Ductile damage of porous materials with two populations of voids

Pierre-Guy Vincent; Yann Monerie; Pierre Suquet

doi:10.1016/j.crme.2007.11.017

Ductile damage of porous materials with two populations of voids
[Endommagement ductile de matériaux poreux contenant deux populations de cavités]

Pierre-Guy Vincent ^1,² ; Yann Monerie ¹ ; Pierre Suquet ²

¹ Institut de radioprotection et de sûreté nucléaire, B.P. 3, 13115 Saint-Paul-lez-Durance cedex, France
² Laboratoire de mécanique et d'acoustique, 31, chemin Joseph-Aiguier, 13402 Marseille cedex 20, France

Comptes Rendus. Mécanique, Duality, inverse problems and nonlinear problems in solid mechanics, Volume 336 (2008) no. 1-2, pp. 245-259.

Résumé
Abstract

Cette étude est consacrée à la modélisation de l'endommagement ductile dans l'oxyde d'uranium. Ce matériau polycristallin présente deux familles de cavités de tailles très différentes. Le problème est abordé ici comme la recherche d'un critère de plasticité pour un matériau de Gurson contenant des cavités ellipsoïdales aplaties distribuées aléatoirement. Dans un premier temps, le cas des cavités sphériques est examiné. La démarche variationnelle de Gurson est reprise en ajoutant une composante compressible au champ de vitesse de Gurson. Cette démarche est ensuite étendue aux ellipsoïdes aplatis et alignés en reprenant et en complétant un champ de vitesse proposé par Gologanu et al. (ASME J. Engrg. Mater. Technol. 116 (1994) 290–297). Enfin l'extension aux ellipsoïdes orientés aléatoirement se fait par une prise de moyenne appropriée sur les orientations. Dans chaque cas, des bornes supérieures rigoureuses ainsi que des estimations sont proposées et comparées (seulement dans le cas des cavités sphériques) avec des calculs par éléments finis.

This study is devoted to the modelling of ductile damage in uranium dioxide. This polycrystalline material contains two populations of voids of well separated size. The problem addressed here is the prediction of the effective flow surface of a Gurson material containing randomly oriented oblate voids. The case of spherical voids is considered first and the variational approach of Gurson is generalized by adding a compressible component to his original velocity field. The case of aligned oblate voids is then considered and a suitable generalization of a velocity field due to Gologanu et al. (ASME J. Engrg. Mater. Technol. 116 (1994) 290–297) is proposed. The extension to randomly oriented voids is achieved by averaging over all orientations. In each case, rigorous upper bounds and approximate estimates are derived and compared (in the case of spherical voids) with Finite Element simulations.

Publié le : 2008-01-01

DOI : 10.1016/j.crme.2007.11.017

Keywords: Damage, Plasticity, Micromechanics
Mots-clés : Endommagement, Plasticité, Micromécanique

Affiliations des auteurs :

Pierre-Guy Vincent ^{1, 2} ; Yann Monerie ¹ ; Pierre Suquet ²

¹ Institut de radioprotection et de sûreté nucléaire, B.P. 3, 13115 Saint-Paul-lez-Durance cedex, France
² Laboratoire de mécanique et d'acoustique, 31, chemin Joseph-Aiguier, 13402 Marseille cedex 20, France

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Pierre-Guy Vincent; Yann Monerie; Pierre Suquet. Ductile damage of porous materials with two populations of voids. Comptes Rendus. Mécanique, Duality, inverse problems and nonlinear problems in solid mechanics, Volume 336 (2008) no. 1-2, pp. 245-259. doi : 10.1016/j.crme.2007.11.017. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2007.11.017/

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