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Three-Dimensional Stochastic Modelling of Wavy Carbon Nanotube Reinforced Epoxy Nanocomposites

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Abstract

Carbon nanotubes (CNTs) are frequently used as the nanoscale filler materials. It has been observed that when they are added to the polymer matrix by a small fraction, they are able to form a strong yet light-weight multifunctional composite materials. Previous studies found these properties to be significantly influenced by the morphology of CNTs embedded in the matrix. In general, long CNTs become wavy and randomly oriented when dispersed in the matrix material. Collectively, they form an interconnected network. Over the past several decades, many theoretical and computational studies have been carried out to capture the mechanics of CNT-reinforced nanocomposites. In most of these models, CNTs are modeled as straight fibers. In addition, a perfect interphase between CNT and epoxy is generally assumed. As such, these models may not capture the realistic morphology of CNT reinforced composites. In the current study, we have developed a method to construct stochastic three-dimensional finite element models of wavy CNT reinforced epoxy nanocomposites. Both aligned type and randomly distributed type are considered. Uniform random distributions are assumed for both waviness and orientation angles of the dispersed CNTs. To study the effect of waviness on the elastic properties, finite element models with maximum CNT waviness angles of 0° (straight), 10° , 20° , and 30° are generated for CNT volume fractions ranging from 0.1 to 1%. A significant decrease in the properties is observed as the maximum allowable waviness angle (θmax) of the embedded CNTs in the epoxy is increased. The obtained values are compared with the theoretical models available in the literature. The three-phase model including CNTs, CNT/epoxy interphase and matrix is also studied to evaluate the effect of ‘soft’ (Ei = 10–75% Em) as well as ‘hard’ interphase (Ei = 110–175% Em) on the composite modulus. These results suggest that due to ineffective load transfer between CNT and epoxy in the presence of CNT waviness, the elastic modulus of the CNT composites is compromised by 4–8%. The modulus is further decreased by nearly 2.5% as the CNT/epoxy interphase modulus decreases by 90%. The ‘hard’ interphase model confirms an efficient load transfer from matrix to CNT fibers, leading to the increase in composite stiffness. It is found that the composite modulus is more sensitive to the ‘soft’ interphase.

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References

  1. R.E. Swain, K.L. Reifsnider, K. Jayaraman, M. El-Zein, Interface/interphase concepts in composite material systems. J. Thermoplast. Compos. Mater. 3(January), 13–23 (1990)

    Google Scholar 

  2. P. Sharma, P. Ahuja, Recent advances in carbon nanotube-based electronics. Mater. Res. Bull. 43(10), 2517–2526 (2008)

    Google Scholar 

  3. H. Sun, J. Ren, X. Qu, Carbon nanomaterials and DNA: from molecular recognition to applications. Acc. Chem. Res. 49(3), 461–470 (2016)

    Google Scholar 

  4. M.H. Al-Saleh, U. Sundararaj, Electromagnetic interference shielding mechanisms of CNT/polymer composites. Carbon NY 47(7), 1738–1746 (2009)

    Google Scholar 

  5. M.S.P. Shaffer, A.H. Windle, Fabrication and characterization of carbon nanotube/poly(vinyl alcohol) Composites. Adv. Mater. 11(11), 937–941 (1999)

    Google Scholar 

  6. G. Pal, S. Kumar, “Modeling of Carbon Nanotubes and Carbon Nanotube-Polymer Composites,” Progress in Aerospace Sciences, vol. 80 (Elsevier Ltd, Amsterdam, 2016), pp. 33–58

    Google Scholar 

  7. S. Imani Yengejeh, S.A. Kazemi, A. Öchsner, Carbon nanotubes as reinforcement in composites: a review of the analytical, numerical and experimental approaches. Comput. Mater. Sci. 136, 85–101 (2017)

    Google Scholar 

  8. Y. Liu, S. Kumar, Polymer/carbon nanotube nano composite fibers—a review. ACS Appl. Mater. Interfaces 6(9), 6069–6087 (2014)

