Abstract
The effects of carbon nanotube (CNT) waviness on the elastic characterizations of polymer nanocomposites are investigated using a three-dimensional unit cell-based micromechanical model. The most important advantages of this model are its accuracy, simplicity, and efficiency. Both random and regular CNT arrangements can be included in the modeling. The wavy CNTs are modeled as sinusoidal solid CNT fibers while at any location along the length of CNT, the CNT is considered as transversely isotropic material. The polymer and interphase formed due to non-bonded interaction between a CNT and the polymer are assumed to be homogeneous and isotropic as well. Results show that the effect of CNT waviness is not important for the effective coefficients \(C_{11}\), \(C_{12}\), and \(C_{13}\) of the nanocomposites. CNT waviness plays a critical role in determining the effective coefficients \(C_{22}\), \(C_{23}\), \(C_{33}\), and \(C_{44}\) of the nanocomposites. Also, it is found that the CNT waviness slightly affects the effective values of \(C_{55}\) and \(C_{66}\). The effects of volume fraction of CNT and interphase on the mechanical properties of the nanocomposite are examined. Comparison of the present model results shows very good agreement with other available micromechanical analysis and experiment. As comparing with the finite element method, the present model requires much less computational time for obtaining the effective properties of the nanocomposites. Consequently, the results emphasize that all four important parameters, i.e., CNT behavior and waviness, CNT random arrangement, and interphase contributions, should be precisely included in the modeling to predict a more realistic outcome.
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References
Qian, D., Dickey, E.C., Andrews, R., Rantell, T.: Load transfer and deformation mechanisms in carbon nanotube–polystyrene composites. Appl. Phys. Lett. 76, 2868–2870 (2000)
Ansari, R., Mirnezhad, M., Rouhi, H.: Torsional buckling analysis of chiral multi-walled carbon nanotubes based on an accurate molecular mechanics model. Acta Mech. 226, 2955–2972 (2015)
Thostenson, E.T., Ren, Z., Chou, T.W.: Advances in the science and technology of carbon nanotubes and their composites: a review. Compos. Sci. Technol. 61, 1899–1912 (2001)
Kundalwal, S.I., Ray, M.C.: Estimation of thermal conductivities of a novel fuzzy fiber reinforced composite. Int. J. Ther. Sci. 76, 90–100 (2014)
Ansari, R., Daliri, M., Hosseinzadeh, M.: On the van der Waals interaction of carbon nanotubes as electromechanical nanothermometers. Acta Mech. Sin. 29, 622–632 (2013)
Gojny, F.H., Wichmann, M.H.G., Fiedler, B., Schulte, K.: Influence of different carbon nanotubes on the mechanical properties of epoxy matrix composites- A comparative study. Compos. Sci. Technol. 65, 2300–2313 (2005)
Coleman, J.N., Khan, U., Blau, W.J., Gun’ko, Y.K.: Small but strong: a review of the mechanical properties of carbon nanotube–polymer composites. Carbon 44, 1624–1652 (2006)
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)
Tan, H., Jiang, L.Y., Huang, Y., Liu, B., Hwang, K.C.: The effect of van der Waals based interface cohesive law on carbon nanotube-reinforced composite materials. Compos. Sci. Technol. 67, 2941–2946 (2007)
Wei, C.: Adhesion and reinforcement in carbon nanotube polymer composite. Appl. Phys. Lett. 88, 093108 (2006)
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, 1689–1703 (2003)
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 (2002)
Xiao, K., Zhang, L.: Effective separation and alignment of long entangled carbon nanotubes in epoxy. J. Mater. Sci. 40, 6513–6516 (2005)
Joshi, U.A., Sharma, S.C., Harsha, S.P.: Effect of carbon nanotube orientation on the mechanical properties of nanocomposites. Compos. Part B. 43, 2063–2071 (2012)
McCarthy, B., Coleman, J.N., Curran, S.A., Dalton, A.B., Davey, A.P., Konya, Z., Fonseca, A., Nagy, J.B., Blau, W.J.: Observation of site selective binding in a polymer nanotube composite. J. Mater. Sci. Lett. 19, 2239–2241 (2000)
Lordi, V., Yao, N.: Molecular mechanics of binding in carbon-nanotube polymer composites. J. Mater. Res. 15, 2770–2779 (2000)
Liao, K., Li, S.: Interfacial characteristics of a carbon nanotube–polystyrene composite system. Appl. Phys. Lett. 79, 4225–4227 (2001)
Seidel, G.D., Lagoudas, D.C.: Micromechanical analysis of the effective elastic properties of carbon nanotube reinforced composites. Mech. Mater. 38, 884–907 (2006)
Shokrieh, M.M., Rafiee, R.: On the tensile behavior of an embedded carbon nanotube in polymer matrix with non-bonded interphase region. Compos. Struct. 92, 647–652 (2010)
