Abstract
Predicting thermomechanical properties of composites containing carbon nanotubes (CNTs) is significantly depending on the assumed microstructural parameters (MSPs) of CNTs and CNT/matrix morphology. These MSPs include geometry, dispersion and orientation. On the other hand, CNT/matrix morphology refers to two microstructural observations. The first is whether or not an interphase exists between CNTs and matrix, whereas the second is whether or not voids exist due to, for example, debonding of CNTs. In this work, the aim is to propose micromechanical constitutive equations, which are based on the micromechanics principles of Eshelby and Mori-Tanaka models, for considering all of these MSPs altogether in addition to the other well-known MSPs. Accordingly, these equations can be used for modeling realistic nanocomposites to predict their effective thermomechanical properties in different directions. The obtained computational results are compared with other results of both experimental and theoretical investigations found in the literature, and good agreement is obtained.
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Lau, K.T.; Lu, M.; Liao, K.: Improved mechanical properties of coiled carbon nanotubes reinforced epoxy nanocomposites. Compos. Part A: Appl. Sci. Manuf. 37, 1837–1840 (2006)
Andrews, R.; Weisenberger, M.C.: Carbon nanotube polymer composites. Curr. Opin. Solid State Mater Sci. 8, 31–37 (2004)
Matveeva, A.Y.; Pyrlin, S.V.; Ramos, M.D.; Böhm, H.J.; Hattum, F.J.: Influence of waviness and curliness of fibres on mechanical properties of composites. Comput. Mater. Sci. 87, 1–11 (2014)
Rafiee, R.: Influence of carbon nanotube waviness on the stiffness reduction of CNT/polymer composites. Compos. Struct. 97, 304–309 (2013)
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. ASME 126, 250–257 (2004)
Joshi, U.A.; Sharma, S.C.; Harsha, S.P.: Effect of carbon nanotube orientation on the mechanical properties of nanocomposites. Compos. Part B: Eng. 43, 2063–2071 (2012)
Tserpes, K.I.; Chanteli, A.: Parametric numerical evaluation of the effective elastic properties of carbon nanotube-reinforced polymers. Compos. Struct. 99, 366–374 (2013)
Bradshaw, R.D.; Fisher, F.T.; Brinson, L.C.: Fiber waviness in nanotube-reinforced polymer composites–II: modeling via numerical approximation of the dilute strain concentration tensor. Compos. Sci. Technol. 63, 1705–1722 (2003)
Fisher, F.; Bradshaw, R.; Brinson, L.: Fiber waviness in nanotube-reinforced polymer composites–I: Modulus predictions using effective nanotube properties. Compos. Sci. Technol. 63, 1689–1703 (2003)
Zhang, J.; Tanaka, M.: Systematic study of thermal properties of CNT composites by the fast multipole hybrid boundary node method. Eng. Anal. Bound. Elements 31, 388–401 (2007)
Yuan, Z.; Lu, Z.: Numerical analysis of elastic-plastic properties of polymer composite reinforced by wavy and random CNTs. Comput. Mater. Sci. 95, 610–619 (2014)
Kundalwal, S.I.; Ray, M.C.: Improved thermoelastic coefficients of a novel short fuzzy fiber-reinforced composite with wavy carbon nanotubes. J. Mech. Mater. Struct. 9, 1–25 (2014)
Odegard, G.M.; Gates, T.S.; Wise, K.E.; Park, C.; Siochi, E.J.: Constitutive modeling of nanotube-reinforced polymer composites. Compos. Sci. Technol. 63, 1671–1687 (2003)
Karevan, M.; Pucha, R.V.; Bhuiyan, M.A.; Kalaitzidou, K.: Effect of interphase modulus and nanofiller agglomeration on the tensile modulus of graphite nanoplatelets and carbon nanotube reinforced polypropylene nanocomposites. Carbon Lett. 11, 325–331 (2010)
Peng, R.D.; Zhou, H.W.; Wang Jr., H.W.; LM, : Modeling of nano-reinforced polymer composites: microstructure effect on Young’s modulus. Comput. Mater. Sci. 60, 19–31 (2012)
Bhuiyan, M.A.; Pucha, R.V.; Worthy, J.; Karevan, M.; Kalaitzidou, K.: 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)