    Google Scholar 

  9. R. Khare, S. Bose, Carbon nanotube based composites—a review. J. Miner. Mater. Charact. Eng. 4(1), 31–46 (2005)

    Google Scholar 

  10. J. Chen, B. Liu, X. Gao, D. Xu, A review of the interfacial characteristics of polymer nanocomposites containing carbon nanotubes. RSC Adv. 8(49), 28048–28085 (2018)

    Google Scholar 

  11. I. Chung, M. Cho, Recent studies on the multiscale analysis of polymer nanocomposites. Multiscale Sci. Eng. 1(3), 167–195 (2019)

    MathSciNet  Google Scholar 

  12. F.T. Fisher, R.D. Bradshaw, L.C. Brinson, Effects of nanotube waviness on the modulus of nanotube-reinforced polymers. Appl. Phys. Lett. 80(24), 4647–4649 (2002)

    Google Scholar 

  13. S. Herasati, L. Zhang, A new method for characterizing and modeling the waviness and alignment of carbon nanotubes in composites. Compos. Sci. Technol. 100, 136–142 (2014)

    Google Scholar 

  14. M.A. Bhuiyan, R.V. Pucha, K. Kalaitzidou, 3D RVE models able to capture and quantify the dispersion, agglomeration, and orientation state of CNT in CNT/PP nanocomposites. Front. Mater. 3(February), 1–13 (2016)

    Google Scholar 

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

    Google Scholar 

  16. D. Qian, E.C. Dickey, R. Andrews, T. Rantell, Load transfer and deformation mechanisms in carbon nanotube-polystyrene composites. Appl. Phys. Lett. 76(20), 2868–2870 (2000)

    Google Scholar 

  17. B. Natarajan et al., The evolution of carbon nanotube network structure in unidirectional nanocomposites resolved by quantitative electron tomography. ACS Nano 9(6), 6050–6058 (2015)

    Google Scholar 

  18. I.Y. Stein, D.J. Lewis, B.L. Wardle, Aligned carbon nanotube array stiffness from stochastic three-dimensional morphology. Nanoscale 7(46), 19426–19431 (2015)

    Google Scholar 

  19. I. Y. Stein, and B. L. Wardle, Mechanics of aligned carbon nanotube polymer matrix nanocomposites simulated via stochastic three-dimensional morphology. Nanotechnology 27(3) (2015)

  20. I.Y. Stein, B.L. Wardle, Packing morphology of wavy nanofiber arrays. Phys. Chem. Chem. Phys. 18(2), 694–699 (2015)

    Google Scholar 

  21. R. Chahal, A. Adnan, and A. Roy, Effect of Carbon Nanotube (CNT) Waviness on Elastic Modulus of CNT/Epoxy Nanocomposites. In: American Society of Composites 34th Technical Conference, (2019)

  22. R. Chahal, A. Adnan, and A. Roy, Elastic constants of carbon nanotube reinforced polymer nanocomposites. In: American Society of Composites 32nd Technical Conference, (2017)

  23. J. Jung, S. Lee, N.M. Pugno, S. Ryu, Orientation distribution dependence of piezoresistivity of metal nanowire-polymer composite. Multiscale Sci. Eng. 2(1), 54–62 (2020)

    Google Scholar 

  24. F. Dalmas, R. Dendievel, L. Chazeau, J.Y. Cavaillé, C. Gauthier, Carbon nanotube-filled polymer composites. Numerical simulation of electrical conductivity in three-dimensional entangled fibrous networks. Acta Mater. 54(11), 2923–2931 (2006)

    Google Scholar 

  25. Y. Liu, Three-dimensional visualization of carbon networks in nanocomposites. Nanotechnology 26(44) (2015)

  26. M. Islam, G.J. Tudryn, C.R. Picu, Microstructure modeling of random composites with cylindrical inclusions having high volume fraction and broad aspect ratio distribution. Comput Mater Sci. 125, 309–318 (2016)

