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Mechanics of Composite Materials

, Volume 46, Issue 2, pp 155–172 | Cite as

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

  • M. M. Shokrieh
  • R. Rafiee
Article

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.

Keywords

carbon nanotubes composites mechanical properties modeling 

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References

  1. 1.
    H. Dai, “Carbon nanotubes: opportunities and challenges,” Surface Sci., 500, 218-241 (2002).ADSGoogle Scholar
  2. 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. 3.
    J. P. Salvetat-Delmotte and A. Rubio, “Mechanical properties of carbon nanotubes: a fiber digest for beginners,” Carbon, 40, 1729-1734 (2002).Google Scholar
  4. 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).ADSGoogle Scholar
  5. 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).Google Scholar
  6. 6.
    T. Belin and F. Epron, “Characterization methods of carbon nanotubes: a review,” Mater. Sci. Eng. B, 199, 105-118 (2005).Google Scholar
  7. 7.
    H. Rafii-Tabar, “Computational modelling of thermo-mechanical and transport properties of carbon nanotubes,” Phys. Rep., 390, 235-452 (2004).ADSGoogle Scholar
  8. 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).ADSGoogle Scholar
  9. 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).ADSGoogle Scholar
  10. 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).ADSGoogle Scholar
  11. 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).ADSGoogle Scholar
  12. 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).PubMedADSGoogle Scholar
  13. 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).PubMedADSGoogle Scholar
  14. 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. 15.
    Y. Omata, Y. Yamagami, K. Tadano, T. Miyake, and S. Saito, “Nanotube nanoscience: a molecular-dynamics study,” Physica E, 29, 454-468 (2005).ADSGoogle Scholar
  16. 16.
    K. J. Bathe, Finite Element Procedures, Prentice-Hall of India Private Ltd., New Delhi — 110 001 (1997), pp. 1-14.Google Scholar
  17. 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).MathSciNetGoogle Scholar
  18. 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).Google Scholar
  19. 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).Google Scholar
  20. 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).zbMATHADSGoogle Scholar
  21. 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. 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).ADSGoogle Scholar
  23. 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).ADSGoogle Scholar
  24. 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).ADSGoogle Scholar
  25. 25.
    R. S. Ruoff and D. C. Lorents, “Mechanical and thermal properties of carbon nanotubes,” Carbon, 33, 925-930 (1995).Google Scholar
  26. 26.
    J. P. Lu, “Elastic properties of carbon nanotubes and nanoropes,” Phys. Rev. Lett., 79, No. 7, 1297-1300 (1997).ADSGoogle Scholar
  27. 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).PubMedADSGoogle Scholar
  28. 28.
    T. Haliciglu, “Stress calculation for carbon nanotubes,” Thin Solid Films, 312, 11-14 (1998).ADSGoogle Scholar
  29. 29.
    N. Yao and V. Lordi, “Young’s modulus of single-walled carbon nanotubes,” J. Appl. Phys., 84, No. 4, 1939-1943 (1998).ADSGoogle Scholar
  30. 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).ADSGoogle Scholar
  31. 31.
    E. Hernandez, C. Goze, P. Bernier, and A. Rubio, “Elastic properties of single-wall nanotubes,” Appl. Phys. A, 68, 287-292 (1999).ADSGoogle Scholar
  32. 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. 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).Google Scholar
  34. 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).Google Scholar
  35. 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).ADSGoogle Scholar
  36. 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).Google Scholar
  37. 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. 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).Google Scholar
  39. 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).ADSGoogle Scholar
  40. 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).ADSGoogle Scholar
  41. 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).Google Scholar
  42. 42.
    Y. Jin and F. G. Yuan, “Simulation of elastic properties of single-walled carbon nanotubes,” Compos. Sci. Technol., 63, 1507-1515 (2003).Google Scholar
  43. 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).ADSGoogle Scholar
  44. 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).Google Scholar
  45. 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).zbMATHADSGoogle Scholar
  46. 46.
    T. Natsuki, K. Tantrakarn, and M. Endo, “Prediction of elastic properties for single-walled carbon nanotubes,” Carbon, 42, 39-45 (2004).Google Scholar
  47. 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).Google Scholar
  48. 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).Google Scholar
  49. 49.
    J. Despres, E. Daguerre, and K. Lafdi, “Flexibility of graphene layers in carbon nanotubes,” Carbon, 33, 87-92 (1995).Google Scholar
  50. 50.
    S. Iijima, C. J. Brabec, A. Maiti, and J. Bernholc, “Structural flexibility of carbon nanotubes,” J. Chem. Phys., 104, 2089-2092 (1996).ADSGoogle Scholar
  51. 51.
    N. Chopra, L. Benedict, V. Crespi, M. Cohen, S. Louie, and A. Zettl, “Fully collapsed carbon nanotubes,” Nature (London), 377, 135-138 (1995).ADSGoogle Scholar
  52. 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).ADSGoogle Scholar
  53. 53.
    V. M. Harik, “Mechanics of carbon nanotubes: applicability of the continuum-beam models,” Comput. Mater. Sci., 24, 328-342 (2002).Google Scholar
  54. 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).ADSGoogle Scholar
  55. 55.
    J. Tersoff and R. S. Ruoff, “Structural properties of a carbon-nanotube crystal,” Phys. Rev. Lett., 73, 676-679 (1994).PubMedADSGoogle Scholar
