. T. E. Karakasidis and C. A. Charitidis, “Multiscale modeling in nanomaterial science,” Mater. Sci. Eng. C, 27, 1082-1089 (2007).

    CAS  Google Scholar 

  81. G. M. Odegard, T. S. Gates, K. E. Wise, C. Park, and E. J. Siochi, “Constitutive modeling of nanotube-reinforced polymer composites,” Compos. Sci. Technol., 63, 1671-1687 (2003).

    CAS  Google Scholar 

  82. C. Li and T. W. Chou, “Elastic moduli of multi-walled carbon nanotubes and the effect of van der Waals forces,” Compos. Sci. Technol., 63, 1517-1524 (2003).

    CAS  Google Scholar 

  83. C. Li and T. W. Chou, “Multiscale modeling of carbon nanotube reinforced polymer composites,” J. Nanosci. Nanotechnol., 3, 423-430 (2003).

    CAS  PubMed  Google Scholar 

  84. C. Li and T. W. Chou, “Multiscale modeling of compressive behavior of carbon nanotube/polymer composites,” Compos. Sci. Technol., 66, 2409-2414 (2006).

    CAS  Google Scholar 

  85. T. S. Gates, G. M. Odegard, S. J. V. Frankland, and T. C. Clancy, “Computational materials: multi-scale modeling and simulation of nanostructured materials,” Compos. Sci. Technol., 65, 2416-2434 (2005).

    CAS  Google Scholar 

  86. R. B. Pipes and P. Hubert, “Helical carbon nanotube arrays: mechanical properties,” Compos. Sci. Technol., 62, 419-428 (2002).

    CAS  Google Scholar 

  87. R. B. Pipes and P. Hubert, “Scale effects in carbon nanostructures: self-similar analysis,” Nano Lett., 3, No. 2, 239-243 (2003).

    CAS  ADS  Google Scholar 

  88. R. F. Gibson, Principles of Composite Material Mechanics, CRC Press (2007).

  89. T. Mori and K. Tanaka, “Average stress in matrix and average elastic energy of materials with misfitting inclusions,” Acta Metallurg., 21, 571-575 (1973).

    Google Scholar 

  90. F. T. Fisher, R. D. Bradshaw, and L. C. Brinson, “Fiber waviness in nanotube-reinforced polymer composites. I. Modulus predictions using effective nanotube properties,” Compos. Sci. Technol., 63, 1689-1703 (2003).

    CAS  Google Scholar 

  91. R. Andrews, D. Jacques, M. Minot, and T. Rantell, “Fabrication of carbon multiwalled nanotube/polymer composites by shear mixing,” Macromol. Mater. Eng., 287, No. 6, 395-403 (2002).

    CAS  Google Scholar 

  92. R. D. Bradshaw, F. T. Fisher, and L. C. Brinson, “Fiber waviness in nanotube-reinforced polymer composites: II. Modeling via numerical approximation of the dilute strain concentration tensor,” Compos. Sci. Technol., 63, 1705-1722 (2003).

    CAS  Google Scholar 

  93. Y. J. Liu and X. L. Chen, “Evaluations of the effective material properties of carbon nanotube-based composites using a nanoscale representative volume element,” Mech. Mater., 35, Nos. 1/2, 69-81 (2003).

    Google Scholar 

  94. X. L. Chen and Y. J. Liu, “Square representative volume elements for evaluating the effective material properties of carbon nanotube-based composites,” Comput. Mater. Sci., 29, 1-11 (2004).

    Google Scholar 

  95. M. Griebel and J. Hamaekers, “Molecular dynamics simulations of the elastic moduli of polymer–carbon nanotube composites,” Comput. Meth. Appl. Mech. Eng., 193, 1773-1788 (2004).

    MATH  MathSciNet  Google Scholar 

  96. W. K. Liu, E. G. Karpov, S. Zhang, and H. S. Park, “An introduction to computational nanomechanics and materials,” Comput. Meth. Appl. Mech. Eng., 193, 1529-1578 (2004).

    MATH  MathSciNet  Google Scholar 

  97. H. Wan, F. Delale, and L. Shen, “Effect of CNT length and CNT-matrix interphase in carbon nanotube (CNT) reinforced composites,” Mech. Res. Commun., 32, 481-489 (2005).

    Google Scholar 

  98. D. Shi, X. Feng, H. Jiang, Y. Y. Huang, and K. Hwang, “Multiscale analysis of fracture of carbon nanotubes embedded in composites,” Int. J. Fract., 134, 369-386 (2005).

    CAS  Google Scholar 

  99. V. A. Buryachenko and A. Roy, “Effective elastic moduli of nanocomposites with prescribed random orientation of nanofibers,” Composites, Pt. B, 36, No. 5, 405-416 (2005).

    Google Scholar 

  100. V. A. Buryachenko, A. Roy, K. Lafdi, K. L. Andeson, and S. Chellapilla, “Multi-scale mechanics of nanocomposites including interface: experimental and numerical investigation,” Compos. Sci. Technol., 65, 2435-246 (2005).

    CAS  Google Scholar 

  101. V. Anumandla and R. F. Gibson, “A comprehensive closed form micromechanics model for estimating the elastic modulus of nanotube-reinforced composites,” Composites, Pt. A, 37, 2178-2185 (2006).

