A theoretical approach of strain localization within thin planar bands in porous ductile materials

Jean-Baptiste Leblond; Gérard Mottet

doi:10.1016/j.crme.2007.11.008

A theoretical approach of strain localization within thin planar bands in porous ductile materials
[Une approche théorique de la localisation de la déformation en minces couches planes dans les matériaux poreux ductiles]

Jean-Baptiste Leblond ¹ ; Gérard Mottet ²

¹ Institut Jean-Le-Rond-d'Alembert, Université Paris VI, tour 65–55, 4, place Jussieu, 75252 Paris cedex 05, France
² ESI Group, Immeuble “Le Récamier”, 70, rue Robert, 69458 Lyon cedex 06, France

Comptes Rendus. Mécanique, Duality, inverse problems and nonlinear problems in solid mechanics, Volume 336 (2008) no. 1-2, pp. 176-189.

Résumé
Abstract

Il est bien connu que la propagation de fissures dans les matériaux poreux ductiles s'effectue suivant deux mécanismes possibles : la coalescence des cavités et la formation de bandes de cisaillement. Le modèle homogénéisé classique de Gurson–Tvergaard–Needleman (GTN) pour ces matériaux contient une modélisation phénoménologique de la coalescence, mais pas de la formation de bandes de cisaillement assistée par la présence de microcavités, et ceci induit certains inconvénients. Afin de résoudre ces difficultés, cet article propose un modèle unifié de la coalescence des vides et de la formation de bandes de cisaillement dans les solides plastiques poreux, incluant les couplages possibles entre les deux phénomènes. Ces derniers sont considérés comme deux manifestations d'un même effet fondamental, à savoir la localisation de la déformation en minces couches planes, la seule différence résidant dans le mode de déformation. Le modèle est d'abord développé en faisant l'hypothèse d'une distribution périodique de cavités, puis validé par comparaison avec des simulations numériques micromécaniques fondées sur la même hypothèse, et finalement étendu au cas d'une distribution aléatoire de vides.

Propagation of cracks in ductile materials is well known to occur through two possible mechanisms: coalescence of cavities and formation of shear bands (‘void sheet mechanism’). The classical Gurson–Tvergaard–Needleman (GTN) homogenized model for such materials incorporates some phenomenological modelling of coalescence, but not of formation of shear bands assisted by the presence of microvoids, and this generates a number of shortcomings. In order to solve these difficulties, this paper presents a unified model of both coalescence and formation of shear bands in porous plastic solids, including the possible couplings between the two. Both phenomena are viewed as expressions of the same basic effect, namely strain localization within thin planar bands, the only difference being the mode of deformation. The model is first developed assuming a periodic distribution of cavities, then critically assessed through comparison with some micromechanical numerical simulations based on the same assumption, and finally extended to the case of a random distribution of voids.

Publié le : 2008-01-01

DOI : 10.1016/j.crme.2007.11.008

Keywords: Ductile damage, Coalescence, Shear bands
Mots-clés : Endommagement ductile, Coalescence, Bandes de cisaillement

Affiliations des auteurs :

Jean-Baptiste Leblond ¹ ; Gérard Mottet ²

¹ Institut Jean-Le-Rond-d'Alembert, Université Paris VI, tour 65–55, 4, place Jussieu, 75252 Paris cedex 05, France
² ESI Group, Immeuble “Le Récamier”, 70, rue Robert, 69458 Lyon cedex 06, France

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Jean-Baptiste Leblond; Gérard Mottet. A theoretical approach of strain localization within thin planar bands in porous ductile materials. Comptes Rendus. Mécanique, Duality, inverse problems and nonlinear problems in solid mechanics, Volume 336 (2008) no. 1-2, pp. 176-189. doi : 10.1016/j.crme.2007.11.008. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2007.11.008/

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