Shao, L.H.; Luo, R.Y.; Bai, S.L.; Wang, J.: Prediction of effective moduli of carbon nanotube-reinforced composites with waviness and debonding. Compos. Struct. 87, 274–281 (2009)
Tohgo, K.; Cho, Y.: Theory of reinforcement damage in discontinuously-reinforced composites and its application. JSME Int. J. Ser. A 42, 521–529 (1999)
Yasser, M.S.: Development of constitutive laws for thermo-mechanical behaviors of composites containing multi-type ellipsoidal reinforcements. Int. J. Solids Struct. 46, 824–836 (2009)
Mesbah, A.; Zairi, F.; Boutaleb, S.; Gloaguen, J.M.; Nait-Abdelaziz, M.; Xie, S.; Boukharouba, T.; Lefebvre, J.M.: Experimental characterization and modeling stiffness of polymer/clay nanocomposites within a hierarchical multiscale framework. J. Appl. Polym. Sci. 114, 3274–3291 (2009)
Nam, T.H.; Goto, K.; Yamaguchi, Y.; Premalal, E.A.; Shimamura, Y.; Inoue, Y.; Naito, K.; Ogihara, S.: Effects of CNT diameter on mechanical properties of aligned CNT sheets and composites. Compos. Part A: Appl. Sci. Manuf. 76, 289–298 (2015)
Shirasu, K.; Yamamoto, G.; Tamaki, I.; Ogasawara, T.; Shimamura, Y.; Inoue, Y.; Hashida, T.: Negative axial thermal expansion coefficient of carbon nanotubes: experimental determination based on measurements of coefficient of thermal expansion for aligned carbon nanotube reinforced epoxy composites. Carbon 95, 904–909 (2015)
Dominkovics, Z.; Hári, J.; Kovács, J.; Fekete, E.; Pukánszky, B.: Estimation of interphase thickness and properties in PP/layered silicate nanocomposites. Eur. Polym. J. 47, 1765–1774 (2011)
Seidel, G.D.: Micromechanics modeling of the multifunctional nature of carbon nanotube-polymer nanocomposites. PhD thesis, Texas A&M University (2007)
Lan, T.; Pinnavaia, T.J.: Clay-reinforced epoxy nanocomposites. Chem. Mater. 6, 2216–2219 (1994)
Fornes, T.D.; Paul, D.R.: Modeling properties of nylon 6/clay nanocomposites using composite theories. Polymer 44, 4993–5013 (2003)
Wang, X.; Jiang, Q.; Xu, W.; Cai, W.; Inoue, Y.; Zhu, Y.: Effect of carbon nanotube length on thermal, electrical and mechanical properties of CNT/bismaleimide composites. Carbon 53, 145–152 (2013)
Odegard, G.M.; Clancy, T.C.; Gates, T.S.: Modeling of the mechanical properties of nanoparticle/polymer composites. Polymer 46, 553–562 (2005)
Ray, M.C.; Kundalwal, S.I.: Effect of carbon nanotube waviness on the load transfer characteristics of short fuzzy fiber-reinforced composite. J. Nanomech. Micromech. 4, A4013010 (2014)
Kundalwal, S.I.; Ray, M.C.: Shear lag analysis of a novel short fuzzy fiber-reinforced composite. Acta Mech. 225, 2621–2643 (2014)
Kundalwal, S.I.; Ray, M.C.; Meguid, S.: Shear lag model for regularly staggered short fuzzy fiber reinforced composite. ASME J. Appl. Mech. 81, 091001 (2014)
Kundalwal, S.I.; Ray, M.C.: Effect of carbon nanotube waviness on the elastic properties of the fuzzy fiber reinforced composites. ASME J. Appl. Mech. 80, 021010 (2013)
Kundalwal, S.I.; Kumar, S.: Multiscale modeling of stress transfer in continuous microscale fiber reinforced composites with nano-engineered interphase. Mech. Mater. 102, 117–131 (2016)
Schelling, P.K.; Keblinski, P.: Thermal expansion of carbon structures. Phys. Rev. B 68, 035425 (2003)
Jiang, H.; Liu, B.; Huang, Y.; Hwang, K.C.: Thermal expansion of single wall carbon nanotubes. J. Eng. Mater. Technol. 126, 265–270 (2004)
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Shabana, Y.M., Morimoto, T. & Ashida, F. Micromechanical Constitutive Equations for the Effective Thermoelastic Properties of Carbon Nanotube-Reinforced Composites. Arab J Sci Eng 44, 763–776 (2019). https://doi.org/10.1007/s13369-018-3271-6
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DOI: https://doi.org/10.1007/s13369-018-3271-6