×

Large-scale 3D random polycrystals for the finite element method: generation, meshing and remeshing. (English) Zbl 1228.74093

Summary: A methodology is presented for the generation and meshing of large-scale three-dimensional random polycrystals. Voronoi tessellations are used and are shown to include morphological properties that make them particularly challenging to mesh with high element quality. Original approaches are presented to solve these problems: (i) “geometry regularization”, which consists in removing the geometrical details of the polycrystal morphology, (ii) “multimeshing” which consists in using simultaneously several meshing algorithms to optimize mesh quality, and (iii) remeshing, by which a new mesh is constructed over a deformed mesh and the state variables are transported, for large strain applications. Detailed statistical analyses are conducted on the polycrystal morphology and mesh quality. The results are mainly illustrated by the high-quality meshing of polycrystals with large number of grains (up to \(10^{5}\)), and the finite element method simulation of a plane strain compression of \(\epsilon = 1.4\) of a 3000-grain polycrystal. The presented algorithms are implemented and distributed in a free (open-source) software package Neper.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74E15 Crystalline structure
PDFBibTeX XMLCite
Full Text: DOI HAL

References:

[1] Zhang, C.; Suzuki, A.; Ishimaru, T.; Enomoto, M., Characterization of three-dimensional grain structure in polycrystalline iron by serial sectioning, Metal. Mater. Trans. A, 35A, 1927-1953 (2004)
[2] Döbrich, K.; Rau, C.; Krill, C., Quantitative characterization of the three-dimensional microstructure of polycrystalline Al-Sn using X-ray microtomography, Metal. Mater. Trans. A, 35A, 1953-1961 (2004)
[3] Rowenhorst, D.; Lewis, A.; Spanos, G., Three-dimensional analysis of grain topology and interface curvature in a \(β\)-titanium alloy, Acta Mater., 58, 5511-5519 (2010)
[4] Marin, E. B.; Dawson, P. R., On modelling the elasto-viscoplastic response of metals using polycrystal plasticity, Comput. Methods Appl. Mech. Engrg., 165, 1-21 (1998) · Zbl 0952.74012
[5] Marin, E. B.; Dawson, P. R., Elastoplastic finite element analyses of metal deformations using polycrystal constitutive models, Comput. Methods Appl. Mech. Engrg., 165, 23-41 (1998) · Zbl 0952.74071
[6] Barbe, F.; Decker, L.; Jeulin, D.; Cailletaud, G., Intergranular and intragranular behavior of polycrystalline aggregates. Part 1: F.E. model, Int. J. Plast., 17, 4, 513-536 (2001) · Zbl 1067.74011
[7] Barbe, F.; Forest, S.; Cailletaud, G., Intergranular and intragranular behavior of polycrystalline aggregates. Part 2: Results, Int. J. Plast., 17, 4, 537-563 (2001) · Zbl 1067.74012
[8] Sarma, G. B.; Dawson, P. R., Effects of interactions among crystals on the inhomogeneous deformations of polycrystals, Acta Mater., 44, 5, 1937-1953 (1996)
[9] Raabe, D.; Zhao, Z.; Mao, W., On the dependence of in-grain subdivision and deformation texture of aluminum on grain interaction, Acta Mater., 50, 17, 4379-4394 (2002)
[10] Zhao, Z.; Kuchnicki, S.; Radovitzky, R.; Cuitiño, A., Influence of in-grain mesh resolution on the prediction of deformation textures in fcc polycrystals by crystal plasticity FEM, Acta Mater., 55, 7, 2361-2373 (2007)
[11] Ritz, H.; Dawson, P. R., Sensitivity to grain discretization of the simulated crystal stress distributions in FCC polycrystals, Model. Simul. Mater. Sci. Engrg., 17, 1-21 (2009)