    Google Scholar 

  27. M.A. Bhuiyan, R.V. Pucha, J. Worthy, M. Karevan, K. Kalaitzidou, Understanding the effect of CNT characteristics on the tensile modulus of CNT reinforced polypropylene using finite element analysis. Comput. Mater. Sci. 79, 368–376 (2013)

    Google Scholar 

  28. J. Gou, B. Minaie, B. Wang, Z. Liang, C. Zhang, Computational and experimental study of interfacial bonding of single-walled nanotube reinforced composites. Comput. Mater. Sci. 31(3–4), 225–236 (2004)

    Google Scholar 

  29. S.J.V. Frankland, V.M. Harik, Analysis of carbon nanotube pull-out from a polymer matrix. Mater. Res. Soc. Symp. Proc. 733E, 86–91 (2006)

    Google Scholar 

  30. S.C. Chowdhury, T. Okabe, Computer simulation of carbon nanotube pull-out from polymer by the molecular dynamics method. Compos. Part A Appl. Sci. Manuf. 38(3), 747–754 (2007)

    Google Scholar 

  31. S. Namilae, N. Chandra, Multiscale model to study the effect of interfaces in carbon nanotube-based composites. J. Eng. Mater. Technol. Trans. ASME 127(2), 222–232 (2005)

    Google Scholar 

  32. R. Chahal, A. Adnan, and A. Roy, Molecular dynamics study of carbon nanotube/epoxy interfaces using ReaxFF. In: American Society of Composites 32nd Technical Conference, 2017.

  33. N. Chandra, Cohesive zone approach to multiscale modelling of nanotube reinforced composites. (2007)

  34. F. Gou, C. Ke, Theoretical predictions of the interfacial stress transfer in nanotube-reinforced polymer nanocomposites by using a strain-hardening shear-lag model. Multiscale Sci. Eng. 1(3), 236–246 (2019)

    Google Scholar 

  35. G.P. Carman, K.L. Reifsnider, Micromechanics of short-fiber composites. Compos. Sci. Technol. 43(2), 137–146 (1992)

    Google Scholar 

  36. A. Haque, A. Ramasetty, Theoretical study of stress transfer in carbon nanotube reinforced polymer matrix composites. Compos. Struct. 71(1), 68–77 (2005)

    Google Scholar 

  37. A. Hernández-Pérez, F. Avilés, Modeling the influence of interphase on the elastic properties of carbon nanotube composites. Comput. Mater. Sci. 47(4), 926–933 (2010)

    Google Scholar 

  38. H. Wan, F. Delale, L. Shen, Effect of CNT length and CNT-matrix interphase in carbon nanotube (CNT) reinforced composites. Mech. Res. Commun. 32(5), 481–489 (2005)

    MATH  Google Scholar 

  39. J. Tsai, C.T. Sun, Effect of platelet dispersion on the load transfer efficiency in nanoclay composites. J. Compos. Mater. 38(7), 567–579 (2004)

    Google Scholar 

  40. G.P. Carman, R.C. Averill, K.L. Reifsnider, J.N. Reddy, Optimization of fiber coatings to minimize stress concentrations in composite materials. J. Compos. Mater. 27(6), 589–612 (1993)

    Google Scholar 

  41. A. Adnan, C.T. Sun, H. Mahfuz, A molecular dynamics simulation study to investigate the effect of filler size on elastic properties of polymer nanocomposites. Compos. Sci. Technol. 67(3–4), 348–356 (2007)

    Google Scholar 

  42. G.M. Odegard, T.C. Clancy, T.S. Gates, Modeling of the mechanical properties of nanoparticle/polymer composites. Polymer (Guildf) 46(2), 553–562 (2005)

    Google Scholar 

  43. M.S. Radue, G.M. Odegard, Multiscale modeling of carbon fiber/carbon nanotube/epoxy hybrid composites: comparison of epoxy matrices. Compos. Sci. Technol. 166, 20–26 (2018)

