Development of numerical tools for the multiscale modelling of recrystallization in metals, based on a digital material framework

• Autorzy: Bernacki M. , Chastel Y. , Digonnet H. , Resk H. , Coupez T. , Logé R.

Warianty tytułu

PL

Opracowanie numerycznego narzędzia dla wieloskalowego modelowania rekrystalizacji w metalach, w oparciu o cyfrową reprezentację materiałów

• Konferencja: 14th KomPlasTech Conference, Zakopane, January 14-17, 2007
• Języki publikacji: EN

Abstrakty

EN

This work is currently under development within the framework of an American-European project (Digimat Project) whose principal purpose is to model recrystallization in metals using a multiscale approach. The modelling effort is centered around a digital material framework. This framework is based on a digital representation of the material structure, where data coming from different scales can be stored or probed. The digital representation can be converted into finite element meshes, which are then used to model plastic deformation and subsequent recrystallization. The local behaviour of individual microstructure components is computed through models operating at different scales. In particular, grain constitutive models are derived from crystal plasticity concepts, with appropriate hardening/recovery laws which are linked to lower scale approaches at the dislocation level. Grain boundary motion is similarly described by connecting the continuum mechanical and thermal fields to simulations at the atomistic/dislocations levels. A detailed confrontation of the multiscale approach with experiment will be done at the ESRF synchrotron facility in Grenoble (France). In this paper, the needed development of numerical tools is presented together with the first finite element simulations. The development of the DIGIMAT software, dedicated to the concept of digital material, is first detailed. The construction of the virtual material consists in building a multi-level Voronoi tesselation. A polycrystalline microstructure made of grains and sub-grains can be obtained in a random or deterministic way. The software is at a stage of its development where it is possible to cut the microstructure along given planes, to approximate the grain shapes by a set of fitting ellipsoids, to roughly optimize the digital microstructure, and to generate a coarse mesh of the microstructure at each level of the microstructure (level 1 = external shape, level 2 =grains, level 3 = sub-grains). A second part of the work concerns the first finite elements simulations of a uniaxial compression test under large strain. The initial mesh is fine and anisotropic, taking into account the presence of interfaces between grains and sub-grains. A level-set approach is used to follow the grain boundaries during the deformation. In fact, with this method, the interface is modelled by the zero level-set of a time dependant level-set function which moves according to the mesh velocity field. The most complex test case carried out to date is a multi-domains Stokes problem, deforming at 85\% a cubic Volume Element made of 250 grains. Boundary conditions use a constant velocity in the compression direction, and free motion in the plane perpendicular to that direction. The constitutive law is a viscoplastic power law with a rate sensitivity of 0.2, and a variable hardness from one grain to another. The constitutive law will soon be replaced by a crystallographic formulation. Automatic isotropic and anisotropic remeshing, and parallel computation were successfully implemented, both features being crucial with respect to the Digimat project objectives (large strain to induce recrystallization, and large number of elements for a good representation of the microstructure). Finally, the bases of our first recrystallization simulations will be explained, including the description of nucleation and grain growth.

PL

Praca jest realizowana w ramach Amerykańsko-Europeskiego projektu (Digimat Project). W artykule opisano rozwój numerycznych narzędzi przeznaczonych do cyfrowej reprezentacji struktur metalicznych oraz do generowania powiązanych siatek anizotropowych dla modelowania metodą elemen­tów skończonych dużych odkształceń polikrystalicznych mikrostruktur. Metoda ustalonych poziomów stosowana do opisu mikrostruktury stanowi wspólną bazę dla wszystkich analizowanych rozwiązań.

Słowa kluczowe

EN

digital microstructure; polycrystal; anisotropic meshing and remeshing; finite element simulation; evel set method

• Wydawca: Wydawnictwa AGH
• Czasopismo: Computer Methods in Materials Science
• Rocznik: 2007
• Tom: Vol. 7, No. 1
• Strony: 142--149
• Opis fizyczny: Bibliogr. 14 poz., rys.

Twórcy

autor

Bernacki M.

autor

Chastel Y.

autor

Digonnet H.

autor

Resk H.

autor

Coupez T.

autor

Logé R.

• Centre de misę en formę des materiaux (CEMEF), Ecole Nationale Superieure des Mines de Paris, UMR CNRS 7635, BP 207, 06904 Sophia Antipolis Cedex, France,

Bibliografia

• Barbe, F. Cailletaud, G., Decker, L., Jeulin, D., 2001, Intergranular and intergranular behavior of polycrystalline aggregates. Int. J. Plast., 17, 513-536.
• Brahme, A. Alvi, M.H. Saylor, D. Fridy, J. Rollett, A.D., 2006, 3D reconstruction of microstructure in a commercial purity aluminium, Scripta Mat., 55, 75-80.
• Cailletaud, G., Diard, O., Leclercq, S., Rousselier, G., 2002, Distribution of normal stress at grain boundaries in multicrystals : application to an intergranular damage modelling, Comp. Mat. Sci., 25, 73-84.
• Coupez T., 2000, Generation et Adaptation de maillage par optimisation locale, La Revue Europeenne des elements finis, 9, 403-423.
• Coupez, T., Digonnet, H., Ducloux, R., 2000, Parallel meshing and remeshing by repartitioning, Appl. Math. Modeling, 25, 153-175.
• Dawson, P.R., 2000, Int. J. Solids Struct., 37, 115-130.
• Dawson, P.R., Miller, M.P., Han, T.-S., Bernier, J., 2005, Metall. Mater. Trans., A, 36A, 1627-1641.
• Kugler, G., Turk, R., 2004, Modeling the dynamic recrystallization under multi-stage hot deformation, Acta Mat., 52, 4659-4668.
• Kugler, G., Turk, R., 2006, Study of the influence of initial microstructure topology on the kinetics of static recrystallization using a cellular automata model, Comp. Mat. Sci., 37, (3), 284-291.
• Loge, R., Chastel, Y., 2006, Coupling the thermal and mechanical fields to metallurgical evolutions within a finite element description of a forming process, Comp. Methods Appl. Mech. Engrg., 195, 6843-6857.
• Raabe, D., Becker, R., Modeli., 2000, Simulation Mater. Sc. Eng., 8, 445.
• Radhakrishnan, B., Sarma, G.B., Zacharia, T., 1998, Modeling the kinetics and microstructural evolution during static recrystallization - Monte Carlo simulation of recrystallization, Acta Mater., 46, 4415-4433.
• Rollett, A.D., 1997, Overview of modeling and simulation of recrystallization, Progress in Mat. Sci., 42, 77-99.
• Sethian, J., 1996, Level Set Methods, Cambridge University Press.