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Synergistic effect of carbon nanotube/graphene nanoplatelet hybrids on the elastic and viscoelastic properties of polymer nanocomposites: finite element micromechanical modeling

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Abstract

A micromechanics procedure performed by the finite element method (FEM) was developed for the sake of examining the synergistic effects of carbon nanotubes (CNTs) and graphene nanoplatelets (GNPs) hybrids on the elastic and viscoelastic properties of polymer nanocomposites. The representative volume element (RVE) approach was employed owing to its capability to consider various nano-additives with disparate dimensions and evaluate microstructure-level aspects. Constant-strain minimization method and linear viscoelastic model were utilized to predict components of elastic stiffness and creep compliance tensors. The validity of the proposed model was assessed by comparison with the well-established Halpin–Tsai micromechanical model and available experimental measurements, providing an acceptable agreement. Effects of orientation (random or unidirectional dispersion), volume content, and variation in the length and thickness of the carbonaceous nano-additives on the Young’s modulus, Poisson’s ratio, and creep compliance of CNT/GNP/epoxy nanocomposites were investigated. The results explicitly revealed that the CNT and GNP contributions to the mechanical reinforcement and the creep resistance in polymer are strongly associated with their distribution and volume content within the hosting matrix. Moreover, the outcomes imply that increasing the length of CNT, reducing the thickness of GNP lead to increasing Young’s modulus, and decreasing creep compliance (or increasing creep resistance) of CNT/GNP/epoxy nanocomposites.

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References

  1. 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(12), 3475–3495 (2016)

    MathSciNet  Google Scholar 

  2. **a, X., Weng, G.J., Zhang, J., Li, Y.: The effect of temperature and graphene concentration on the electrical conductivity and dielectric permittivity of graphene–polymer nanocomposites. Acta Mech. 231, 1305–1320 (2020)

    MathSciNet  Google Scholar 

  3. Njuguna, J., Pielichowski, K., Fan, J.: Polymer nanocomposites for aerospace applications. Adv. Polym. Nanocompos. (2012). https://doi.org/10.1533/9780857096241.3.472

    Article  Google Scholar 

  4. Aghadavoudi, F., Golestanian, H., Zarasvand, K.A.: Elastic behaviour of hybrid cross-linked epoxy-based nanocomposite reinforced with GNP and CNT: experimental and multiscale modelling. Polym. Bull. 76, 4275–4294 (2019)

    Google Scholar 

  5. Hu, K., Kulkarni, D.D., Choi, I., Tsukruk, V.V.: Graphene-polymer nanocomposites for structural and functional applications. Prog. Polym. Sci. 39(11), 1934–1972 (2014)

    Google Scholar 

  6. Park, S., Ruoff, R.S.: Chemical methods for the production of graphenes. Nat. Nanotechnol. 4(4), 217–224 (2009)

    Google Scholar 

  7. Hu, Y.G., Li, Y.F., Han, J., Hu, C.P., Chen, Z.H., Gu, S.: Prediction of interface stiffness of single-walled carbon nanotube-reinforced polymer composites by shear-lag model. Acta Mech. 230, 2771–2782 (2019)

    MathSciNet  Google Scholar 

  8. Kundalwal, S.I., Ray, M.C.: Shear lag analysis of a novel short fuzzy fiber-reinforced composite. Acta Mech. 225, 2621–2643 (2014)

    MathSciNet  Google Scholar 

  9. Kundalwal, S.I., Meguid, S.A.: Micromechanics modelling of the effective thermoelastic response of nano-tailored composites. Eur. J. Mech. A. Solids 53, 241–253 (2015)

    MathSciNet  Google Scholar 

  10. Huang, C., Qian, X., Yang, R.: Thermal conductivity of polymers and polymer nanocomposites. Mater. Sci. Eng. R. Rep. 132, 1–22 (2018)

    Google Scholar 

  11. Liu, W., Liu, Z., Guo, Z., **e, W., Tang, A., Huang, G.: A computational model for characterizing electrical properties of flexible polymer composite filled with CNT/GNP nanoparticles. Mater. Today Commun. 32, 104177 (2022)

    Google Scholar 

  12. Ngabonziza, Y., Li, J., Barry, C.F.: Electrical conductivity and mechanical properties of multiwalled carbon nanotube-reinforced polypropylene nanocomposites. Acta Mech. 220, 289–298 (2011)

