The aim of this paper is to study the design of isotropic composites reinforced by aligned spheroidal particles made of a transversely isotropic material. The problem is investigated analytically using the framework of mean-field homogenization. Conditions of macroscopic isotropy of particle-reinforced composites are derived for the dilute and Mori–Tanaka's schemes. This leads to a system of three nonlinear equations linking seven material constants and two geometrical constants. A design tool is finally proposed, which permits to determine admissible particles achieving macroscopic isotropy for a given isotropic matrix behavior and a given particle aspect ratio. Correlations between transverse and longitudinal moduli of admissible particles are studied for various particle shapes. Finally, the design of particles is investigated for aluminum and steel matrix composites.
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@article{CRMECA_2018__346_12_1123_0,
author = {Katell Derrien and L\'eo Morin and Pierre Gilormini},
title = {Designing isotropic composites reinforced by aligned transversely isotropic particles of spheroidal shape},
journal = {Comptes Rendus. M\'ecanique},
pages = {1123--1135},
publisher = {Elsevier},
volume = {346},
number = {12},
year = {2018},
doi = {10.1016/j.crme.2018.09.004},
language = {en},
}
TY - JOUR AU - Katell Derrien AU - Léo Morin AU - Pierre Gilormini TI - Designing isotropic composites reinforced by aligned transversely isotropic particles of spheroidal shape JO - Comptes Rendus. Mécanique PY - 2018 SP - 1123 EP - 1135 VL - 346 IS - 12 PB - Elsevier DO - 10.1016/j.crme.2018.09.004 LA - en ID - CRMECA_2018__346_12_1123_0 ER -
%0 Journal Article %A Katell Derrien %A Léo Morin %A Pierre Gilormini %T Designing isotropic composites reinforced by aligned transversely isotropic particles of spheroidal shape %J Comptes Rendus. Mécanique %D 2018 %P 1123-1135 %V 346 %N 12 %I Elsevier %R 10.1016/j.crme.2018.09.004 %G en %F CRMECA_2018__346_12_1123_0
Katell Derrien; Léo Morin; Pierre Gilormini. Designing isotropic composites reinforced by aligned transversely isotropic particles of spheroidal shape. Comptes Rendus. Mécanique, Volume 346 (2018) no. 12, pp. 1123-1135. doi : 10.1016/j.crme.2018.09.004. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2018.09.004/
[1] Composite Materials: Design and Applications, CRC Press, 2014
[2] Nonlinear composites, Adv. Appl. Mech., Volume 34 (1997), pp. 171-302
[3] The Theory of Composites, Cambridge University Press, 2002
[4] A numerical method for computing the overall response of nonlinear composites with complex microstructure, Comput. Methods Appl. Mech. Eng., Volume 157 (1998), pp. 69-94
[5] Mechanics of Composite Materials, CRC Press, 1998
[6] Contribution théorique à l'étude de l'écrouissage et des lois de l'écoulement plastique, Munich, Germany (1964), pp. 502-509
[7] The essential structure of constitutive laws for metal composites and polycrystals, J. Mech. Phys. Solids, Volume 15 (1967), pp. 79-95
[8] A variational approach to the theory of the elastic behaviour of multiphase materials, J. Mech. Phys. Solids, Volume 11 (1963), pp. 127-140
[9] Elasticity theory of composites, Mechanics of Solids, Pergamon, Oxford, UK, 1982, pp. 653-686
[10] A new approach to the application of Mori–Tanaka's theory in composite materials, Mech. Mater., Volume 6 (1987), pp. 147-157
[11] Average stress in matrix and average elastic energy of materials with misfitting inclusions, Acta Metall., Volume 21 (1973), pp. 571-574
[12] A self-consistent mechanics of composite materials, J. Mech. Phys. Solids, Volume 13 (1965), pp. 213-222
[13] Solutions for effective shear properties in three phase sphere and cylinder models, J. Mech. Phys. Solids, Volume 27 (1979), pp. 315-330
[14] The determination of the elastic field of an ellipsoidal inclusion, and related problems, Proc. R. Soc. Lond. A, Volume 241 (1957), pp. 376-396
[15] On the overall elastic moduli of composite materials, J. Mech. Phys. Solids, Volume 17 (1969), pp. 235-251
[16] Log-Euclidean metrics for fast and simple calculus on diffusion tensors, Magn. Reson. Med., Volume 56 (2006), pp. 411-421
[17] The closest elastic tensor of arbitrary symmetry to an elasticity tensor of lower symmetry, J. Elast., Volume 85 (2006), pp. 215-263
[18] Particulate reinforced metal matrix composites — a review, J. Mater. Sci., Volume 26 (1991), pp. 1137-1156
[19] Optical Constants of Crystalline and Amorphous Semiconductors: Numerical Data and Graphical Information, Springer Science & Business Media, 1999
[20] Lattice dynamics of SiC polytypes within the bond-charge model, Phys. Rev. B, Volume 50 (1994), pp. 13401-13411
[21] The elastic constants of silicon carbide: a Brillouin-scattering study of 4H and 6H SiC single crystals, J. Appl. Phys., Volume 82 (1997), pp. 3152-3154
[22] In-situ experimental and numerical studies of the damage evolution and fracture in a Fe–TiB2 composite, Mater. Sci. Eng. A, Volume 724 (2018), pp. 594-605
[23] Elastic constants of TiC and TiB2, J. Appl. Phys., Volume 32 (1961), p. 1405
[24] Anisotropic elastic constants and thermal expansivities in monocrystal CrB2, TiB2, and ZrB2, Acta Mater., Volume 58 (2010), pp. 76-84
[25] The effect of spatial distribution on the effective behavior of composite materials and cracked media, J. Mech. Phys. Solids, Volume 43 (1995), pp. 1919-1951
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