Comparative Analysis Estimates of Elastic Moduli for Composite. Isotropic Spherical Inclusions

A comparative quantitative analysis of the estimates of elastic characteristics of composite with isotropic spherical inclusions has been carried out. Various approaches to the mathematical model-building of stress-strain state in the composite which allow to build bilateral boundary values of the elastic moduli and evaluate the maximum possible error of calculation of these values have been considered. Calculated dependences, which establish connection of the composite elastic characteristics with the volume concentration of inclusions and elastic properties of the matrix and inclusions, have been obtained using the method of self-consistency. The calculation results have been compared with known experimental measurements of the longitudinal modulus of the composite with a matrix of cobalt, reinforced with dispersed particles of tungsten carbide.

References

[1] Eshelby J.D., Seitz F., Turnbul D., eds. The continuum theory of lattice defects. In Collected Works of J.D. Eshelby "Progress in Solid State Physics", New York, Academic Press Publ., 1956, vol. 3, pp. 79-303.

[2] Hashin Z. Theory of mechanical behaviour of heterogeneous media. Appl. Mech. Rev. 1964, vol. 17, iss. 1, pp. 1-10.

[3] Hill R. A self-consistent mechanics of composite materials. J. Mech. Phys. Solids, 1965, vol. 13, iss. 4, pp. 21-22.

[4] Khoroshun L.P. A method of determining elastic moduli of reinforced bodies. Mekh. Polim. [Polymer Mechanics], 1968, no. 1, pp. 78-87 (in Russ.).

[5] Yeh R.H.T. Variational principles of elastic moduli of composite materials. J. Appl. Phys., 1970, vol. 41, iss. 8, pp. 3353-3356.

[6] Shermergor T.D. Teoriya uprugosti mikroneodnorodnykh sred [The theory of elasticity of micro-inhomogeneous media]. Moscow, Nauka Publ., 1977. 400 p.

[7] Brautman L. Kroc R., Sendetsky J., eds. Composite Materials. In 8 volums. Vol. 2. Mechanics of Composite Materials. N.Y, 1975. (Russ. Ed.: Brautman L. Krok R. Mekhanika kompozitsionnykh materialov. Pod red. Dzh. Sendetski; per. s angl. Moscow, Mir Publ., 1978. 564 p.).

[8] Christensen R.M. Mechanics of composite materials. N.Y., Wiley-Interscience Publ., 1979. 348 p. (Russ. ed.: Kristensen R.M. Vvedenie v mekhaniku kompozitov. Moscow, Mir, 1982. 334 p.).

[9] Vanin G.A. Mikromekhanika kompozitsionnykh materialov [Micromechanics of composite materials]. Kiev, Naukova Dumka Publ., 1985. 304 p.

[10] Shaskol’skaya M.S. Kristallografiya [Crystallography]. Мoscow, Vysshaya Shkola Publ., 1976. 392 p.

[11] Zarubin V.S. Prikladnye zadachi termoprochnosti elementov konstruktsiy [Applied problems of thermal strength of elements of designs]. Moscow, Mashinostroenie Publ., 1985. 296 p.

[12] Dimitrienko Yu.I. Tenzornoe ischislenie [Tensor calculus]. Мoscow, Vysshaya Shkola Publ., 2001. 576 p.

[13] Golovin N.N., Zarubin V.S., Kuvyrkin G.N. Mixture models of composite mechanics. P. 1. Thermal mechanics and thermoelasticity of multicomponent mixture. Vestn. Mosk. Gos. Tekh. Univ. im. N.E. Baumana, Estestv. Nauki [Herald of the Bauman Moscow State Tech. Univ., Nat. Sci.], 2009, no. 3, pp. 36-49 (in Russ.).

[14] Hill R. The elastic behaviour of a crystalline aggregates. Proceedings of Physical Society, 1952, vol. A65 349, pp. 349-354. DOI:10.1088/0370-1298/65/5/307

[15] Onami M., eds. Vvedenie v mikromekhaniku [Introduction to micro-mechanics]. Trans. from Japanese. Moscow, Metallurgiia, 1987. 280 p.

[16] Zarubin V.S., Kuvyrkin G.N. Matematicheskie modeli mekhaniki i elektrodinamiki sploshnoy sredy [Mathematical models of mechanics and electrodynamics of continuous media]. Moscow, MGTU im. N.E. Baumana Publ., 2008. 512 p.

[17] Hashin Z., Shtrikman S. A variational approach to the theory of the elastic behaviour of multiphase materials. J. Mech. Phys. Solids, 1963, vol. 11, iss. 2, pp. 127-140.

[18] Nishimatsu C., Gurland J. Experimental survey of the deformation of the hard-ductile two-phase alloy system W-Co. Trans. Amer. Soc. Metals, 1960, vol. 52, iss. 2, pp. 469-484.

[19] Doi H., Fujiwara Y, Miyake K., Oosawa Y A systematic investigation of elastic moduli of W-Co alloys. Met. Trans, 1970, vol. 1, iss. 5, pp. 1417-1425.