    Google Scholar 

  13. Moradi, A., Ansari, R., Hassanzadeh-Aghdam, M.K., Jamali, J.: Finite element modeling of the effective creep compliance of carbon nanotube-polymer nanocomposites: A critical microstructure-level investigation. Mech. Adv. Mater. Struct. (2023). https://doi.org/10.1080/15376494.2023.2225052

    Article  Google Scholar 

  14. Iijima, S.: Helical microtubules of graphitic carbon. Nature 354(6348), 56–58 (1991)

    Google Scholar 

  15. Ruoff, R.S., Qian, D., Liu, W.K.: Mechanical properties of carbon nanotubes: theoretical predictions and experimental measurements. C. R. Phys. 4(9), 993–1008 (2003)

    Google Scholar 

  16. Yu, M.F., Lourie, O., Dyer, M.J., Moloni, K., Kelly, T.F., Ruoff, R.S.: Strength and breaking mechanism of multiwalled carbon nanotubes under tensile load. Science 287(5453), 637–640 (2000)

    Google Scholar 

  17. Ansari, R., Gholami, R., Rouhi, H.: Vibration analysis of single-walled carbon nanotubes using different gradient elasticity theories. Compos. B Eng. 43(8), 2985–2989 (2012)

    Google Scholar 

  18. Hassanzadeh-Aghdam, M.K.: Evaluating the effective creep properties of graphene-reinforced polymer nanocomposites by a homogenization approach. Compos. Sci. Technol. 209, 108791 (2021)

    Google Scholar 

  19. Ramanathan, T., Abdala, A.A., Stankovich, S., Dikin, D.A., Herrera-Alonso, M., Piner, R.D., Adamson, D.H., Schniepp, H.C., Chen, X.R.R.S., Ruoff, R.S., Nguyen, S.T.: Functionalized graphene sheets for polymer nanocomposites. Nat. Nanotechnol. 3(6), 327–331 (2008)

    Google Scholar 

  20. Gao, C., Zhan, B., Chen, L., Li, X.: A micromechanical model of graphene-reinforced metal matrix nanocomposites with consideration of graphene orientations. Compos. Sci. Technol. 152, 120–128 (2017)

    Google Scholar 

  21. Gojny, F.H., Wichmann, M.H., Fiedler, B., Schulte, K.: Influence of different carbon nanotubes on the mechanical properties of epoxy matrix composites–a comparative study. Compos. Sci. Technol. 65(15–16), 2300–2313 (2005)

    Google Scholar 

  22. Ahmadi-Moghadam, B., Sharafimasooleh, M., Shadlou, S., Taheri, F.: Effect of functionalization of graphene nanoplatelets on the mechanical response of graphene/epoxy composites. Mater. Des. 1980–2015(66), 142–149 (2015)

    Google Scholar 

  23. Rafiee, M.A., Rafiee, J., Wang, Z., Song, H., Yu, Z.Z., Koratkar, N.: Enhanced mechanical properties of nanocomposites at low graphene content. ACS Nano 3(12), 3884–3890 (2009)

    Google Scholar 

  24. Hassanzadeh-Aghdam, M.K., Ansari, R., Darvizeh, A.: Micromechanical analysis of carbon nanotube-coated fiber-reinforced hybrid composites. Int. J. Eng. Sci. 130, 215–229 (2018)

    Google Scholar 

  25. Topkaya, T., Çelik, Y.H., Kilickap, E.: Mechanical properties of fiber/graphene epoxy hybrid composites. J. Mech. Sci. Technol. 34, 4589–4595 (2020)

    Google Scholar 

  26. Li, D., Müller, M.B., Gilje, S., Kaner, R.B., Wallace, G.G.: Processable aqueous dispersions of graphene nanosheets. Nat. Nanotechnol. 3(2), 101–105 (2008)

    Google Scholar 

  27. Zhou, T., Zha, J.W., Hou, Y., Wang, D., Zhao, J., Dang, Z.M.: Surface-functionalized MWNTs with emeraldine base: preparation and improving dielectric properties of polymer nanocomposites. ACS Appl. Mater. Interfaces 3(12), 4557–4560 (2011)

    Google Scholar 

  28. Rafiee, R., Eskandariyun, A.: Predicting Young’s modulus of agglomerated graphene/polymer using multi-scale modeling. Compos. Struct. 245, 112324 (2020)

