Comptes Rendus
no. 3
A generalized-secant homogenization scheme for viscoplastic polycrystalline solids under imposed deformations
[Une méthode d'homogénéisation sécante généralisée pour des matériaux polycristallins viscoplastiques en déformations imposées]
Martín I. Idiart1, 2  ; Pierre-Guy Vincent3, 4
1 Departamento de Aeronáutica, Facultad de Ingeniería, Universidad Nacional de La Plata, Avda. 1 esq. 47, La Plata B1900TAG, Argentina
2 Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), CCT La Plata, Calle 8 No 1467, La Plata B1904CMC, Argentina
3 Institut de radioprotection et de sûreté nucléaire (IRSN), BP 3, 13115 Saint-Paul-Lez-Durance cedex, France
4 Laboratoire de micromécanique et d'intégrité des structures, IRSN–CNRS–UMII, BP 3, 13115 Saint-Paul-lez-Durance Cedex, France
Comptes Rendus. Mécanique, Volume 343 (2015) no. 3, pp. 179-186.

Des estimations relatives à l'homogénéisation de polycristaux viscoplastiques sont obtenues en appliquant la méthode de linéarisation sécante généralisée de Liu et Ponte Castañeda (2004) [1] au cas d'une relation constitutive où les taux de déformation sont des variables primaires. Les estimations obtenues sont particulièrement adaptées pour simuler des chargements mécaniques où les déformations sont imposées et où le matériau s'adoucit. La précision de ces estimations est évaluée au préalable dans le cas d'un système matériau modèle. Un bon accord est obtenu avec des estimations antérieures.

Homogenization estimates for viscoplastic polycrystals are derived by applying the generalized-secant linearization scheme of Liu and Ponte Castañeda (2004) [1] to the constitutive description with strain rates as primary variables. The resulting estimates are thus particularly suitable for simulating mechanical processes where deformations are imposed and where the material softens. Their accuracy is preliminarily assessed in the context of a model material system. Good agreement with previous estimates is found.

Reçu le :
Accepté le :
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DOI : 10.1016/j.crme.2014.12.006
Keywords: Polycrystals, Plasticity, Homogenization, Softening
Mot clés : Polycristaux, Plasticité, Homogénéisation, Adoucissement
Martín I. Idiart 1, 2 ; Pierre-Guy Vincent 3, 4

1 Departamento de Aeronáutica, Facultad de Ingeniería, Universidad Nacional de La Plata, Avda. 1 esq. 47, La Plata B1900TAG, Argentina
2 Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), CCT La Plata, Calle 8 No 1467, La Plata B1904CMC, Argentina
3 Institut de radioprotection et de sûreté nucléaire (IRSN), BP 3, 13115 Saint-Paul-Lez-Durance cedex, France
4 Laboratoire de micromécanique et d'intégrité des structures, IRSN–CNRS–UMII, BP 3, 13115 Saint-Paul-lez-Durance Cedex, France 
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     title = {A generalized-secant homogenization scheme for viscoplastic polycrystalline solids under imposed deformations},
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Martín I. Idiart; Pierre-Guy Vincent. A generalized-secant homogenization scheme for viscoplastic polycrystalline solids under imposed deformations. Comptes Rendus. Mécanique, Volume 343 (2015) no. 3, pp. 179-186. doi : 10.1016/j.crme.2014.12.006. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2014.12.006/

[1] Y. Liu; P. Ponte Castañeda Second-order theory for the effective behavior and field fluctuations in viscoplastic polycrystals, J. Mech. Phys. Solids, Volume 52 (2004), pp. 467-495

[2] R.A. Lebensohn; M.I. Idiart; P. Ponte Castañeda; P.-G. Vincent Dilatational viscoplasticity of polycrystalline solids with intergranular cavities, Philos. Mag., Volume 91 (2011), pp. 3038-3067

[3] Y. Liu; P. Ponte Castañeda Homogenization estimates for the average behavior and field fluctuations in cubic and hexagonal viscoplastic polycrystals, J. Mech. Phys. Solids, Volume 52 (2004), pp. 1175-1211

[4] Y. Liu; P. Gilormini; P. Ponte Castañeda Variational self-consistent estimates for texture evolution in viscoplastic polycrystals, Acta Mater., Volume 51 (2003), pp. 5425-5437

[5] J.R. Willis Variational and related methods for the overall properties of composites, Adv. Appl. Mech., Volume 21 (1981), pp. 1-78

[6] J. van Tiel Convex Analysis, Wiley, New York, USA, 1984

[7] M.I. Idiart; P. Ponte Castañeda Field statistics in nonlinear composites. I. Theory, Proc. R. Soc. Lond. A, Volume 463 (2007), pp. 183-202

[8] G. deBotton; P. Ponte Castañeda Variational estimates for the creep behavior of polycrystals, Proc. R. Soc. Lond. A, Volume 448 (1995), pp. 121-142

[9] M.I. Idiart Macroscopic behavior and field statistics in viscoplastic composites, University of Pennsylvania, Philadelphia, PA, USA, 2006 (Ph.D. thesis)

[10] M.I. Idiart; P. Ponte Castañeda Variational linear comparison bounds for nonlinear composites with anisotropic phases. II. Crystalline materials, Proc. R. Soc. Lond. A, Volume 463 (2007), pp. 925-943

[11] M.I. Idiart Modeling the macroscopic behavior of two-phase nonlinear composites by infinite-rank laminates, J. Mech. Phys. Solids, Volume 56 (2008), pp. 2599-2617

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