Abstract
Macroscopic properties of a porous ductile medium are analysed on the basis of an axisymmetric numerical model and on the basis of a set of approximate constitutive equations for a voided material suggested by Gurson. Both models are used to analyse bifurcation into a localized mode. A number of predictions obtained by the two different approaches are in reasonable agreement; but it is found under several different loading conditions that the critical strain for localization is considerably overestimated by the approximate continuum model. A relatively simple modification of the constitutive equations for a voided medium results in considerably improved predictions.
Résumé
On analyse les propriétés macroscopiques d'un milieu poreux ductile sur base d'un modèle numérique axysimétrique et d'une série d'équations constitutives représentant avec une approximation suffisante un matériau comportant des vides, ainsi que le suggère Gurson. Ces deux modèles sont utilisés pour analyser la biffurcation dans un model local. Les deux méthodes, qui sont différentes, permettent d'établir plusieurs prédictions qui sont en accord raisonnable. On trouve néanmoins que sous des conditions de charge différentes la déformation critique conduisant à localisation est considérablement surestimée par le modèle d'approximation du continuum. Une modification relativement simple des équations constitutives dans le cas d'un milieu comportant des vides entraîne des prédictions considérablement améliorées.
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Tvergaard, V. On localization in ductile materials containing spherical voids. Int J Fract 18, 237–252 (1982). https://doi.org/10.1007/BF00015686
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DOI: https://doi.org/10.1007/BF00015686