Effect of interphase layers on the elastic properties of a carbon-nanotube-reinforced composite

  • R. D. Maksimov
  • E. Plume


A variant of a stepwise analysis of the elastic properties of a carbon-nanotube-reinforced composite with account of the effect of interphase layers between the nanotubes and the polymer matrix is reported. The preliminary calculation of the elastic constants of a structural element incorporating a nanotube and an interphase layer and the subsequent calculation of independent elastic constants of a composite with such transversely isotropic structural elements oriented in one direction are both performed by using the Mori–Tanaka theory of an equivalent medium. The calculations are carried out for a wide range of ratios between the elastic moduli of the interphase layer and matrix. The elastic constants of a composite with randomly oriented nanotubes are obtained by using the method of orientational averaging.


carbon nanotubes polymer nanocomposite interphase layer elastic constants anisotropy orientational averaging 


  1. 1.
    Yu. S. Lipatov, Physicochemical Foundations of Filling of Polymers [in Russian], Khimiya, Moscow (1991).Google Scholar
  2. 2.
    K. Wise and J. Hinkley, “Molecular dynamics simulations of nanotube-polymer composites,” Amer. Phys. Soc. Spring Meeting, Seattle, April 12–16 (2001).Google Scholar
  3. 3.
    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).CrossRefGoogle Scholar
  4. 4.
    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).CrossRefGoogle Scholar
  5. 5.
    T. Mori and K. Tanaka, “Average stress in matrix and average elastic energy of materials with misfitting inclusions,” Acta Metallurgica, 21, No. 5, 571–574 (1973).CrossRefGoogle Scholar
  6. 6.
    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).CrossRefGoogle Scholar
  7. 7.
    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).CrossRefGoogle Scholar
  8. 8.
    H. Wan, F. Delale, and L. Shen, “Effect of CNT length and CNT-matrix interphase in carbon nanotube (CNT) reinforced composites,” Mechanics, 32, 481–489 (2005).Google Scholar
  9. 9.
    R. Hill, “Elastic properties of reinforced solids; some theoretical principles,” J. Mech. Phys. Solids, 11, No. 5, 357–372 (1963).CrossRefGoogle Scholar
  10. 10.
    R. Hill, “A self-consistent mechanics of composite materials,” J. Mech. Phys. Solids, 13, No. 4, 213–222 (1965).CrossRefGoogle Scholar
  11. 11.
    J. D. Eshelby, “The determination of the elastic field of an ellipsoidal inclusion, and related problems,” Proc. Roy. Soc. Ser. A, 241, 376–396 (1957).CrossRefGoogle Scholar
  12. 12.
    E. Plume, R. D. Maksimov, and A. Lagzdins, “Effect of anisometry of a platelike nanofiller on the elastic constants of a transversely isotropic composite,” Mech. Compos. Mater., 44, No. 4, 341–348 (2008).CrossRefGoogle Scholar
  13. 13.
    T. D. Shermergor, Theory of Elasticity of Microinhomogeneous Media [in Russian], Nauka, Moscow (1977).Google Scholar
  14. 14.
    A. Lagzdins, R. D. Maksimov, and E. Plume, “Anisotropy of elasticity of a composite with irregularly oriented anisometric filler particles,” Mech. Compos. Mater., 45, No. 4, 345–358 (2009).CrossRefGoogle Scholar
  15. 15.
    M. M. Shokrieh and R. Rafiee, “A review of the mechanical properties of isolated carbon nanotubes and carbon nanotube composites,” Mech. Compos. Mater., 46, No. 2, 229–252 (2010).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2011

Authors and Affiliations

  1. 1.Institute of Polymer MechanicsUniversity of LatviaRigaLatvia

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