Tsai, J.L., Tzeng, S.H., Chiu, Y.T.: Characterizing elastic properties of carbon nanotube/polymer nanocomposites using multi-scale simulation. Compos. Part B. 41, 106–115 (2010)
Ayatollahi, M.R., Shadlou, S., Shokrieh, M.M.: Multiscale modeling for mechanical properties of carbon nanotube reinforced nanocomposites subjected to different types of loading. Compos. Struct. 93, 2250–2259 (2011)
Tserpes, K.I., Chanteli, A.: Parametric numerical evaluation of the effective elastic properties of carbon nanotube-reinforced polymers. Compos. Struct. 99, 366–374 (2013)
Joshi, P., Upadhyay, S.H.: Effect of interphase on elastic behavior of multiwalled carbon nanotube reinforced composite. Comput. Mater. Sci. 87, 267–273 (2014)
Herasati, S., Zhang, L.: Interphase effect on the macroscopic elastic properties of non-bonded single-walled carbon nanotube composites. Compos. Part B. 77, 52–58 (2015)
Ansari, R., Hassanzadeh-Aghdam, M.K.: Micromechanics-based viscoelastic analysis of carbon nanotube-reinforced composites subjected to uniaxial and biaxial loading. Compos. Part B. 90, 512–522 (2016)
Cao, A., Dickrell, P.L., Sawyer, W.G., Ghasemi-Nejhad, M.N., Ajayan, P.M.: Super-compressible foam-like carbon nanotube films. Science 310, 1307–1310 (2005)
Yamamoto, N., Hart, A.J., Garcia, E.J., Wicks, S.S., Duong, H.M., Slocum, A.H., Wardle, B.L.: High-yield growth and morphology control of aligned carbon nanotubes on ceramic fibers for multifunctional enhancement of structural composites. Carbon 47, 551–560 (2009)
Anumand, V., Gibson, R.F.: A comprehensive closed form micromechanics model for estimating the elastic modulus of nanotube-reinforced composites. Compos. Part A. 37, 2178–2185 (2006)
Li, C., Chou, T.W.: Failure of carbon nanotube/polymer composites and the effect of nanotube waviness. Compos. Part A. 40, 1580–1586 (2009)
Shady, E., Gowayed, Y.: Effect of nanotube geometry on the elastic properties of nanocomposites. Compos. Sci. Technol. 70, 1476–1481 (2010)
Kundalwal, S.I., Ray, M.C.: Effect of carbon nanotube waviness on the elastic properties of the fuzzy fiber reinforced composites. J. Appl. Mech. 80, 021010 (2013)
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)
Farsadi, M., Ochsner, A., Rahmandoust, M.: Numerical investigation of composite materials reinforced with waved carbon nanotubes. J. Comp. Mater. 47, 1325–1434 (2012)
Yazdchi, K., Salehi, M.: The effects of CNT waviness on interfacial stress transfer characteristics of CNT/polymer composites. Compos. Part A. 42, 1301–1309 (2011)
Chen, X.L., Liu, Y.J.: Square representative volume elements for evaluating the effective material properties of carbon nanotube-based composites. Comput. Mater. Sci. 29, 1–11 (2004)
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)
Griebel, M., Hamaekers, J.: Molecular dynamics simulations of the elastic moduli of polymer carbon nanotube composites. Comput. Meth. Appl. Mech. Eng. 193, 1773–1788 (2004)
Han, Y., Elliott, J.: Molecular dynamics simulations of the elastic properties of polymer/carbon nanotube composites. Comput. Mater. Sci. 39, 315–323 (2007)
Mahmoodi, M.J., Aghdam, M.M., Shakeri, M.: The effects of interfacial debonding on the elastoplastic response of unidirectional silicon carbide–titanium composites. Part C J. Mech. Eng. Sci. 223, 259–269 (2010)
Mahmoodi, M.J., Aghdam, M.M., Shakeri, M.: Micromechanical modeling of interface damage of metal matrix composites subjected to off-axis loading. Mater. Des. 31, 829–836 (2010)
Mahmoodi, M.J., Aghdam, M.M.: Damage analysis of fiber reinforced Ti-alloy subjected to multi-axial loading-a micromechanical approach. Mater. Sci. Eng. A 528, 7983–7990 (2011)
Hassanzadeh-Aghdam, M.K., Mahmoodi, M.J., Ansari, R.: Interphase effects on the thermo-mechanical properties of three-phase composites. Part C J. Mech. Eng. Sci. (2015). doi:10.1177/0954406215612830
Pan, Y., Weng, G.J., Meguid, S.A., Bao, W.S., Zhu, Z.H., Hamoud, A.M.S.: Interface effects on the viscoelastic characteristics of carbon nanotube polymer matrix composites. Mech. Mater. 58, 1–11 (2013)
Hsiao, H.M., Daniel, I.M.: Elastic properties of composites with fiber waviness. Compos. Part A 27, 931–941 (1996)
Kundalwal, S.I., Ray, M.C.: Effect of carbon nanotube waviness on the effective thermoelastic properties of a novel continuous fuzzy fiber reinforced composite. Compos. Part B 57, 199–209 (2014)
Mortazavi, B., Bardon, J., Ahzi, S.: Interphase effect on the elastic and thermal conductivity response of polymer nanocomposite materials: 3D finite element study. Comput. Mater. Sci. 69, 100–106 (2013)
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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). https://doi.org/10.1007/s00707-016-1666-6
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DOI: https://doi.org/10.1007/s00707-016-1666-6