Comptes Rendus
Approximate yield criteria for anisotropic metals with prolate or oblate voids
Comptes Rendus. Mécanique, Volume 334 (2006) no. 7, pp. 431-439.

Following the study of Gologanu et al. (1997) which has extended the well-known approach of Gurson (1975), we propose approximate yield criteria for anisotropic plastic voided metals containing non spherical cavities. The plastic anisotropy of the matrix is described by means of Hill's quadratic criterion. The procedure to establish the closed form expression of approximate macroscopic criteria, in which void shape and plastic anisotropic effects are included, is detailed. The new criteria allow us to recover existing results in the cases of spherical and cylindrical voids in an Hill type plastic matrix. Moreover, they agree with previous criteria for non spherical voids in an isotropic plastic matrix. Finally, for validation purposes, we provide, in the general case of non spherical cavities in the anisotropic matrix, a comparison with the numerical exact two field criteria.

En se basant sur les travaux de Gologanu et al. (1997) qui étendent l'approche bien connue de Gurson, on propose des critères macroscopiques pour des métaux plastiques anisotropes contenant des cavités non sphériques. L'anisotropie plastique de la matrice est décrite à l'aide du critère quadratique de Hill. On détaille la procédure pour établir les critères approchés incluant la forme des cavités ainsi que les effets d'anisotropie plastique. Les nouveaux critères analytiques obtenus permettent de retrouver les résultats existants dans les cas de cavités sphériques ou cylindriques dans une matrice de type Hill. De plus, ils concordent avec ceux qui sont disponibles pour des cavités non sphériques dans un milieu plastique isotrope. Enfin, dans un but de validation, on fournit, dans le cas général de cavités non sphériques dans la matrice anisotrope, une comparaison avec les expressions des critères issues des solutions numériques exactes du problème à deux champs.

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Accepted:
Published online:
DOI: 10.1016/j.crme.2006.06.001
Keywords: Computational solid mechanics, Ductile porous metals, Anisotropy, Hill criterion, Prolate and oblate voids
Mot clés : Mécanique des solides numérique, Métaux ductiles poreux, Anisotropie, Critère de Hill, Cavités allongées et aplaties

Vincent Monchiet 1; Cosmin Gruescu 1; Eric Charkaluk 1; Djimedo Kondo 1

1 Laboratoire de mécanique de Lille-UMR CNRS 8107, université de sciences et technologies Lille, cité scientifique, boulevard Paul-Langevin, 59655 Villeneuve d'Ascq cedex, France
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Vincent Monchiet; Cosmin Gruescu; Eric Charkaluk; Djimedo Kondo. Approximate yield criteria for anisotropic metals with prolate or oblate voids. Comptes Rendus. Mécanique, Volume 334 (2006) no. 7, pp. 431-439. doi : 10.1016/j.crme.2006.06.001. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2006.06.001/

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