DESCRIPTION OF THE 3D MORPHOLOGY OF GRAIN BOUNDARIES IN ALUMINUM ALLOYS USING TESSELLATION MODELS GENERATED BY ELLIPSOIDS

Ondřej Šedivý; Jules Mullen Dake; Carl Emil Krill III; Volker Schmidt; Aleš Jäger

doi:10.5566/ias.1656

Authors

Ondřej Šedivý Institute of Stochastics, Ulm University Institute of Physics, Czech Academy of Sciences
Jules Mullen Dake Institute of Micro and Nanomaterials, Ulm University
Carl Emil Krill III Institute of Micro and Nanomaterials, Ulm University
Volker Schmidt Institute of Stochastics, Ulm University
Aleš Jäger Institute of Physics, Czech Academy of Sciences

DOI:

https://doi.org/10.5566/ias.1656

Keywords:

curvature, dihedral angle, grain boundary, polycrystalline material, tessellation

Abstract

Parametric tessellation models are often used to approximate complex grain morphologies of polycrystalline microstructures. A big advantage of such models is the substantial reduction in disk space required to store large, three-dimensional data sets, especially when compared with voxel-based alternatives. By selection of an appropriate tessellation model, a reasonably small loss of information on the real grain shapes can usually be achieved. Special attention has recently been devoted to models based on ellipsoidal approximations fitted to each grain. Faces of these tessellations are portions of quadric surfaces whose parameters can be derived easily. In this paper, we deal with geometric features of the structure, notably curvatures and dihedral angles, which are closely related to the kinetics of grain growth. These characteristics are computed for ellipsoidbased tessellations fitted to two different aluminum alloys with nominal composition Al-3 wt% Mg-0.2 wt% Sc and Al-1 wt% Mg. The results are then compared with estimations based on meshed empirical data. We observe that the model offers more consistent estimations of grain shape characteristics than do the meshed empirical data. Precise description of grain boundaries by the model is also promising with respect to possible applications of these tessellations in stochastic space-time modeling of grain growth.

References

Alpers A, Brieden A, Gritzmann P, Lyckegaard A, Poulsen HF (2015). Generalized balanced power diagrams for 3D representations of polycrystals. Phil Mag 95(9):1016-28.

Altendorf H, Latourte F, Jeulin D, Faessel M, Saintoyant L (2015). 3D reconstruction of a multiscale microstructure by anisotropic tessellation models. Image Anal Stereol 33(2):121-30.

Chen F, Shen L, Deng J (2007). Implicitization and parametrization of quadratic and cubic surfaces by mu-bases. Computing 79:131-42.

Chiu SN, Stoyan D, Kendall WS, Mecke J (2013). Stochastic Geometry and its Applications. 3rd edition. J. Wiley & Sons.

Groeber MA, Jackson MA (2014). DREAM.3D: A digital representation environment for the analysis of microstructure in 3D. Integrat Mater Manuf Innov 3(1):1-17.

Dake JM, Oddershede J, Sorensen H, Werz T, Shatto JC, Uesegi K, Schmidt S, Krill III, CE (2016). Direct observation of grain rotations during coarsening of a semisolid Al-Cu alloy. PNAS 113: E5998-E6006.

Goldman R (2005). Curvature formulas for implicit curves and surfaces. Comput Aided Geom D 22:632–58.

Gottstein G, Shvindlerman LS (2010). Grain Boundary Migration in Metals. 2nd edition. CRC Press.

Grimvall G (1999). Thermophysical Properties of Materials. Elsevier Science B.V..

Jeulin D (2013). Random tessellations and Boolean random functions. In: Mathematical Morphology and Its Applications to Signal and Image Processing. Editors: Luengo Hendriks CL, Borgefors G, Strand R. Springer. 25-36.

Kumar S, Kurtz SK (1994). Simulation of material microstructure using a 3D Voronoi tesselation: Calculation of effective thermal expansion coefficient of polycrystalline materials. Acta Metall Mater 42(12):3917-27.

Lautensack C, Zuyev S (2008). Random Laguerre tessellations. Adv Appl Probab 40(3):630-50.

Lobkovsky AE, Karma A, Mendelev MI, Haataja M, Srolovitz DJ (2003). Grain shape, grain boundary mobility and the Herring relation. Acta Mater 52:285-92.

Lyckegaard A, Lauridsen EM, Ludwig W, Fonda RW, Poulsen HF (2011). On the use of Laguerre tessellations for representations of 3D grain structures. Adv Eng Mater 13(3):165-70.

Okabe A, Boots B, Sugihara K, Chiu SN (2010). Spatial Tessellations: Concepts and Applications of Voronoi Diagrams. 2nd edition. J. Wiley &

Sons.

Schwartz AJ, Kumar M, Adams BL, Field DP (editors, 2009). Electron Backscatter Diffraction in Materials Science. Springer.

Šedivý O, Brereton T, Westhoff D, Polívka L, Beneš V, Schmidt V, Jäger A (2016). 3D reconstruction of grains in polycrystalline materials using a tessellation model with curved grain boundaries. Phil Mag 96(18):1926-49.

Šedivý O, Jäger A (2017). On correction of translational misalignments between section planes in 3D EBSD. J Microsc, in print.

Spettl A, Brereton T, Duan Q, Werz T, Krill CE III, Kroese DP, Schmidt V (2016). Fitting Laguerre tessellation approximations to tomographic image data. Phil Mag 96(2):166-89.

Teferra K, Graham-Brady L (2015). Tessellation growth models for polycrystalline microstructures. Comp Mater Sci 102:57-67.

Valiev RZ, Langdon TG (2006). Principles of equal-channel angular pressing as a processing tool for grain refinement. Prog Mater Sci 51(7):881-981.