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C2 - Material model (funding period 1)



Development of a material model for metal sheets at finite deformation

Project Status: finished

Last Update: 01.06.2012



Members


Within their granular microstructure, metals show crystalline nature: the atoms are arranged on a regular space lattice. The macroscopically observable plastic deformation can be traced back to shearing or sliding of atoms on defined slip planes in the crystal. Depending on the present structure, predictions can be made about the slip behaviour. At the same time, crystal grains can be observed in the microstructure; regions, where atomic dislocation movements in the same directions take place and at whose borders atoms can pile up.

                         survey_photo                             EBSD_01_DC04

                            Real microstructure of a DC04 steel                                                 EBSD image of a DC04 steel

 

A suitable material model considering plastic anisotropy through atomic dislocations is to be found on the microstructural level, whereas the elastic and plastic material parameters will be determined in cooperation with the research project C4. For the representative volume elements, randomly distributed geometries on the microscale are assumed, based on the received microstructural data. Through homogenisation, effective stress-strain relations are gained for different boundary conditions being the outcome for an effective material model. After an assumption for an effective material model has been made, the material parameters have to be determined through optimisation techniques. The results obtained by simulations will be validated with experimental data obtained from material specimens and formed structures.

 

           rve_100_200

                                                Finding the representative volume element: polycrystals of different sizes

 

                                                  hom_stress_strain

                                                                                    Homogenised stress-strain-curves

To carry out the entire computational simulation, it is necessary to model and discretise the polycrystalline structures of the microstructure. In order to develop an anisotropic elastoplastic material model, the slip systems are considered in the plastic part of the deformation gradient and plastic gliding is modelled within these systems. The continuum mechanical model is gained through consistent derivation of the stress response and the elastic and plastic material tangent. As the slip systems are more easily actived under deviatoric deformation, it is split from the volumetric deformation.

                                rves_Hdev_Hvol_graycubes_int

                                               The polycrystalline structure is subjected to deviatoric and volumetric loading.

 

The geometry of polycrystalline materials will be simulated by three-dimensional Voronoi tesselations, whereas a single crystal of the material is represented by a Voronoi cell. Meshing will be done with respect to the borders of every crystal, so that crystals may have different material properties and orientations. The problems concerning the geometry generation and the interface development lead to questions about the manipulation of three-dimensional subdivisions. A three-dimensional Voronoi tesselation can be obtained by its dual graph, the Delaunay tesselation, by making use of space duality concepts. For the two-dimensional case, space duality,  Delaunay and Voronoi decompositions can be implemented by using the quad-edge data structure. A three dimensional generalisation of the quad-edge data structure and its topological operations are to be found.


Working Groups


Publications

    2012

    • Lehmann, E.; Schmaltz, S.; Germain, S.; Faßmann, D.; Weber, C.; Löhnert, S.; Schaper, M.; Steinmann, P.; Willner, K.; Wriggers, P.: Material model identification for DC04 based on the numerical modelling of the polycrystalline microstructure and experimental data. In: ESAFORM 2012 - Key Engineering Materials (Edt.): 504(2012), doi:10.4028/www.scientific.net/KEM.504-506.993, pp. 993-998
    • Lehmann, E.; Löhnert, S.; Wriggers, P.: Computational Homogenisation of Polycrystalline Elastoplastic Microstructures at Finite Deformation. In: Technische Mechanik, 32(2012)2, pp. 369-379

    2011

    • Lehmann, E.; Schmaltz, S.; Faßmann, D.; Germain, S.; Weber, C.; Löhnert, S.; Schaper, M.; Bach, F.; Steinmann, P.; Willner, K.; Wriggers, P.: Identifikation eines Materialmodells für den DC04 basierend auf der numerischen Modellierung der polykristallinen Mikrostruktur und experimentellen Daten(2011), In: M. Merklein, Fr.-W. Bach, A.E. Tekkaya (Hrsg.): Tagungsband zum 1. Workshop Blechmassivumformung 2011, pp. 13-32
    • Lehmann, E.; Löhnert, S.; Wriggers, P.: Towards the effective behaviour of polycrystalline materials for sheet bulk metal forming processes(2011), AIP Conf. Proc., 1353, pp. 1179-1184
    • Lehmann, E.; Löhnert, S.; Wriggers, P.: Towards the effective behaviour of polycrystalline microstructures at finite strains(2011), COMPLAS XI., Barcelona, Spain, accepted
    • Lehmann, E.; Löhnert, S.; Wriggers, P.: Computational Homogenisation of Polycrystalline Elastoplastic Microstructures at Finite Deformation. In: Proc. Appl. Math. Mech., 11(2011)1, pp. 401-402

    2010

    • Weber, C.; Löhnert, S.; Wriggers, P.: Aspects of the Facet-Edge Data Structure for the Construction of Voronoi Cells. In: Proc. Appl. Math. Mech., 10(2010)1, pp. 645 – 646
    • Lehmann, E.; Löhnert, S.; Wriggers, P.: Modelling Metals at Finite Deformation. In: Proc. Appl. Math. Mech., 10(2010)1, pp. 305-306

    Presentations

      2012

      • 14.03.2012: Germain, S.; Lehmann, E.; Schmaltz, S.; Faßmann, D.; Weber, C.; Löhnert, S.; Schaper, M.; Bach, F.; Steinmann, P.; Willner, K.; Wriggers, P.: Material model identification for DC04 based on the numerical modelling of the polycrystalline microstructure and experimental data, ESAFORM 2012, Erlangen, Germany
      • 27.03.2012: Lehmann, E.; Löhnert, S.; Wriggers, P.: About the Microstructural Effects of Polycrystalline Materials and their Macroscopic Representation at Finite Deformation, GAMM 83rd Annual Meeting, Darmstadt
      • 10.07.2012: Lehmann, E.; Löhnert, S.; Wriggers, P.: Towards an Effective Material Model for Elastoplastic Polycrystalline Materials through Homogenisation, 8th European Solid Mechanics Conference, Graz

      2011

      • 19.04.2011: Lehmann, E.; Löhnert, S.; Wriggers, P.: Computational Homogenisation of Polycrystalline Elastoplastic Microstructures at Finite Deformation, 82nd GAMM Annual Meeting, Graz, Österreich
      • 27.04.2011: Lehmann, E.; Löhnert, S.; Wriggers, P.: Towards the Effective Behaviour of Polycrystalline Materials for Sheet Bulk Metal Forming Processes, ESAFORM 2011, Belfast, Vereinigtes Königreich
      • 31.08.2011: Lehmann, E.; Löhnert, S.; Wriggers, P.: Computational Homogenisation of Polycrystalline Elastoplastic Microstructures at Finite Deformation, 2nd International Conference on Material Modelling, Paris, Frankreich
      • 08.09.2011: Lehmann, E.; Löhnert, S.; Wriggers, P.: Towards the Effective Behaviour of Polycrystalline Microstructures at Finite Strains, COMPLAS XI., Barcelona, Spanien

      2010

      • 23.03.2010: Lehmann, E.; Löhnert, S.; Wriggers, P.: Modelling Metals at Finite Deformation, GAMM 81st Annual Meeting, Karlsruhe
      • 24.03.2010: Weber, C.: Aspects of the Facet-Edge Data Structure for the Construction of Voronoi Cells, GAMM, Karlsruhe