[12] Barbe, F.; Quey, R.; Musienko, A.; Cailletaud, G., Three-Dimensional characterization of strain localization bands in a high-resolution elastoplastic polycrystal, Mech. Res. Commmun., 36, 762-768 (2009) · Zbl 1273.74044
[13] Kanit, T.; Forest, S.; Galliet, I.; Mounoury, V.; Jeulin, D., Determination of the size of the representative volume element for random composites: statistical and numerical approach, Int. J. Solids Struct., 40, 13-14, 3647-3679 (2003) · Zbl 1038.74605
[14] Diard, O.; Leclercq, S.; Rousselier, G.; Cailletaud, G., Evaluation of finite element based analysis of 3D multicrystalline aggregates plasticity: application to crystal plasticity model identification and the study of stress and strain fields near grain boundaries, Int. J. Plast., 21, 4, 691-722 (2005) · Zbl 1112.74508
[15] Lebensohn, R.; Montagnat, M.; Mansuy, P.; Duval, P.; Meysonnier, J.; Philip, A., Modeling viscoplastic behavior and heterogeneous intracystalline deformation of culumnar ice polycrystals, Acta Mater., 57, 1405-1415 (2009)
[16] F. Barbe, R. Quey, A numerical modelling of 3D polycrystal-to-polycrystal diffusive phase transformations involving crystal plasticity, Int. J. Plast., uncorrected proofs, doi: <doi:10.1016/j.ijplas.2010.09.008>; F. Barbe, R. Quey, A numerical modelling of 3D polycrystal-to-polycrystal diffusive phase transformations involving crystal plasticity, Int. J. Plast., uncorrected proofs, doi: <doi:10.1016/j.ijplas.2010.09.008> · Zbl 1453.74069
[17] Wakai, F.; Enomoto, N.; Ogawa, H., Three-dimensional microstructural evolution in ideal grain growth - General statistics, Acta Mater., 48, 1297-1311 (2000)
[18] Krill, C.; Chen, L.-Q., Computer simulation of 3D grain growth using a phase-field model, Acta Mater., 50, 3057-3073 (2002)
[19] Resk, H.; Delannay, L.; Bernacki, M.; Coupez, T.; Logé, R., Adaptative mesh refinement and automatic remeshing in crystal plasticity finite element simulations, Model. Simul. Mater. Sci. Engrg., 17, 1-22 (2009)
[20] Brahme, A.; Alvi, M.; Saylor, D.; Fridy, J.; Rollett, A., 3D reconstruction of microstructure in a commercial purity aluminum, Scr. Mater., 55, 75-80 (2006)
[21] Lebensohn, R., N-site modeling of a 3D viscoplastic polycrystal using fast Fourier transform, Acta Mater., 49, 2723-2737 (2001)
[22] Zhao, Z.; Ramesh, M.; Raabe, D.; Cuitiño, A.; Radovitzky, R., Investigation of three-dimensional aspects of grain-scale plastic surface deformation of an aluminum oligocrystal, Int. J. Plast., 24, 2278-2297 (2008) · Zbl 1156.74010
[23] Wei, Y.; Anand, L., Grain-boundary sliding and separation in polycrystalline metals: application to nanocrystalline fcc metals, J. Mech. Phys. Solids, 52, 2587-2616 (2004) · Zbl 1084.74014
[24] Osipov, N.; Gourgues Lorenzon, A.; Marini, B.; Mounoury, V.; Nguyen, F.; Cailletaud, G., FE modelling of bainitic steels using crystal plasticity, Phil. Mag., 88, 3757-3777 (2008)
[25] Musienko, A.; Cailletaud, G., Simulation of inter- and transgranular crack propagation in polycrystalline aggregates due to stress corrosion cracking, Acta Mater., 57, 3840-3855 (2009)
[26] Gilbert, E., Random subdivisions of space into crystals, Ann. Math. Stat., 33, 958-972 (1962) · Zbl 0242.60009
[27] Nygårds, M.; Gudmundson, P., Three-dimensional periodic Voronoi grain models and micromechanical FE-simulations of a two-phase steel, Comput. Mater. Sci., 24, 4, 513-519 (2002)
[28] Fritzen, F.; Böhlke, T.; Schnack, E., Periodic three-dimensional mesh generation for crystalline aggregates based on Voronoi tessellations, Comput. Mech., 43, 701-713 (2009)
[29] Gérard, C.; Bacroix, B.; Bornert, M.; Cailletaud, G.; Crépin, J.; Leclercq, S., Hardening description for FCC materials under complex loading paths, Comput. Mater. Sci., 45, 751-755 (2009)
