Acta Mechanica

, Volume 230, Issue 1, pp 265–280 | Cite as

Micromechanics modeling of the elastic moduli of rGO/ANF nanocomposites

  • Tianyang Zhou
  • James G. BoydEmail author
  • Jodie L. Lutkenhaus
  • Dimitris C. Lagoudas
Original Paper


Energy storage materials that also provide structural integrity are needed to decrease the weight of electrically powered ground and air vehicles. Toward this end, structural supercapacitor electrodes consisting of aramid nanofiber (ANF) and reduced graphene oxide (rGO) were reported in our previous work. Surprisingly, the experimentally measured tensile moduli of these rGO/ANF nanocomposites were not bounded by the experimentally measured moduli of the ANF and rGO materials and were an order of magnitude lower than those of Kevlar fibers and graphene sheets. The purpose of the present work is to develop a micromechanics model for elastic moduli to support the development of rGO/ANF multifunctional composite electrodes. Both the ANF and the rGO are transversely isotropic, wavy and randomly oriented, and no traditional isotropic polymeric matrix is present. We are aware of no existing micromechanics model that is applicable to such a composite. The Mori–Tanaka model is used three times, to model the rGO and ANF separately, and then the rGO/ANF composite films. The model predictions of elastic moduli were compared with experimental results. Waviness was found to be the main factor controlling the effective composite moduli, due to the extreme anisotropy of the rGO. This implies that the effective elastic moduli of rGO/ANF composites can be considerably increased by developing processing methods that reduce waviness. The experimentally observed unbounded moduli were attributed to the relationship between waviness and the volume fraction of the ANF.