    Google Scholar 

  29. Maghsoudlou, M.A., Isfahani, R.B., Saber-Samandari, S., Sadighi, M.: Effect of interphase, curvature and agglomeration of SWCNTs on mechanical properties of polymer-based nanocomposites: experimental and numerical investigations. Compos. B Eng. 175, 107119 (2019)

    Google Scholar 

  30. Rafiee, R., Eskandariyun, A.: Estimating Young’s modulus of graphene/polymer composites using stochastic multi-scale modeling. Compos. B Eng. 173, 106842 (2019)

    Google Scholar 

  31. Jia, Y., Jiang, Z., Peng, J., Gong, X., Zhang, Z.: Resistance to time-dependent deformation of polystyrene/carbon nanotube composites under cyclic tension. Compos. A Appl. Sci. Manuf. 43(9), 1561–1568 (2012)

    Google Scholar 

  32. Jia, Y., Peng, K., Gong, X.L., Zhang, Z.: Creep and recovery of polypropylene/carbon nanotube composites. Int. J. Plast. 27(8), 1239–1251 (2011)

    Google Scholar 

  33. Guedes, R.M. (ed.): Creep and Fatigue in Polymer Matrix Composites. Woodhead Publishing, Sawston (2019)

    Google Scholar 

  34. Yang, J., Zhang, Z., Friedrich, K., Schlarb, A.K.: Creep resistant polymer nanocomposites reinforced with multiwalled carbon nanotubes. Macromol. Rapid Commun. 28(8), 955–961 (2007)

    Google Scholar 

  35. Varela-Rizo, H., Weisenberger, M., Bortz, D.R., Martin-Gullon, I.: Fracture toughness and creep performance of PMMA composites containing micro and nanosized carbon filaments. Compos. Sci. Technol. 70(7), 1189–1195 (2010)

    Google Scholar 

  36. Khabazaghdam, A., Behjat, B., Yazdani, M., Da Silva, L.F., Marques, E.A.S., Shang, X.: Creep behaviour of a graphene-reinforced epoxy adhesively bonded joint: experimental and numerical investigation. J. Adhes. 97(13), 1189–1210 (2021)

    Google Scholar 

  37. Tang, L.C., Wang, X., Gong, L.X., Peng, K., Zhao, L., Chen, Q., Wu, L.B., Jiang, J.X., Lai, G.Q.: Creep and recovery of polystyrene composites filled with graphene additives. Compos. Sci. Technol. 91, 63–70 (2014)

    Google Scholar 

  38. Shokrieh, Z., Shokrieh, M.M., Zhao, Z.: A modified micromechanical model to predict the creep modulus of polymeric nanocomposites. Polym. Test. 65, 414–419 (2018)

    Google Scholar 

  39. Hassanzadeh-Aghdam, M.K., Mahmoodi, M.J., Ansari, R.: Creep performance of CNT polymer nanocomposites—an emphasis on viscoelastic interphase and CNT agglomeration. Compos. B Eng. 168, 274–281 (2019)

    Google Scholar 

  40. **a, X., Guo, X., Weng, G.J.: Creep rupture in carbon nanotube-based viscoplastic nanocomposites. Int. J. Plast. 150, 103189 (2022)

    Google Scholar 

  41. Al-Saleh, M.H.: Electrical and mechanical properties of graphene/carbon nanotube hybrid nanocomposites. Synth. Met. 209, 41–46 (2015)

    Google Scholar 

  42. Li, W., Dichiara, A., Bai, J.: Carbon nanotube–graphene nanoplatelet hybrids as high-performance multifunctional reinforcements in epoxy composites. Compos. Sci. Technol. 74, 221–227 (2013)

    Google Scholar 

  43. Pontefisso, A., Mishnaevsky, L., Jr.: Nanomorphology of graphene and CNT reinforced polymer and its effect on damage: micromechanical numerical study. Compos. B Eng. 96, 338–349 (2016)

    Google Scholar 

  44. Safdari, M., Al-Haik, M.S.: Synergistic electrical and thermal transport properties of hybrid polymeric nanocomposites based on carbon nanotubes and graphite nanoplatelets. Carbon 64, 111–121 (2013)

    Google Scholar 

  45. Jen, Y.M., Huang, J.C., Zheng, K.Y.: Synergistic effect of multi-walled carbon nanotubes and graphene nanoplatelets on the monotonic and fatigue properties of uncracked and cracked epoxy composites. Polymers 12(9), 1895 (2020)

