3D RECONSTRUCTION OF A MULTISCALE MICROSTRUCTURE BY ANISOTROPIC TESSELLATION MODELS
DOI:
https://doi.org/10.5566/ias.v33.p121-130Keywords:
anisotropic tessellation, martensitic steel, multiscale 3D microstructure, stochastic modelingAbstract
In the area of tessellation models, there is an intense activity to fully understand the classical models of Voronoi, Laguerre and Johnson-Mehl. Still, these models are all simulations of isotropic growth and are therefore limited to very simple and partly convex cell shapes. The here considered microstructure of martensitic steel has a much more complex and highly non convex cell shape, requiring new tessellation models. This paper presents a new approach for anisotropic tessellation models that resolve to the well-studied cases of Laguerre and Johnson-Mehl for spherical germs. Much better reconstructions can be achieved with these models and thus more realistic microstructure simulations can be produced for materials widely used in industry like martensitic and bainitic steels.References
Albert S, Matsui M, Watanabe T, Hongo H, Kubo K,
Tabuchi M (2003). Variation in the type iv cracking
behaviour of a high cr steel weld with post weld heat
treatment. International Journal of Pressure Vessels and
Piping :405–13.
Blaschke W (1921-29). Vorlesungen über
Differentialgeometrie III. Springer, Berlin.
Descartes R (1644). Les Principes de la Philosophie.
Elzevier, Amsterdam.
Dirichlet GL (1850). Über die Reduktion der positiven
quadratischen Formen mit drei unbestimmten ganzen
Zahlen. Journal fur die Reine und Angewandte
Mathematik 40:209–27.
Jeulin D (2013). Random tessellations and boolean random
functions. In: Hendriks C, Borgefors G, Strand R,
eds., Mathematical Morphology and Its Applications
to Signal and Image Processing, vol. 7883 of Lecture
Notes in Computer Science. Springer Berlin Heidelberg,
–36.
Johnson WA, Mehl RF (1939). Reaction kinetics in
processes of nucleation and growth. Trans AIME
:416–58.
Lautensack C (2007). Random Laguerre Tessellations.
Ph.D. thesis, Universität Karlsruhe (TH).
McCartin BJ (2007). On concentration and inertia
ellipsoids. Applied Mathematical Sciences 1:1–11.
Vivier F (2009). Fluage à 500°C d'un joint soudé d'un
acier 9Cr-1Mo modifié: évolution de la microstructure
et comportement mécanique. Ph.D. thesis, ParisTech -
MAT- Centre des matériaux PM Fourt.
Voronoi G (1908). Nouvelles applications des paramtères
continus la théorie des formes quadratiques. premier
mémoire. sur quelques propriétés des formes quadratiques
positives parfaites. Journal für die reine und angewandte
Mathematik Crelles Journal 1908:97–102.