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  1. 1.
    Kwon, S.R., Harris, J., Zhou, T., Loufakis, D., Boyd, J.G., Lutkenhaus, J.L.: Mechanically strong graphene/aramid nanofibers composite electrodes for structural energy and power. ACS Nano 11, 6682–6690 (2017)CrossRefGoogle Scholar
  2. 2.
    Snyder, J., Gienger, E., Wetzel, E.: Performance metrics for structural composites with electrochemical multifunctionality. J. Compos. Mater. 49, 1835–1848 (2015)CrossRefGoogle Scholar
  3. 3.
    Shirshova, N., Qian, H., Shaffer, M.S.P., Steinke, J.H.G., Greenhalgh, E.S., Curtis, P.T., Kucernak, A., Bismarck, A.: Structural composite supercapacitors. Compos. Part A Appl. Sci. Manuf. 46, 96–107 (2013)CrossRefGoogle Scholar
  4. 4.
    Asp, L.E., Greenhalgh, E.S.: Structural power composites. Compos. Sci. Technol. 101, 41–61 (2014)CrossRefGoogle Scholar
  5. 5.
    Carlson, T., Ordéus, D., Wysocki, M., Asp, L.E.: Structural capacitor materials made from carbon fibre epoxy composites. Compos. Sci. Technol. 70, 1135–1140 (2010)CrossRefGoogle Scholar
  6. 6.
    Carlson, T., Asp, L.E.: Structural carbon fibre composite/PET capacitors—effects of dielectric separator thickness. Compos. Part B Eng. 49, 16–21 (2013)CrossRefGoogle Scholar
  7. 7.
    Qian, H., Kucernak, A.R., Greenhalgh, E.S., Bismarck, A., Shaffer, M.S.P.: Multifunctional structural supercapacitor composites based on carbon aerogel modified high performance carbon fiber fabric. ACS Appl. Mater. Interfaces 5, 6113–6122 (2013)CrossRefGoogle Scholar
  8. 8.
    Ke, Q., Wang, J.: Graphene-based materials for supercapacitor electrodes—a review. J. Mater. 2, 37–54 (2016)Google Scholar
  9. 9.
    Yoon, Y., Lee, K., Baik, C., Yoo, H., Min, M., Park, Y., Lee, S.M., Lee, H.: Anti-solvent derived non-stacked reduced graphene oxide for high performance supercapacitors. Adv. Mater. 25, 4437–4444 (2013)CrossRefGoogle Scholar
  10. 10.
    Kuo, C.M., Takahashi, K., Chou, T.W.: Effect of fiber waviness on the nonlinear elastic behavior of flexible composites. J. Compos. Mater. 22, 1004–1025 (1988)CrossRefGoogle Scholar
  11. 11.
    Chou, T.W., Takahashi, K.: Non-linear elastic behaviour of flexible fibre composites. Composites 18, 25–34 (1987)CrossRefGoogle Scholar
  12. 12.
    Yanase, K., Moriyama, S., Ju, J.W.: Effects of CNT waviness on the effective elastic responses of CNT-reinforced polymer composites. Acta Mech. 224, 1351–1364 (2013)CrossRefGoogle Scholar
  13. 13.
    Ansari, R., Hassanzadeh-Aghdam, M.K., Mahmoodi, M.J.: Three-dimensional micromechanical analysis of the CNT waviness influence on the mechanical properties of polymer nanocomposites. Acta Mech. 227, 3475–3495 (2016)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Fisher, F.T., Bradshaw, R.D., Brinson, L.C.: Effects of nanotube waviness on the modulus of nanotube-reinforced polymers. Appl. Phys. Lett. 80, 4647–4649 (2002)CrossRefGoogle Scholar
  15. 15.
    Shi, D.-L., Feng, X.-Q., Huang, Y.Y., Hwang, K.-C., Gao, H.: The effect of nanotube waviness and agglomeration on the elastic property of carbon nanotube-reinforced composites. J. Eng. Mater. Technol. 126, 250 (2004)CrossRefGoogle Scholar
  16. 16.
    Tandon, G.P., Weng, G.J.J.: Average stress in the matrix and effective moduli of randomly oriented composites. Compos. Sci. Technol. 27, 111–132 (1986)CrossRefGoogle Scholar
  17. 17.
    Sakthivel, M., Arockiarajan, A.: Thermo-electro-mechanical response of 1-3-2 piezoelectric composites: effect of fiber orientations. Acta Mech. 223, 1353–1369 (2012)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Mori, T., Tanaka, K.: Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta Metall. 21, 571–574 (1973)CrossRefGoogle Scholar
  19. 19.
    Eshelby, J.D.: The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proc. R. Soc. Lond. A 241, 376–396 (1957)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Hill, R.: A self-consistent mechanics of composite materials. J. Mech. Phys. Solids 13, 213–222 (1965)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Weng, G.J.: Some elastic properties of reinforced solids, with special reference to isotropic ones containing spherical inclusions. Int. J. Eng. Sci. 22, 845–856 (1984)CrossRefGoogle Scholar
  22. 22.
    Gavazzi, A.C., Lagoudas, D.C.: On the numerical evaluation of Eshelby’s tensor and its application to elastoplastic fibrous composites. Comput. Mech. 7, 13–19 (1990)CrossRefGoogle Scholar
  23. 23.
    Seidel, G.D., Lagoudas, D.C.: A micromechanics model for the electrical conductivity of nanotube-polymer nanocomposites. J. Compos. Mater. 43, 917–941 (2009)CrossRefGoogle Scholar
  24. 24.
    Christensen, R.M.: Mechanics of Composite Materials. Krieger Pub. Co, Malabar (1991)Google Scholar
  25. 25.
    Lee, J., Boyd, J.G., Lagoudas, D.C.: Effective properties of three-phase electro-magneto-elastic composites. Int. J. Eng. Sci. 43, 790–825 (2005)MathSciNetCrossRefGoogle Scholar
  26. 26.
    Ting, T.C.T.: Anisotropic Elasticity Theory and Applications. Oxford University Press, Oxford (1996)CrossRefGoogle Scholar
  27. 27.
    Huang, H., Talreja, R.: Effects of void geometry on elastic properties of unidirectional fiber reinforced composites. Compos. Sci. Technol. 65, 1964–1981 (2005)CrossRefGoogle Scholar
  28. 28.
    Wan, C., Frydrych, M., Chen, B.: Strong and bioactive gelatin–graphene oxide nanocomposites. Soft Matter 7, 6159 (2011)CrossRefGoogle Scholar
  29. 29.
    Cao, G.: Guoxin: atomistic studies of mechanical properties of graphene. Polymers 6, 2404–2432 (2014)CrossRefGoogle Scholar
  30. 30.
    Yao, J., Bastiaansen, C., Peijs, T.: High strength and high modulus electrospun nanofibers. Fibers 2, 158–186 (2014)CrossRefGoogle Scholar
  31. 31.
    Nakamae, K., Nishino, T.: Integration of Fundamental Polymer Science and Technology. Springer, Berlin (1991)Google Scholar
  32. 32.
    Yao, J., Jin, J., Lepore, E., Pugno, N.M., Bastiaansen, C.W.M., Peijs, T.: Electrospinning of \(p\)-aramid fibers. Macromol. Mater. Eng. 300, 1238–1245 (2015)CrossRefGoogle Scholar
  33. 33.
    Sockalingam, S., Gillespie, J.W., Keefe, M.: On the transverse compression response of Kevlar KM2 using fiber-level finite element model. Int. J. Solids Struct. 51, 2504–2517 (2014)CrossRefGoogle Scholar
  34. 34.
    McAllister, Q.P., Gillespie, J.W., VanLandingham, M.R.: Evaluation of the three-dimensional properties of Kevlar across length scales. J. Mater. Res. 27, 1824–1837 (2012)CrossRefGoogle Scholar
  35. 35.
    Andres Leal, A., Deitzel, J.M., Gillespie, J.W.: Assessment of compressive properties of high performance organic fibers. Compos. Sci. Technol. 67, 2786–2794 (2007)CrossRefGoogle Scholar
  36. 36.
    Kawabata, S.: Measurement of the transverse mechanical properties of high-performance fibres. J. Text. Inst. 81, 432–447 (1990)CrossRefGoogle Scholar
  37. 37.
  38. 38.
    Graphenea: Reduced graphene oxide. Accessed 10 Oct 2017
  39. 39.
    Ansari, R., Ajori, S., Motevalli, B.: Mechanical properties of defective single-layered graphene sheets via molecular dynamics simulation. Superlattices Microstruct. 51, 274–289 (2012)CrossRefGoogle Scholar
  40. 40.
    Mortazavi, B., Ahzi, S.: Thermal conductivity and tensile response of defective graphene: a molecular dynamics study. Carbon 63, 460–470 (2013)CrossRefGoogle Scholar
  41. 41.
    Zhang, Y.Y., Wang, C.M., Cheng, Y., Xiang, Y.: Mechanical properties of bilayer graphene sheets coupled by \(\text{ sp }^{3}\) bonding. Carbon 49, 4511–4517 (2011)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2018

Authors and Affiliations

  • Tianyang Zhou
    • 1
  • James G. Boyd
    • 2
    Email author
  • Jodie L. Lutkenhaus
    • 1
    • 3
  • Dimitris C. Lagoudas
    • 1
    • 2
  1. 1.Department of Materials Science and EngineeringTexas A&M UniversityCollege StationUSA
  2. 2.Department of Aerospace EngineeringTexas A&M UniversityCollege StationUSA
  3. 3.Artie McFerrin Department of Chemical EngineeringTexas A&M UniversityCollege StationUSA

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