    Google Scholar 

  102. Y. S. Song and J. R. Youn, “Modeling of effective elastic properties for polymer based carbon nanotube composites,” Polymer, 47, 1741-1748 (2006).

    CAS  Google Scholar 

  103. L. Schadler, S. C. Giannaris, and P. M. Ajayan, “Load transfer in carbon nanotube epoxy composites,” Appl. Phys. Lett., 73, No. 26, 3842-3844 (1998).

    CAS  ADS  Google Scholar 

  104. J. Zhu, H. Peng, F. Rodriguez-Macias, J. Margrave, V. Khabashesku, A. Imam, et al., “Reinforcing epoxy polymer composites through covalent integration of functionalized nanotubes,” Adv. Funct. Mater., 14, No. 7, 643-648 (2004).

    CAS  Google Scholar 

  105. S. Yang, J. Castilleja, E. Barrera, and K. Lozano, “Thermal analysis of an acrylonitrile-butadiene-styrene/SWNT composite,” Polym. Degrad. Stabil., 83, 383-388 (2004).

    CAS  Google Scholar 

  106. R. Hill, “A self-consistent mechanics of composite materials,” J. Mech. Phys. Solids, 13, 213-235 (1965).

    ADS  Google Scholar 

  107. B. Ashrafi and P. Hubert, “Modeling the elastic properties of carbon nanotube array/polymer composites,” Compos. Sci. Technol., 66, 387-396 (2006).

    CAS  Google Scholar 

  108. Y. Han and J. Elliott, “Molecular dynamics simulations of the elastic properties of polymer/carbon nanotube composites,” Comput. Mater. Sci., 39, 315-323 (2007).

    CAS  Google Scholar 

  109. D. Luo, W. X. Wang, and Y. Takao, “Effects of the distribution and geometry of carbon nanotubes on the macroscopic stiffness and microscopic stresses of nanocomposites,” Compos. Sci. Technol., 67, 2947-2958 (2007).

    CAS  Google Scholar 

  110. S. Y. Fu, C. Y. Yue, X. Hu, and Y. W. Mai, “On the elastic transfer and longitudinal modulus of unidirectional multi-short-fiber composites,” Compos. Sci. Technol., 60, 3001-3013 (2000).

    Google Scholar 

  111. B. Lauke, “Theoretical considerations on deformation and toughness of short-fiber reinforced polymers,” J. Polym. Eng., 11, 103-154 (1992).

    CAS  Google Scholar 

  112. R. G. Villoria and A. Miravete, “Mechanical model to evaluate the effect of the dispersion in nanocomposites,” Acta Mater., 55, 3025-3031 (2007).

    Google Scholar 

  113. S. Kanagaraj, F. R. Varanda, T. V. Zhiltsova, M. S. A. Oliveira, and J. A. O. Simoes, “Mechanical properties of high density polyethylene/carbon nanotube composites,” Compos. Sci. Technol., 66, 3071-3077 (2007).

    Google Scholar 

  114. K. I. Tserpes, P. Panikos, G. Labeas, and Sp. G. Panterlakis, “Multi-scale modeling of tensile behavior of carbon nanotube-reinforced composites,” Theor. Appl. Fract. Mech., 49, 51-60 (2008).

    CAS  Google Scholar 

  115. P. D. Spanos and A. Kontsos, “A multiscale Monte Carlo finite element method for determining mechanical properties of polymer nanocomposites,” Prob. Eng. Mech. (2008); doi:10.1016/j.probengmech.2007.09.002

  116. S. J. V. Frankland, V. M. Harik, G. M. Odegard, D. W. Brenner, and T. S. Gates, “The stress–strain behavior of polymer–nanotube composites from molecular dynamics simulation,” Compos. Sci. Technol., 63, 1655-1661 (2003).

    CAS  Google Scholar 

  117. V. V. Mokashi, D. Qian, and Y. Liu, “A study on the tensile response and fracture in carbon nanotube-based composites using molecular mechanics,” Compos. Sci. Technol., 67, 530-540 (2007).

    CAS  Google Scholar 

  118. L. H. Shao, R. Y. Luo, S. L. Bai, and J. Wang, “Prediction of effective moduli of carbon nanotube-reinforced composites with waviness and debonding,” Compos. Struct., 87, 274-281 (2009).

    Google Scholar 

  119. K. P. A. Saffar, N. Jamalipour, A. R. Najafi, G. Rouhi, A. R. Arshi, and A. Fereidoon, “A finite element model for estimating Young’s modulus of carbon nanotube reinforced composites incorporating elastic cross-links,” Int. J. Mech. Syst. Sci. Eng. 2, 3, 172-175 (2008).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to M. M. Shokrieh.

Additional information

Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 46, No. 2, pp. 229-252, March-April, 2010.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shokrieh, M.M., Rafiee, R. A review of the mechanical properties of isolated carbon nanotubes and carbon nanotube composites. Mech Compos Mater 46, 155–172 (2010). https://doi.org/10.1007/s11029-010-9135-0

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11029-010-9135-0

Keywords

Navigation