Abstract
The modelling of the inelastic deformation of metals requires consideration of their microstructure. The homogenization techniques currently employed for the macroscopic description of the microstructure focus generally on the averaging over all grains of a polycrystal, frequently oversimplifying the structural rearrangement within the grains. In addition, these techniques do not lead yet to sufficiently manageable models to be included in the analysis of structural elements. It therefore seems desirable to supplement this quantitative micro-macro transition by a less rigorous but more flexible heuristic approach, aiming at injecting into phenomenological models the microstructural information that seems to be most relevant for a certain class of materials and deformation processes. The present chapter begins by setting forth this kind of approach within the general framework of the models with internal state variables. Subsequently the procedure is illustrated by some typical examples concerning hot working, deep drawing, plastic deformation of single crystals, and anisotropic hardening.
Résumé
La modélisation de la déformation non-élastique des métaux exige la prise en compte de leur réalité microscopique. Les techniques d’homogénéisation couramment utilisées pour la description macroscopique de la microstructure concernent surtout le calcul des moyennes sur les différentes orientations des grains, en simplifiant parfois d’une manière trop sommaire l’évolution de la microstructure à l’interieur des grains. De plus, ces techniques ne conduisent pas encore à des modèles assez maniables pour qu’ils puissent être utilisés en calcul de structure. Il est par conséquent souhaitable de développer, à coté de ces approches quantitatives de passage micro-macro, une démarche plutôt heuristique, moins exigeante mais plus souple, permettant d’injecter dans des modèles phénoménologiques les informations microstructurales qui sont jugées les plus significatives pour une certaine classe de matériaux et de processus de déformation. Le présent travail situe cette démarche dans le cadre général des modèles à variables internes d’état et propose pour son illustration quelques exemples représentatifs, concernant notamment le formage à chaud, l’emboutissage, la déformation plastique des monocristaux et l’écrouissage anisotrope.
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Sidoroff, F., Teodosiu, C. (1986). Microstructure and Phenomenological Models for Metals. 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_11
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DOI: https://doi.org/10.1007/978-94-009-3407-8_11
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