    Google Scholar 

  46. Sokołowski, D., Kamiński, M.: Homogenization of carbon/polymer composites with anisotropic distribution of particles and stochastic interface defects. Acta Mech. 229, 3727–3765 (2018)

    MathSciNet  Google Scholar 

  47. Doagou-Rad, S., Jensen, J.S., Islam, A., Mishnaevsky, L., Jr.: Multiscale molecular dynamics-FE modeling of polymeric nanocomposites reinforced with carbon nanotubes and graphene. Compos. Struct. 217, 27–36 (2019)

    Google Scholar 

  48. Christensen, R.: Theory of Viscoelasticity: an Introduction. Elsevier, London (2012)

    Google Scholar 

  49. Naik, A., Abolfathi, N., Karami, G., Ziejewski, M.: Micromechanical viscoelastic characterization of fibrous composites. J. Compos. Mater. 42(12), 1179–1204 (2008)

    Google Scholar 

  50. Brinson, H.F., Brinson, L.C.: Polymer Engineering Science and Viscoelasticity. An Introduction, pp. 99–157. Springer, New York (2008)

    Google Scholar 

  51. Martone, A., Faiella, G., Antonucci, V., Giordano, M., Zarrelli, M.: The effect of the aspect ratio of carbon nanotubes on their effective reinforcement modulus in an epoxy matrix. Compos. Sci. Technol. 71(8), 1117–1123 (2011)

    Google Scholar 

  52. Navidfar, A., Trabzon, L.: Graphene type dependence of carbon nanotubes/graphene nanoplatelets polyurethane hybrid nanocomposites: micromechanical modeling and mechanical properties. Compos. B Eng. 176, 107337 (2019)

    Google Scholar 

  53. Suquet, P.: Elements of homogenization for inelastic solid mechanics. Homog. Tech. Compos. Media. 278, 193–278 (1987)

    MathSciNet  Google Scholar 

  54. Press, W.H., Flannery, B.P., Teukolsky, S.A., Vetterling, W.T.: Numerical Recipes. Cambridge University Press, Cambridge (1989)

    Google Scholar 

  55. Schapery, R.A.: Viscoelastic behavior and analysis of composite materials. Mech. Compos. Mater. (1974)

  56. Fisher, F.T., Bradshaw, R.D., Brinson, L.C.: Fiber waviness in nanotube-reinforced polymer composites—I: modulus predictions using effective nanotube properties. Compos. Sci. Technol. 63(11), 1689–1703 (2003)

    Google Scholar 

  57. Mählich, D., Eberhardt, O., Wallmersperger, T.: Numerical simulation of the mechanical behavior of a carbon nanotube bundle. Acta Mech. 232, 483–494 (2021)

    Google Scholar 

  58. Shokrieh, Z., Shokrieh, M.M.: A new model to simulate the creep behavior of graphene/epoxy nanocomposites. Polym. Test. 75, 321–326 (2019)

    Google Scholar 

  59. Kundalwal, S.I.: Review on micromechanics of nano-and micro-fiber reinforced composites. Polym. Compos. 39(12), 4243–4274 (2018)

    Google Scholar 

  60. Tsai, J.L., Tzeng, S.H., Chiu, Y.T.: Characterizing elastic properties of carbon nanotubes/polyimide nanocomposites using multi-scale simulation. Compos. B Eng. 41(1), 106–115 (2010)

    Google Scholar 

  61. Kundalwal, S.I., Ray, M.C.: Effective properties of a novel continuous fuzzy-fiber reinforced composite using the method of cells and the finite element method. Eur. J. Mech. A. Solids 36, 191–203 (2012)

    Google Scholar 

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Authors and Affiliations

  1. Faculty of Mechanical Engineering, University of Guilan, Rasht, Iran

    A. Moradi & R. Ansari

  2. Department of Engineering Science, Faculty of Technology and Engineering, East of Guilan, University of Guilan, Rudsar-Vajargah, Iran

    M. K. Hassanzadeh-Aghdam

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Moradi, A., Ansari, R. & Hassanzadeh-Aghdam, M.K. Synergistic effect of carbon nanotube/graphene nanoplatelet hybrids on the elastic and viscoelastic properties of polymer nanocomposites: finite element micromechanical modeling. Acta Mech 235, 1887–1909 (2024). https://doi.org/10.1007/s00707-023-03782-1

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