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Application of Mathematical Modeling to Determine the Thermoelastic Characteristics of Nano-Reinforced Composites

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Abstract

A two-level mathematical model is constructed to describe the thermomechanical interaction between structural elements of a composite (nanoclusters formed by randomly distributed anisotropic single-walled carbon nanotubes and matrix particles) and an isotropic medium possessing the desired thermoelastic characteristics. This model was first employed to obtain the thermoelastic properties of a nanocluster by the self-consistency method and then the same technique was used to describe the thermomechanical interaction of nanoclusters with an isotropic matrix of the composite. A comparative analysis of the calculated dependences for the elastic moduli of the composite and its thermal coefficient of linear expansion was carried out with two-sided estimates of these characteristics based on the dual variational formulation of the thermoelasticity problem. For comparison, the results of a numerical experiment are also used. The presented relationships make it possible to predict the thermoelastic properties of promising composites reinforced by nanoclusters.

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References

  1. J. Bieksha, The Use of Composite Materials in the Military and Aerospace Industry (Bishop & Associates Inc., St. Charles, IL, 2008).

    Google Scholar 

  2. Handbook of Composites, Ed. by G. Lubin (Van Nostrand Reinold, New York, 1982).

    Google Scholar 

  3. V. V. Vasilev, Mechanics and Analysis of Composite Materials (Mashinostroenie, Moscow, 1988; Elsevier, Amsterdam, 2001).

    MATH  Google Scholar 

  4. P. Palermo, “Structural ceramic nanocomposites: a review of properties and powders’ synthesis methods,” Nanomaterials 5, 656–696 (2015).

    Article  Google Scholar 

  5. R. Casati and M. Vedani, “Metal matrix composites reinforced by nano-particles: a review,” Metals 4, 65–83 (2014).

    Article  Google Scholar 

  6. O. L. Blakslee, D. G. Proctor, E. J. Seldin, G. B. Spence, and T. Weng, “Elastic constants of compression-annealed pyrolytic graphite,” J. Appl. Phys. 41, 3373–3382 (1970).

    Article  Google Scholar 

  7. E. S. Sergeeva, “Study of elastic properties of composite with ellipsoidal inclusions,” Vestn. MGTU im. N. E. Baumana, Elektron. Zh., No. 5 (2016).

    Google Scholar 

  8. J. D. Eshelby, “The continuum theory of lattice defects,” in Progress in Solid State Physics (Academic, New York, 1956), Vol. 3, pp. 79–303.

    Article  Google Scholar 

  9. T. D. Shermergor, Theory of Elasticity of Microinhomogeneous Media (Nauka, Moscow, 1977) [in Russian].

    Google Scholar 

  10. V. S. Zarubin, Applied Problems of Thermal Strength of Structural Elements (Mashinostroenie, Moscow, 1985) [in Russian].

    Google Scholar 

  11. V. S. Zarubin and E. S. Sergeeva, “Investigation of the relationship between elastic properties of a single-walled carbon nanotubes and graphene,” Vestn. MGTU im. N. E. Baumana, Ser. Estestv. Nauki, No. 1, 100–110 (2016).

    Google Scholar 

  12. H. Jiang, B. Liu, Y. Huang, and K. C. Hwang, “Thermal expansion of single wall carbon nanotubes,” J. Eng. Mater. Technol. 126, 265–270 (2004).

    Article  Google Scholar 

  13. I. Yu. Tsvelodub, “The inverse Eshelby tensor,” Vestn. ChGPU im. I. Ya. Yakovleva, Ser. Mekh. Predel. Sostoyaniya 8, 530–535 (2010).

    MathSciNet  MATH  Google Scholar 

  14. V. S. Zarubin and G. N. Kuvyrkin, Mathematical Models of Continuous Media Mechanics and Electrodynamics (Mosk. Gos. Tekh. Univ. im. N. E. Baumana, Moscow, 2008) [in Russian].

    MATH  Google Scholar 

  15. V. S. Zarubin, G. N. Kuvyrkin, and I. Yu. Savel’eva, “Estimation by the self-consistency method of temperature coefficient of linear expansion with disperse inclusions,” Nauka Obrazov., El. Zh., No. 2, 197–215 (2015).

    Google Scholar 

  16. V. S. Zarubin, G. N. Kuvyrkin, and I. Yu. Savel’eva, “Comparative analysis modulus elasticity estimates for composite anisotropic spherical inclusions,” Vestn. MGTU im. N. E. Baumana, Ser. Mashinostroen., No. 6, 20–31 (2014).

    Google Scholar 

  17. V. S. Zarubin, G. N. Kuvyrkin, and I. Yu. Savel’eva, “Evaluation of the thermal expansion coefficient of a composite with disperse anisotropic inclusions by the self-consistency method,” Mech. Compos. Mater. 52, 143–154 (2016).

    Article  Google Scholar 

  18. M. S. Shaskolskaia, Crystallography (Vyssh. Shkola, Moscow, 1976) [in Russian].

    Google Scholar 

  19. V. S. Zarubin and I. V. Stankevich, Calculation of Heat Strained Constructions (Mashinostroenie, Moscow, 2005) [in Russian].

    Google Scholar 

  20. N. N. Golovin, V. S. Zarubin, and G. N. Kuvyrkin, “Mixture models of composite mechanics. 1. Thermal mechanics and thermoelasticity of multicomponent mixture,” Vestn. MGTU im. N. E. Baumana, Ser. Estestv. Nauki, No. 3, 36–49 (2009).

    Google Scholar 

  21. Physical Values, The Handbook, Ed. by I. S. Grigor’ev and E. Z. Meilikhov (Energoatomizdat, Moscow, 1991) [in Russian].

    Google Scholar 

  22. E. S. Sergeeva, “Study of elastic properties of composites armed by nanosized inclusions,” Vestn. MGTU im. N. E. Baumana, El. Zh., No. 9 (2016).

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Authors and Affiliations

  1. Bauman Moscow State Technical University, Moscow, Russia

    V. S. Zarubin & E. S. Sergeeva

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  1. V. S. Zarubin
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  2. E. S. Sergeeva
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Correspondence to E. S. Sergeeva.

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Original Russian Text © V.S. Zarubin, E.S. Sergeeva, 2017, published in Matematicheskoe Modelirovanie, 2017, Vol. 29, No. 10, pp. 45–59.

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Zarubin, V.S., Sergeeva, E.S. Application of Mathematical Modeling to Determine the Thermoelastic Characteristics of Nano-Reinforced Composites. Math Models Comput Simul 10, 288–298 (2018). https://doi.org/10.1134/S2070048218030134

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  • DOI: https://doi.org/10.1134/S2070048218030134

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