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Micromechanical simulation of thermal expansion, elastic stiffness and piezoelectric constants of graphene/unidirectional BaTiO3 fiber reinforced epoxy hybrid nanocomposites

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Abstract

One mechanism that is expected to play a key role in the enhanced properties of fiber-reinforced composites is adding nano-scale fillers as the second reinforcing agents in the polymer matrix. In this paper, micromechanical analysis of a hybrid smart nanocomposite in which continuous BaTiO3 fibers are embedded into the graphene nanosheet (GNS)-contained epoxy matrix is performed. The Mori–Tanaka model is used at a multi-step procedure to predict the thermal expansion (TE), elastic stiffness and piezoelectric constants of BaTiO3 fiber/graphene hybrid nanocomposites. The micromechanical model has the ability to describe the non-uniform dispersion of GNSs into the epoxy matrix. Further, the effect of the interfacial interaction between the graphene nanoparticles and polymer is captured in the smart nanocomposite modeling through the inclusion of an equivalent solid interphase. Our results indicate that by adding GNSs into the epoxy resin, all stiffness constants, transverse coefficient of TE and piezoelectric constants \({e}_{31}\) and \({e}_{15}\) of the hybrid nanocomposite are significantly improved. However, non-uniform dispersion and agglomeration of GNSs can decrease the thermo-mechanical and piezoelectric performances of the BaTiO3 fiber/graphene hybrid nanocomposite. In addition, the dependence of effective properties on the interphase characteristics and alignment of GNSs is tested and discussed in details. Comparison studies are carried out in order to show the validity of the present model.

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Acknowledgements

The authors are grateful to the Raytheon Chair for Systems Engineering for the funding.

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Authors and Affiliations

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

    Y. Keramati & 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

  3. Raytheon Chair for Systems Engineering (RCSE Chair), Advanced Manufacturing Institute, King Saud University, Riyadh, 11421, Saudi Arabia

    Usama Umer

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Appendix 1

Appendix 1

Nonzero components of Eshelby tensor \({\hat{\mathbf{S}}}\) for a long fibrous reinforcement are expressed as

$$\begin{gathered} \hat{S}_{1111} = \hat{S}_{2222} = \frac{{5C_{11}^{m} + C_{12}^{m} }}{{8C_{11}^{m} }} \hfill \\ \hat{S}_{1212} = \hat{S}_{2121} = \hat{S}_{1221} = \hat{S}_{2112} = \frac{{3C_{11}^{m} - C_{12}^{m} }}{{8C_{11}^{m} }} \hfill \\ \hat{S}_{1313} = \hat{S}_{3131} = \hat{S}_{1331} = \hat{S}_{3113} = \hat{S}_{2323} = \hat{S}_{3232} = \hat{S}_{2332} = \hat{S}_{3223} = \frac{1}{4} \hfill \\ \hat{S}_{1122} = \hat{S}_{2211} = \frac{{3C_{12}^{m} - C_{11}^{m} }}{{8C_{11}^{m} }} \hfill \\ \hat{S}_{1133} = \hat{S}_{2233} = \frac{{C_{13}^{m} }}{{2C_{11}^{m} }}, \hat{S}_{1143} = \hat{S}_{2243} = \frac{{e_{31}^{m} }}{{2C_{11}^{m} }}, \hat{S}_{4141} = \hat{S}_{4242} = \frac{1}{2} \hfill \\ \end{gathered}$$
(24)

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Keramati, Y., Ansari, R., Hassanzadeh-Aghdam, M.K. et al. Micromechanical simulation of thermal expansion, elastic stiffness and piezoelectric constants of graphene/unidirectional BaTiO3 fiber reinforced epoxy hybrid nanocomposites. Acta Mech 234, 6251–6270 (2023). https://doi.org/10.1007/s00707-023-03710-3

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