Résistance d'un polycristal avec interfaces intergranulaires imparfaites

Luc Dormieux; Julien Sanahuja; Yamen Maalej

doi:10.1016/j.crme.2006.11.005

Résistance d'un polycristal avec interfaces intergranulaires imparfaites

Présenté par : Évariste Sanchez-Palencia

Luc Dormieux ¹ ; Julien Sanahuja ² ; Yamen Maalej ¹

¹ LMSGC, UMR 113 CNRS/ENPC/LCPC, 77455 Marne-la-Vallée, France
² Lafarge centre de recherche, 95, rue du Montmurier, BP 15, 38291 Saint-Quentin Fallavier cedex, France

Comptes Rendus. Mécanique, Volume 335 (2007) no. 1, pp. 25-31.

Résumé
Abstract

On s'intéresse à un polycristal poreux constitué de grains en contact le long d'interfaces. On met tout d'abord en œuvre un schéma autocohérent faisant intervenir des pores sphériques ainsi qu'un motif constitué d'un noyau élastique entouré d'une interface également élastique. On établit ensuite une formule permettant de déterminer la moyenne quadratique de la discontinuité de déplacement tangentiel dans les interfaces entre grains. Dans la dernière partie, on applique la méthode sécante modifiée pour déterminer le critère de rupture d'un tel milieu dans l'hypothèse où le solide et les interfaces sont respectivement de type von Mises et Tresca.

A porous polycrystal made up of grains in contact along interfaces is considered. First, a self-consistent scheme including spherical pores and a pattern comprising a spherical elastic core surrounded by an elastic interface is implemented. Then, a formula giving the quadratic average of the tangential displacement discontinuity in the interfaces is established. Finally, the modified secant method is applied to the determination of the effective strength criterion in the case of a von Mises solid and interfaces of the Tresca type.

Reçu le : 2006-07-25
Accepté le : 2006-11-14
Publié le : 2006-12-19

DOI : 10.1016/j.crme.2006.11.005

Mots-clés : Mécanique des solides numérique, Milieux granulaires, Milieux poreux, Interface, Micromécanique, Résistance, Schéma auto-cohérent
Keywords: Computational solid mechanics, Granular media, Porous media, Interface, Micromechanics, Strength, Self-consistent scheme

Affiliations des auteurs :

Luc Dormieux ¹ ; Julien Sanahuja ² ; Yamen Maalej ¹

¹ LMSGC, UMR 113 CNRS/ENPC/LCPC, 77455 Marne-la-Vallée, France
² Lafarge centre de recherche, 95, rue du Montmurier, BP 15, 38291 Saint-Quentin Fallavier cedex, France

@article{CRMECA_2007__335_1_25_0,
     author = {Luc Dormieux and Julien Sanahuja and Yamen Maalej},
     title = {R\'esistance d'un polycristal avec interfaces intergranulaires imparfaites},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {25--31},
     publisher = {Elsevier},
     volume = {335},
     number = {1},
     year = {2007},
     doi = {10.1016/j.crme.2006.11.005},
     language = {fr},
}

TY  - JOUR
AU  - Luc Dormieux
AU  - Julien Sanahuja
AU  - Yamen Maalej
TI  - Résistance d'un polycristal avec interfaces intergranulaires imparfaites
JO  - Comptes Rendus. Mécanique
PY  - 2007
SP  - 25
EP  - 31
VL  - 335
IS  - 1
PB  - Elsevier
DO  - 10.1016/j.crme.2006.11.005
LA  - fr
ID  - CRMECA_2007__335_1_25_0
ER  -

%0 Journal Article
%A Luc Dormieux
%A Julien Sanahuja
%A Yamen Maalej
%T Résistance d'un polycristal avec interfaces intergranulaires imparfaites
%J Comptes Rendus. Mécanique
%D 2007
%P 25-31
%V 335
%N 1
%I Elsevier
%R 10.1016/j.crme.2006.11.005
%G fr
%F CRMECA_2007__335_1_25_0

Luc Dormieux; Julien Sanahuja; Yamen Maalej. Résistance d'un polycristal avec interfaces intergranulaires imparfaites. Comptes Rendus. Mécanique, Volume 335 (2007) no. 1, pp. 25-31. doi : 10.1016/j.crme.2006.11.005. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2006.11.005/

