An improvement of Gurson-type models of porous materials by using Eshelby-like trial velocity fields

Vincent Monchiet; Eric Charkaluk; Djimedo Kondo

doi:10.1016/j.crme.2006.12.002

An improvement of Gurson-type models of porous materials by using Eshelby-like trial velocity fields

Presented by: Pierre Suquet

Vincent Monchiet ¹ ; Eric Charkaluk ¹; Djimedo Kondo ¹

¹ Laboratoire de mécanique de Lille-UMR CNRS 8107, université de sciences et technologies de Lille, cité scientifique, 59655 Villeneuve d'Ascq cedex, France

Comptes Rendus. Mécanique, Volume 335 (2007) no. 1, pp. 32-41.

Abstract
Résumé

New expressions of the macroscopic criteria of perfectly plastic rigid matrix containing prolate and oblate cavities are presented. The proposed approach, derived in the framework of limit analysis, consists in the consideration of Eshelby-like trial velocity fields for the determination of the macroscopic dissipation. It is shown that the obtained results significantly improve existing criteria for ductile porous media. Moreover, for low stress triaxialities, these new results also agree perfectly with the (nonlinear) Hashin–Shtrikhman bound established by Ponte-Castañeda and Suquet.

On présente de nouvelles expressions du critère macroscopique de milieux poreux constitués d'une matrice rigide parfaitement plastique contenant des cavités allongées ou aplaties. L'approche proposée, formulée dans le cadre de l'analyse limite, repose sur la considération de champs test de vitesse de type Eshelby pour la détermination de la dissipation macroscopique. On démontre que les résultats obtenus améliorent de manière significative les critères de milieux poreux ductiles existants. De plus, pour les faibles triaxialités de contrainte, ces nouveaux résultats s'accordent aussi parfaitement avec les bornes (non linéaires) d'Hashin–Shtrikhman établies par Ponte-Castañeda et par Suquet.

Received: 2006-07-11
Accepted: 2006-10-27
Published online: 2007-01-01

DOI: 10.1016/j.crme.2006.12.002

Keywords: Computational solid mechanics, Ductile porous metals, Generalized Gurson criterion, Prolate and oblate voids, Eshelby velocity fields, Limit analysis
Mot clés : Mécanique des solides numériques, Métaux ductiles poreux, Critère de Gurson généralisé, Cavités allongées et aplaties, Champ de vitesse d'Eshelby, Analyse limite

Author's affiliations:

Vincent Monchiet ¹; Eric Charkaluk ¹; Djimedo Kondo ¹

¹ Laboratoire de mécanique de Lille-UMR CNRS 8107, université de sciences et technologies de Lille, cité scientifique, 59655 Villeneuve d'Ascq cedex, France

@article{CRMECA_2007__335_1_32_0,
     author = {Vincent Monchiet and Eric Charkaluk and Djimedo Kondo},
     title = {An improvement of {Gurson-type} models of porous materials by using {Eshelby-like} trial velocity fields},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {32--41},
     publisher = {Elsevier},
     volume = {335},
     number = {1},
     year = {2007},
     doi = {10.1016/j.crme.2006.12.002},
     language = {en},
}

TY  - JOUR
AU  - Vincent Monchiet
AU  - Eric Charkaluk
AU  - Djimedo Kondo
TI  - An improvement of Gurson-type models of porous materials by using Eshelby-like trial velocity fields
JO  - Comptes Rendus. Mécanique
PY  - 2007
SP  - 32
EP  - 41
VL  - 335
IS  - 1
PB  - Elsevier
DO  - 10.1016/j.crme.2006.12.002
LA  - en
ID  - CRMECA_2007__335_1_32_0
ER  -

%0 Journal Article
%A Vincent Monchiet
%A Eric Charkaluk
%A Djimedo Kondo
%T An improvement of Gurson-type models of porous materials by using Eshelby-like trial velocity fields
%J Comptes Rendus. Mécanique
%D 2007
%P 32-41
%V 335
%N 1
%I Elsevier
%R 10.1016/j.crme.2006.12.002
%G en
%F CRMECA_2007__335_1_32_0

Vincent Monchiet; Eric Charkaluk; Djimedo Kondo. An improvement of Gurson-type models of porous materials by using Eshelby-like trial velocity fields. Comptes Rendus. Mécanique, Volume 335 (2007) no. 1, pp. 32-41. doi : 10.1016/j.crme.2006.12.002. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2006.12.002/

References
Cited by

[1] A.L. Gurson Continuum theory of ductile rupture by void nucleation and growth: Part I—Yield criterion and flow rules for porous ductile media, J. Engrg. Mat. Technol., Volume 99 (1977), pp. 2-15

[2] G. Perrin, Contribution à l'Étude Théorique et Numérique de la Rupture Ductile des Métaux, PhD thesis, Ecole Polytechnique Palaiseau, France, 1992

[3] P. Ponte-Castañeda The effective mechanical properties of nonlinear isotropic composites, J. Mech. Phys. Solids, Volume 39 (1991), pp. 45-71

[4] P. Suquet On bounds for the overall potential of power law materials containing voids with an arbitrary shape, Mech. Res. Commun., Volume 19 (1992), pp. 51-58

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

[6] M. Gologanu; J.-B. Leblond; G. Perrin; J. Devaux Recent extensions of Gurson's model for porous ductile metals (P. Suquet, ed.), Continuum Micromechanics, Springer-Verlag, Berlin/New York, 1997, pp. 61-130

[7] M. Garajeu; J.C. Michel; P. Suquet A micromechanical approach of damage in viscoplastic materials by evolution in size, shape and distribution of voids, Comput. Methods Appl. Mech. Engrg., Volume 183 (2000), pp. 223-246

[8] M. Gologanu; J.-B. Leblond; J. Devaux Approximate models for ductile metals containing non-spherical voids—case of axisymmetric prolate ellipsoidal cavities, J. Mech. Phys. Solids, Volume 41 (1993) no. 11, pp. 1723-1754

[9] M. Gologanu; J.-B. Leblond; J. Devaux Approximate models for ductile metals containing non-spherical voids—case of axisymmetric oblate ellipsoidal cavities, J. Engrg. Mat. Technol., Volume 116 (1994), pp. 290-297

[10] J.D. Eshelby The determination of the elastic field of an ellipsoidal inclusion, and related problem, Proc. R. Soc. Lond. A, Volume 241 (1957), pp. 376-396

[11] T. Mura Micromechanics of Defects in Solids, Martinus Nijhoff, Dordrecht, 1987

[12] B.J. Lee; M.E. Mear Axisymmetric deformation of power-law solids containing a dilute concentration of aligned spheroidal voids, J. Mech. Phys. Solids, Volume 40 (1992), pp. 1805-1836

[13] V. Monchiet; C. Gruescu; E. Charkaluk; D. Kondo Approximate yield criteria for anisotropic metals with non spherical voids, C. R. Mecanique, Volume 334 (2006), pp. 431-439

[14] P. Ponte-Castañeda; P. Suquet Nonlinear composites, Adv. Appl. Mech., Volume 34 (1998), pp. 171-302

Cited by Sources:

Comments - Policy