Simulation of recrystallization by cellular automata
Abstract
A cellular automata (CA) model for recrystallization is introduced. Its behviour is investigated under the influence of different model parameters and algorithms that simulate the kinetics of nucleation and growth of recrystallizing grains. The rate of released energy is calculated by the CA-model so that comparisons with calorimetric measurements are possible. The CA-model givesthe same results as the theory of Johnson, Mehl, Avrami and Kolmogorov (JMAK) for the same model assumptions. Systematic deviations of experimental data from the JMAK-theory are simulated by special model assumptions of the CA. This leads to good agreement with experimental data. It is shown that the CA-model is easy to handle, very simple in the basic algorithm and extremely flexible for introducing special model assumptions.
Résumé
Un modèle d'automate cellulaire (CA) est introduit pour la recristallisation. Son comportement est examiné sous l'influence des paramètres et des algorithmes différentes, qui simulent la cinétique de nucléation et de croissance des grains recristallisants. La vitesse d'énergie libérée est calculée des automates cellulaires; aussi est-il possible de la comparer à des mesurages caloriques. Le modèle CA optient les même résultats que la théorie de Johnson, Mehl, Avrami et Kolmogorov (JMAK) pour les même hypothèses de modèle. Les déviations systématiques des résultats expérimentaux de la théorie de JMAK sont simulées par des hypothèses spéciales pour le modèle CA. Les rèsultats concordent de façcon très satisfaisante avec ceux des expériences. Cette publication montre comme le modèle CA est facile appliquer, avec un algorithme fondamental très simple et très flexible qui permet d'introduire des hypothèses particulères.
Zusammenfassung
Es wird ein Zellularautomatenmodell (CA) zur Beschreibung von Rekristallisation eingeführt. Das Modellverhalten wird untersucht unter dem Einfluß verschiedener Modellparameter und -algorithmen, die die Kinetik von Keimbildung und Wachstum rekristallisierender Körner beschreiben. Die Energiefreisetzungsrate wird mit dem CA-Modell bestimmt, so daß Vergleiche mit kalorischen Messungen möglich sind. Das CA-Modell liefert dieselben Ergebnisse wie die Theorie von Johnson, Mehl, Avrami und Kolmogorov (JMAK) für dieselben Modellannahmen. Systematische Abweichungen der experimentellen Werte von der JMAK-Theorie werden durch spezielle Modellannahmen für den CA simuliert. Dies führt zu einer guten Übereinstimmung mit experimentellen Ergebnissen. Es wird gezeigt, daß das CA-Modell einfach zu handhaben ist, einen sehr einfachen Grundalgorithmus besitzt und sehr flexibel bei der Einführung besonderer Modellannahmen ist.
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