  56. 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).zbMATHADSGoogle Scholar
  57. 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).Google Scholar
  58. 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).zbMATHGoogle Scholar
  59. 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).Google Scholar
  60. 60.
    X. L. Gao and K. Li, “Finite deformation continuum model for single-walled carbon nanotubes,” Int. J. Solids Struct., 40, 7329-7337 (2003).zbMATHMathSciNetGoogle Scholar
  61. 61.
    Q. Wang, “Effective in-plane stiffness and bending rigidity of armchair and zigzag carbon nanotubes,” Int. J. Solids Struct., 41, 5451-5461 (2004).zbMATHGoogle Scholar
  62. 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).zbMATHGoogle Scholar
  63. 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).zbMATHGoogle Scholar
  64. 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. 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).zbMATHGoogle Scholar
  66. 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. 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).Google Scholar
  68. 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).Google Scholar
  69. 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).zbMATHADSGoogle Scholar
  70. 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. 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. 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. 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. 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. 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).Google Scholar
  76. 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. 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. 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).Google Scholar
  79. 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).ADSGoogle Scholar
  80. 80.
    T. E. Karakasidis and C. A. Charitidis, “Multiscale modeling in nanomaterial science,” Mater. Sci. Eng. C, 27, 1082-1089 (2007).Google Scholar
  81. 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).Google Scholar
  82. 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).Google Scholar
  83. 83.
    C. Li and T. W. Chou, “Multiscale modeling of carbon nanotube reinforced polymer composites,” J. Nanosci. Nanotechnol., 3, 423-430 (2003).PubMedGoogle Scholar
  84. 84.
    C. Li and T. W. Chou, “Multiscale modeling of compressive behavior of carbon nanotube/polymer composites,” Compos. Sci. Technol., 66, 2409-2414 (2006).Google Scholar
  85. 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).Google Scholar
  86. 86.
    R. B. Pipes and P. Hubert, “Helical carbon nanotube arrays: mechanical properties,” Compos. Sci. Technol., 62, 419-428 (2002).Google Scholar
  87. 87.
    R. B. Pipes and P. Hubert, “Scale effects in carbon nanostructures: self-similar analysis,” Nano Lett., 3, No. 2, 239-243 (2003).ADSGoogle Scholar
  88. 88.
    R. F. Gibson, Principles of Composite Material Mechanics, CRC Press (2007).Google Scholar
  89. 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. 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).Google Scholar
  91. 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).Google Scholar
  92. 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).Google Scholar
  93. 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. 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. 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).zbMATHMathSciNetGoogle Scholar
  96. 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).zbMATHMathSciNetGoogle Scholar
  97. 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. 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).Google Scholar
  99. 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. 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).Google Scholar
  101. 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. 102.
    Y. S. Song and J. R. Youn, “Modeling of effective elastic properties for polymer based carbon nanotube composites,” Polymer, 47, 1741-1748 (2006).Google Scholar
  103. 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).ADSGoogle Scholar
  104. 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).Google Scholar
  105. 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).Google Scholar
  106. 106.
    R. Hill, “A self-consistent mechanics of composite materials,” J. Mech. Phys. Solids, 13, 213-235 (1965).ADSGoogle Scholar
  107. 107.
    B. Ashrafi and P. Hubert, “Modeling the elastic properties of carbon nanotube array/polymer composites,” Compos. Sci. Technol., 66, 387-396 (2006).Google Scholar
  108. 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).Google Scholar
  109. 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).Google Scholar
  110. 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. 111.
    B. Lauke, “Theoretical considerations on deformation and toughness of short-fiber reinforced polymers,” J. Polym. Eng., 11, 103-154 (1992).Google Scholar
  112. 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. 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. 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).Google Scholar
  115. 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. 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).Google Scholar
  117. 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).Google Scholar
  118. 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. 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

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© Springer Science+Business Media, Inc. 2010

Authors and Affiliations

  1. 1.Composites Research Laboratory, Mechanical Engineering DepartmentIran University of Science and TechnologyTehranIran

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