    Google Scholar 

  44. Y. Li, G.D. Seidel, Multiscale modeling of the interface effects in CNT-epoxy nanocomposites. Comput. Mater. Sci. 153(February), 363–381 (2018)

    Google Scholar 

  45. M.A. Bhuiyan, R.V. Pucha, J. Worthy, M. Karevan, K. Kalaitzidou, Defining the lower and upper limit of the effective modulus of CNT/polypropylene composites through integration of modeling and experiments. Compos. Struct. 95, 80–87 (2013)

    Google Scholar 

  46. M.A. Bhuiyan, R.V. Pucha, M. Karevan, K. Kalaitzidou, Tensile modulus of carbon nanotube/polypropylene composites—a computational study based on experimental characterization. Comput. Mater. Sci. 50(8), 2347–2353 (2011)

    Google Scholar 

  47. T. Mori, K. Tanaka, Average stress in matrix and average elastic energy of materials with misfitting inclusions. Acta. Metall. 21(5), 571–574 (1973)

    Google Scholar 

  48. T. Mura, Micromechanics of defects in solids. The Hague: Martinus Nijhoff (1982)

  49. K. Yanase, S. Moriyama, J.W. Ju, Effects of CNT waviness on the effective elastic responses of CNT-reinforced polymer composites. Acta. Mech. 224(7), 1351–1364 (2013)

    Google Scholar 

  50. N.F. Dow, in Space Mechanics Memo, Study of stresses near a discontinuity in a filament-reinforced composite metal (General Electric Space Sciences Lab, 1963), p. 102

  51. J.L. Worthy III, Design tool for simulation of nanocomposite material properties, Thesis, Undergraduate Research (Georgia Institute of Technology, 2013)

  52. J.C.H. Affdl, J.L. Kardos, The Halpin-Tsai equations: a review. Polym. Eng. Sci. 16(5), 344–352 (1976)

    Google Scholar 

  53. P. Papanikos, D.D. Nikolopoulos, K.I. Tserpes, Equivalent beams for carbon nanotubes. Comput. Mater. Sci. 43(2), 345–352 (2008)

    Google Scholar 

  54. A. Matveeva, V. Romanov, S. Lomov, L. Gorbatikh, Application of the embedded element technique to the modelling of nano-engineered fiber-reinforced composites. ICCM Int. Conf. Compos. Mater. 2015, 19–24 (2015)

    Google Scholar 

  55. E.T. Thostenson, T.W. Chou, Erratum: On the elastic properties of carbon nanotube-based composites: Modelling and characterization (J. Phys. D: Appl. Phys. 36 2003 (573)). J. Phys. D. Appl. Phys. 47(7), 2014 (2014)

    Google Scholar 

  56. H.W. Wang, H.W. Zhou, R.D. Peng, L. Mishnaevsky, Nanoreinforced polymer composites: 3D FEM modeling with effective interface concept. Compos. Sci. Technol. 71(7), 980–988 (2011)

    Google Scholar 

  57. R.E. Lavengood, L.A. Goettler, Stiffness of non-aligned fiber reinforced composites, U.S. Government R&D Reports, AD886372, National Technical Information Service (Springfield, Virginia, 1971)

  58. S. Deogekar, R.C. Picu, On the strengthof random fiber networks. J. Mech. Phys. Solids 116, 1–16 (2018)

    MathSciNet  Google Scholar 

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Acknowledgements

The authors would like to thank Institute for Predictive Performance Methodologies (IPPM) at The University of Texas at Arlington Research Institute (UTARI) for providing the computational resources.

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  1. Department of Mechanical and Aerospace Engineering, The University of Texas at Arlington, Arlington, TX, 76019, USA

    Rajni Chahal & Ashfaq Adnan

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Chahal, R., Adnan, A. Three-Dimensional Stochastic Modelling of Wavy Carbon Nanotube Reinforced Epoxy Nanocomposites. Multiscale Sci. Eng. 3, 51–61 (2021). https://doi.org/10.1007/s42493-020-00052-3

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