[30] Kumar, S.; Kurtz, S. K., Monte-Carlo study of angular and edge length distributions in a three-dimensional Poisson-Voronoi tesselation, Mater. Charact., 34, 1, 15-27 (1995)
[31] Geuzaine, C.; Remacle, J.-F., Gmsh: a three-dimensional finite element mesh generator with built-in pre- and post-processing facilities, Int. J. Numer. Methods Engrg., 79, 1309-1331 (2009) · Zbl 1176.74181
[32] Schoberl, J., Netgen, an advancing front 2D/3D-mesh generator based on abstract rules, Comput. Visual. Sci., 52, 1-41 (1997) · Zbl 0883.68130
[33] Delannay, L.; Melchior, M. A.; Signorelli, J. W.; Remacle, J.-F.; Kuwabara, T., Influence of grain shape on the planar anisotropy of rolled steel sheets - Evaluation of three models, Comput. Mater. Sci., 45, 739-743 (2009)
[34] Pascal, J.; George, P.-L., Mesh Generation (2000), Hermes Science Publishing
[35] Shewchuk, J., Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangulator, Applied Computational Geometry: Towards Geometric Engineering, Lecture Notes in Computer Science, 1148, 203-222 (1996)
[36] Neper: a 3D random polycrystal generator for the finite element method (version 1.9), <http://neper.sourceforge.net>; Neper: a 3D random polycrystal generator for the finite element method (version 1.9), <http://neper.sourceforge.net>
[37] F. Pellegrini, Scotch and libScotch 5.1 User’s Guide, INRIA Bordeaux Sud-Ouest, ENSEIRB & LaBRI, UMR CNRS 5800, 2008.; F. Pellegrini, Scotch and libScotch 5.1 User’s Guide, INRIA Bordeaux Sud-Ouest, ENSEIRB & LaBRI, UMR CNRS 5800, 2008.
[38] Povray: the persistence of vision raytracer, <http://www.povray.org>; Povray: the persistence of vision raytracer, <http://www.povray.org>
[39] Quey, R.; Piot, D.; Driver, J. H., Microtexture tracking in hot-deformed polycrystalline aluminium: experimental results, Acta Mater., 58, 1629-1642 (2010)
[40] Quey, R.; Piot, D.; Driver, J. H., Microtexture tracking in hot-deformed polycrystalline aluminium: comparison with simulations, Acta Mater., 58, 2271-2281 (2010)
[41] Kumar, A.; Dawson, P. R., Computational modeling of f.c.c. deformation textures over Rodrigues’ space, Acta Mater., 48, 10, 2719-2736 (2000)
[42] Maurice, C.; Driver, J. H., Hot rolling textures of f.c.c. metals - Part I. Experimental results on Al single and polycrystals, Acta Mater., 45, 11, 4627-4638 (1997)
[43] Maurice, C.; Driver, J. H., Hot rolling textures of f.c.c. metals - Part II. Numerical simulations, Acta Mater., 45, 11, 4639-4649 (1997)
[44] Krieger Lassen, N. C.; Jensen, D. J.; Conradsen, K., On the statistical analysis of orientation data, Acta Crystall., A50, 741-748 (1994)
[45] Humbert, M.; Gey, N.; Muller, J.; Esling, C., Determination of a mean orientation from a cloud of orientations. Application to electron back-scattering pattern measurements, J. Appl. Crystallogr., 26, 662-666 (1996)
[46] Humphreys, F. J.; Bate, P. S.; Hurley, P. J., Orientation averaging of electron backscattered diffraction data, J. Microstruc., 201, 50-58 (2001)
[47] Glez, J.-C.; Driver, J. H., Orientation distribution analysis in deformed grains, J. Appl. Crystallogr., 34, 280-288 (2001)
[48] Orilib: a collection of routines for orientation manipulation (version 2.0), <http://orilib.sourceforge.net>; Orilib: a collection of routines for orientation manipulation (version 2.0), <http://orilib.sourceforge.net>
[49] Benson, D. J., Momentum advection on unstructured staggered quadrilateral meshes, Int. J. Numer. Methods Engrg., 75, 1549-1580 (2008) · Zbl 1158.74478
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.