Bibliographie
Cité par

[1] A. Zaoui Structural morphology and constitutive behavior of microheterogeneous materials (P. Suquet, ed.), Continuum Micromechanics, CISM Courses and Lectures, vol. 377, Springer-Verlag, Berlin, 1997

[2] Z. Hashin The spherical inclusion with imperfect interface, J. Appl. Mech., Volume 58 (1991), pp. 444-449

[3] Z. Zhong; S.A. Meguid On the elastic field of a spherical inhomogeneity with an imperfectly bonded interface, J. Elasticity, Volume 46 (1997), pp. 91-113

[4] E. Hervé; A. Zaoui n-Layered inclusion-based micromechanical modelling, Internat. J. Engr. Sci., Volume 31 (1993) no. 1, pp. 1-10

[5] W. Kreher Residual stresses and stored elastic energy of composites and polycrystals, J. Mech. Phys. Solids, Volume 38 (1990), pp. 115-128

[6] L. Dormieux; D. Kondo; F.-J. Ulm Microporomechanics, Wiley, New York, 2006

[7] P. Suquet Effective behavior of non linear composites (P. Suquet, ed.), Continuum Micromechanics, CISM Courses and Lectures, vol. 377, Springer-Verlag, Berlin/New York, 1997

[8] P. Ponte-Castaneda The effective mechanical properties of non linear isotropic composites, J. Mech. Phys. Solids, Volume 39 (1991), pp. 45-71

[9] M.V. Nebozhyn; P. Gilormini; P. Ponte-Castaneda Variational self-consistent estimates for cubic viscoplastic polycrystals: the effect of grain anisotropy and shape, J. Mech. Phys. Solids, Volume 49 (2001), pp. 313-340

