Abstract
Issues germane to the theoretical foundations of micromechanical modeling and analysis of metals at finite strain are investigated. Established concepts and results are concisely reviewed and integrated, and some new relationships, both general and specific, are obtained. The proof, by Hill and Havner (1982), that plastic potentials for individual crystal deformation depend solely upon Green elasticity of the underlying crystal lattice is presented afresh and extended to polycrystalline metals, using the averaging theorem of Hill (1972) and the aggregate model of Havner (1974). A specialization of the general theory for individual crystals is emphasized, corresponding to a postulated constitutive inequality that is invariant under change in strain measure and a saddle potential function for nominal stress rate. For the polycrystalline aggregate model, in addition to plastic potential laws, other macroscopic relationships are derived making use of the recent analysis in Hill (1984), Various equations for incremental work are presented that involve open questions requiring further research.
Résumé
Les fondations théoriques de la modelisation micromécanique et l’analyse des métaux en grandes déformations sont étudiées. Les concepts et les résultats classiques sont brièvement rapelés et des nouvelles relations, à la fois générales et particulières, sont obtenues. La démonstration de Hill et Havner (1982), que les potentiels plastiques pour la déformation du cristal individuel ne dépendent que de l’élasticité de Green du réseau cristallin, est présentée de nouveau et étendue aux polycristaux métalliques en utilisant le théorème de la moyenne de Hill (1972) et le modèle d’agrégats d’Havner (1974). Une spécialisation de la théorie générale pour les cristaux individuels est soulignée; elle correspond avec une inégalité constitutive postulée qui est invariante avec un chargement de la mesure des déformations et avec une fonction-selle potentielle pour la vitesse des contraintes nominales. Pour le modèle de l’agrégat polycristallin, en plus des lois de potentiel plastique, d’autres relations macroscopiques sont déduites à partir de la récente analyse de Hill (1984). Diverses équations pour le travail incrémental sont présentées; elles impliquent des questions ouvertes pour des recherches futures.
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Havner, K.S. (1986). Fundamental Considerations in Micromechanical Modeling of Polycrystalline Metals at Finite Strain. In: Gittus, J., Zarka, J., Nemat-Nasser, S. (eds) Large Deformations of Solids: Physical Basis and Mathematical Modelling. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3407-8_15
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DOI: https://doi.org/10.1007/978-94-009-3407-8_15
Publisher Name: Springer, Dordrecht
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