Application of mathematical modeling to obtaining thermoelastic characteristics of composite materials reinforced with nanostructure inclusions

V. S. Zarubin ; E. S. Sergeeva

Matematičeskoe modelirovanie, Tome 29 (2017) no. 10, pp. 45-59.

Résumé

Two-level mathematical model describing the thermo-mechanical interaction of the elements of the composite structure (nanoclusters formed from randomly assigned anisotropic single-walled carbon nanotubes and the matrix particles) with an isotropic medium with thermoelastic characteristics was built. This model was used for the first time for the self-consistent method of thermo-elastic properties of nanoclusters and then the same method was used to describe the thermo-mechanical interaction of nanoclusters with an isotropic matrix composite. A comparative analysis of the received dependencies for the composite modulus of elasticity and the coefficient of linear thermal expansion with two-sided estimates of these characteristics, based on the dual variational formulation of the thermoelasticity problem, was provided. Also for comparison the results of a numerical experiment was used. Presented relations allow to predict the thermoelastic properties of advanced composite materials reinforced with these nanocluster.

Détail

Keywords: model of the composite structure, thermoelastic characteristics, method of selfconsistent, two-sided estimates, nanoclusters
Mots-clés : carbon nanotubes.

Bibliographie

[1] J. Bieksha, The Use of Composite Materials in the Military and Aerospace Industry, Bishop Associates Inc., 2008

[2] G. Lubin (ed.), Handbook of composites, Van Nostrand Reinold Company, New York, 1982, 786 pp.

[3] V.V. Vasilev, Mehanika konstrukcii iz kompozicionnyh materialov, Mashinostroenie, M., 1988, 272 pp.

[4] P. Palermo, “Structural Ceramic Nanocomposites: A Review of Properties and Powders' Synthesis Methods”, Nanomaterials, 5:2 (2015), 656–696 | DOI

[5] R. Casati, M. Vedani, “Metal Matrix Composites Reinforced by Nano-Particles – A Review”, Metals, 4 (2014), 65–83 | DOI

[6] O.L. Blakslee, D.G. Proctor, E.J. Seldin, G.B. Spence, T. Weng, “Elastic constants of compressionan-nealed pyrolytic graphite”, J. Appl. Phys., 41:8 (1970), 3373–3382 | DOI

[7] E.S. Sergeeva, “Issledovanie uprugih harakteristik kompozita s ellipsoidalnymi vkliucheniami”, Molodezhnyi nauchno-tehnicheskii vestnik MGTU im. N.E. Baumana. Elektron. zhurn., 2016, no. 5

[8] J.D. Eshelby, “The continuum theory of lattice defects”, Progress in Solid State Physics, v. 3, Academic Press, N.Y., 1956, 79–303 | DOI

[9] T.D. Shermergor, Teoriia uprugosti mikroneodnorodnyh sred, Nauka, M., 1977, 400 pp.

[10] V.S. Zarubin, Prikladnye zadachi termoprochnosti elementov konstrukcii, Mashinostroenie, M., 1985, 296 pp.

[11] V.S. Zarubin, E.S. Sergeeva, “Issledovanie sviazi uprugih harakteristik odnosloinoi uglerodnoi nanotrubki i grafena”, Vestnik MGTU im. N.E. Baumana. Ser. Estestvennye nauki, 2016, no. 1, 100–110

[12] H. Jiang, B. Liu, Y. Huang, K.C. Hwang, “Thermal Expansion of Single Wall Carbon Nanotubes”, Journal of Engineering Materials and Technology, 126 (2004), 265–270 | DOI

[13] I. Ju. Cvelodub, “Ob obratnom tenzore Eshelbi”, Vestnik ChGPU im. I. Ia. Iakovleva. Ser. Mehanika predelnogo sostoianiia, 8:2 (2010), 530–535

[14] V.S. Zarubin, G.N. Kuvyrkin, Matematicheskie modeli mehaniki i elektrodinamiki sploshnoi sredy, Izd-vo MGTU im. N.E. Baumana, M., 2008, 512 pp.

[15] V.S. Zarubin, G.N. Kuvyrkin, I.Iu. Savel'eva, “Otcenka metodom samosoglasovaniia temperaturnogo koefficienta lineinogo rasshireniia s dispersnymi vkliucheniiami”, Nauka i obrazovanie. MGTU im. N.E. Baumana. Elektron. zhurn., 2015, no. 2, 197–215

[16] V.S. Zarubin, G.N. Kuvyrkin, I.Iu. Savel'eva, “Sravnitelnyi analiz otcenok modulei uprugosti kompozita. Anizotropnye sharovye vkliucheniia”, Vest. MGTU im. N. E. Baumana. Ser. Mashinostroenie, 2014, no. 6, 20–31

[17] V.S. Zarubin, G.N. Kuvyrkin, I.Yu. Savel'eva, “Evaluation of the thermal expansion coefficient of a composite with disperse anisotropic inclusions by the self-consistency method”, Mechanics of Composite Materials, 52:2 (2016), 143–154 | DOI

[18] M.S. Shaskolskaia, Kristallografiia, Vysshaia shkola, M., 1976, 392 pp.

[19] V.S. Zarubin, I.V. Stankevich, Raschet teplonapriazhennyh konstrukcii, Mashinostroenie, M., 2005, 352 pp.

[20] N.N. Golovin, V.S. Zarubin, G.N. Kuvyrkin, “Smesevye modeli mehaniki kompozitov. Ch.1. Termomehanika i termouprugost mnogokomponentnoi smesi”, Vestnik MGTU im. N.E. Baumana. Ser. Estestvennye nauki, 2009, no. 3, 36–49

[21] I.S. Grigorev, E.Z. Melihov (red.), Fizicheskie velichiny, Spravochnik, Energoatomizdat, M., 1991, 1232 pp.

[22] E.S. Sergeeva, “Issledovanie uprugih harakteristik kompozitov, armirovannyh nanorazmernymi vkliucheniiami”, Molodezhnyi nauchno-tehnicheskii vestnik MGTU im. N.E. Baumana. Elektron. zhurn., 2016, no. 9