François Bignonnet; Ghazi Hassen; Luc Dormieux Fourier-based strength homogenization of porous media, Computational Mechanics, Volume 58 (2016) no. 5, p. 833 | DOI:10.1007/s00466-016-1319-6
François Bignonnet; Luc Dormieux; Djimédo Kondo A micro-mechanical model for the plasticity of porous granular media and link with the Cam clay model, International Journal of Plasticity, Volume 79 (2016), p. 259 | DOI:10.1016/j.ijplas.2015.07.003
François Bignonnet; Luc Dormieux; Eric Lemarchand Strength of a matrix with elliptic criterion reinforced by rigid inclusions with imperfect interfaces, European Journal of Mechanics - A/Solids, Volume 52 (2015), p. 95 | DOI:10.1016/j.euromechsol.2015.02.003
Maged Sidhom; Luc Dormieux; Eric Lemarchand Poroelastic Properties of a Nanoporous Granular Material with Interface Effects, Journal of Nanomechanics and Micromechanics, Volume 5 (2015) no. 3 | DOI:10.1061/(asce)nm.2153-5477.0000097
Yamen Maalej; Luc Dormieux; Eric Lemarchand An energy-based equivalent inclusion for the determination of nanocomposite behavior, Science and Engineering of Composite Materials, Volume 22 (2015) no. 5, p. 475 | DOI:10.1515/secm-2013-0154
Markus Königsberger; Bernhard Pichler; Christian Hellmich; J. Olek Micromechanics of ITZ–Aggregate Interaction in Concrete Part I: Stress Concentration, Journal of the American Ceramic Society, Volume 97 (2014) no. 2, p. 535 | DOI:10.1111/jace.12591
Z. He; L. Dormieux; E. Lemarchand; D. Kondo Cohesive Mohr–Coulomb interface effects on the strength criterion of materials with granular-based microstructure, European Journal of Mechanics - A/Solids, Volume 42 (2013), p. 430 | DOI:10.1016/j.euromechsol.2013.06.009
Jean‐François Barthélémy; Christine Souque; Jean‐Marc Daniel Nonlinear homogenization approach to the friction coefficient of a quartz‐clay fault gouge, International Journal for Numerical and Analytical Methods in Geomechanics, Volume 37 (2013) no. 13, p. 1948 | DOI:10.1002/nag.2115
Z. He; G. Caratini; L. Dormieux; D. Kondo Homogenization of anisotropic elastoplastic behaviors of a porous polycrystal with interface effects, International Journal for Numerical and Analytical Methods in Geomechanics, Volume 37 (2013) no. 18, p. 3213 | DOI:10.1002/nag.2186
Z. He; L. Dormieux; E. Lemarchand; D. Kondo A poroelastic model for the effective behavior of granular materials with interface effect, Mechanics Research Communications, Volume 43 (2012), p. 41 | DOI:10.1016/j.mechrescom.2012.02.009
L. Dormieux; L. Jeannin; N. Gland Homogenized models of stress-sensitive reservoir rocks, International Journal of Engineering Science, Volume 49 (2011) no. 5, p. 386 | DOI:10.1016/j.ijengsci.2010.12.010
L. Dormieux; L. Jeannin; J. Sanahuja Effective Hydraulic and Mechanical Properties of Heterogeneous Media with Interfaces, Multiscale Methods in Computational Mechanics, Volume 55 (2011), p. 179 | DOI:10.1007/978-90-481-9809-2_10
Stefan Scheiner; Bernhard Pichler; Christian Hellmich; Herbert A. Mang Computational Multiscale Model for NATM Tunnels: Micromechanics-Supported Hybrid Analyses, Multiscale Methods in Computational Mechanics, Volume 55 (2011), p. 305 | DOI:10.1007/978-90-481-9809-2_16
L. Dormieux; L. Jeannin; E. Bemer; T. H. Le; J. Sanahuja Micromechanical models of the strength of a sandstone, International Journal for Numerical and Analytical Methods in Geomechanics, Volume 34 (2010) no. 3, p. 249 | DOI:10.1002/nag.804
Julien Sanahuja; Luc Dormieux; Sylvain Meille; Christian Hellmich; Andreas Fritsch Micromechanical Explanation of Elasticity and Strength of Gypsum: From Elongated Anisotropic Crystals to Isotropic Porous Polycrystals, Journal of Engineering Mechanics, Volume 136 (2010) no. 2, p. 239 | DOI:10.1061/(asce)em.1943-7889.0000072
H. A. Mang; S. Scheiner; B. Pichler; C. Hellmich Damage Assessment and Disaster Prevention in Natm Tunnels During Construction: Micromechanics-Supported Hybrid Analyses, Damage Assessment and Reconstruction after War or Natural Disaster (2009), p. 223 | DOI:10.1007/978-90-481-2386-5_9
Yamen Maalej; Luc Dormieux; Julien Sanahuja Micromechanical approach to the failure criterion of granular media, European Journal of Mechanics - A/Solids, Volume 28 (2009) no. 3, p. 647 | DOI:10.1016/j.euromechsol.2008.10.010
H. K. Lee; S. H. Pyo 3D-Damage Model for Fiber-Reinforced Brittle Composites with Microcracks and Imperfect Interfaces, Journal of Engineering Mechanics, Volume 135 (2009) no. 10, p. 1108 | DOI:10.1061/(asce)em.1943-7889.0000039
Emmanuel Bertrand; Christian Hellmich Multiscale Elasticity of Tissue Engineering Scaffolds with Tissue-Engineered Bone: A Continuum Micromechanics Approach, Journal of Engineering Mechanics, Volume 135 (2009) no. 5, p. 395 | DOI:10.1061/(asce)0733-9399(2009)135:5(395)
Bernhard Pichler; Stefan Scheiner; Christian Hellmich From micron-sized needle-shaped hydrates to meter-sized shotcrete tunnel shells: micromechanical upscaling of stiffness and strength of hydrating shotcrete, Acta Geotechnica, Volume 3 (2008) no. 4, p. 273 | DOI:10.1007/s11440-008-0074-z
Andreas Fritsch; Luc Dormieux; Christian Hellmich; Julien Sanahuja Micromechanics of crystal interfaces in polycrystalline solid phases of porous media: fundamentals and application to strength of hydroxyapatite biomaterials, Journal of Materials Science, Volume 42 (2007) no. 21, p. 8824 | DOI:10.1007/s10853-007-1859-4

Cité par 21 documents. Sources : Crossref

Commentaires - Politique