Abstract
The effect of material rate sensitivity on the localization of deformation in a porous visco-plastic solid is examined under plane strain tension and axisymmetric tension conditions. The plastic flow rule proposed by Gurson [3], modified to account for material rate sensitivity, is adopted to model the plastic softening behavior that arises due to void nucleation and growth. An initial imperfection in the form of a planar band is assumed and a material instability is sought as the deformation proceeds.
Comparisons are made with the results of a rate-independent analysis [10]. The present rate-dependent results show that the retardation effect on flow localization is larger when the material is more rate-sensitive, and that, with a given rate sensitivity, the retardation effect on flow localization is greater in plane strain tension than in axisymmetric tension. Results are also obtained by employing parameter values representative of spheroidized carbon steels studied by Fisher [21], and the predictions of the model are in good agreement with experimental observations.
Résumé
On examine sous des conditions d'état plan de déformation et de tension axisymétrique l'effet de la sensibilité d'un matériau à la vitesse sur la localisation d'une déformation dans un solide poreux visco-plastique. On adopte la règle d'écoulement plastique proposée par Gurson, modifiée pour tenir compte de la sensibilité du matériau à la vitesse, en vue de modéliser le comportement d'adoucissement plastique qui résulte de la nucléation de lacunes et de leur croissance. On suppose une imperfection initiale sous forme d'une bande planaire et on recherche une instabilité du matériau au fur et à mesure que la déformation avance.
Les comparaisons sont faites avec des résultats d'une analyse où il y avait indépendance par rapport à la vitesse. Les résultats présents montrent un effet retardateur sur la localisation de l'écoulement, qui est d'autant plus grand que le matériau est plus sensible à la vitesse. D'autre part, pour une sensibilité à la vitesse donnée, l'effet retardateur sur la localisation de l'écoulement est plus grand en état plan de déformation qu'en tension axisymétrique. Les résultats sont également obtenus en utilisant des valeurs paramétriques représentatives des aciers au carbone sphéroïdé étudiés par Fisher et les prédictions du modèle sont en bon accord avec les observations expérimentales.
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Pan, J., Saje, M. & Needleman, A. Localization of deformation in rate sensitive porous plastic solids. Int J Fract 21, 261–278 (1983). https://doi.org/10.1007/BF00942345
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DOI: https://doi.org/10.1007/BF00942345