Probabilistic modelling of microstructure formation in solidification processes
Abstract
A new approach to the modelling of grain structure formation in solidification processes is proposed. Based upon a two-dimensional cellular automata technique, the model includes the mechanisms of heterogeneous nucleation and of grain growth. Nucleation occurring at the mould wall as well as in the liquid metal are treated by using two distributions of nucleation sites. The location and the crystallographic orientation of the grains are chosen randomly among a large number of cells and a certain number of orientation classes, respectively. The growth kinetics of the dendrite tip and the preferential 〈100〉 growth directions of cubic metals are taken into account. The model is then applied to small specimens of uniform temperature. The columnar-to-equiaxed transition, the selection and extension of columnar grains which occur in the columnar zone and the impingement of equiaxed grains are clearly shown by this technique. The calculated effect of the alloy concentration and cooling rate upon the resultant microstructure agree with experimental observations.
Résumé
Une nouvelle approche est proposée pour modéliser la formation de microstructures de solidification. Se basant sur une technique d'automate cellulaire bi-dimensionnel, le modèle tient compte des mécanismes der germination hétérogène et de croissance de grains. La germination est décrite par deux distributions de sites appliquées sur les parois du moule et dans le métal liquide. La localisation et l'orientation cristallographique des grains sont choisies aléatoirement parmi un grand nombre de cellules et de classes d'orientation, respectivement. La cinétique de croissance de la pointe de la dendrite et les directions de croissance 〈100〉 préférentielles des métaux cubiques sont reproduites. Le modèle est appliqué à de petits échantillons de température uniforme. La transition colonnaire-équiaxe, la sélection et la propagation des grains colonnaires ainsi que la recontre des grains équiaxes sont clairement reproduits par cette technique. Les effets de la concentration de l'alliage et de la vitesse de refroidissement sur la microstructure simulée s'accordent avec les observations expérimentales.
Zusammenfassung
Ein neues Verfahren zur Modellisierung der Kornstruktur bei Erstarrungsprozessen wird vorgeschlagen. Basierend auf einer zweidimensionalen Zellularautomatentechnik berücksichtigt das Modell die Mechanismen der heterogenen Keimbildung und des Kornwachstums. Keimbildung an der Wand sowie im flüssigen Metall werden mit jeweils vershhiedenen Verteilungsfunktionen der Keimdichte behandelt. Die Orte für die Kornentstehung werden statistisch aus einer grossen Zahl von Zellen bestimmt. Ebenso wird die kristallographische Orientierung der Körner statistisch aus einer bestimmten Zahl von Orientierungsklassen ausgewählt. Die Wachstumskinetik der Dendritenspitzen sowie das bevorzugte Wachstum kubischer Metalle in 〈100〉 Richtung werden berücksichtigt. Das Modell wird auf kleine Proben mit gleichförmiger Temperaturverteilung angewandt. Der Übergang von säulenförmigem zu globularem Wachstum, die Kornauswahl und das Wachstum säulenförmiger Kristalle sowie das Aufeinanderstossen globularer Körner werden von dieser Technik klar simuliert. Die Berechnungen des Einflusses von Legierungskonzentration und Abkühlgeschwindigkeit auf das resultierende Gefüge stimmen gut mit den experimentellen Beobachtungen überein.
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