Subgrain growth occurring by boundary migration
Abstract
Models for subgrain growth occurring by boundary migration in pure elements, in solid solutions and in two-phase alloys are derived. The contribution from subgrain coalescence is considered in the previous paper. It turns out that the models for pure elements and for two-phase alloys have similar mathematical form as the corresponding models for conventional grain growth although the operating mechanisms are entirely different. The growth rate is inversely proportional to the subgrain size and proportional to the creep mobility and the line tension for dislocations. For two-phase alloys a factor appears which takes into account the particle drag acting on the subboundaries. For solid solutions the interaction energy ΔE between the solute atoms and the dislocations slows down the growth rate if ΔE is sufficiently large. Comparison to experiments will be made in a forthcoming paper.
Résumé
On présente des modèles pour la croissance des sous-grains par migration des joints dans les éléments purs, les solutions solides et les alliages diphasés. In étudiera la contribution de la coalescence des sous-grains dans un article ultérieur. Il se trouve que les modèles pour les éléments purs et pour les alliages diphasés présentent la même forme mathématique que les modèles correspondants pour la croissance/classique des grains, bien que les mécanismes qui opèrent soient entièrement différents. La vitesse de croissance est inversement proportionnelle à la taille des sous-grains et proportionnelle à la mobilité en fluage et à la tension de ligne des dislocations. Dans le cas des alliages diphasés, il apparait un facteur qui tient compte du freinage des sous-joints par les particules. Dans les solutions solides, l'énergie d'interaction ΔE entre les atomes de soluté et les dislocations diminue la vitesse de croissance si ΔE est suffisamment grande. On comparera avec les résultats expérimentaux dans un article ultérieur.
Zusammenfassung
Für das Wachsen von Subkörnern in reinen Elementen, in festen Lösungen und in zweiphasigen Legierungen durch Korngrenzwanderung werden Modelle abgeleitet. Der Beitrag des Zusammenwachsens von Subkörnern wird in einer späteren Arbeit betrachtet. Es zeigt sich, daβ die Modelle für reine Elemente und zweiphasige Legierungen eine ähnliche mathematische Form haben wie die zugehörigen Modelle für konventionelles Kornwachstum, obwohl die ablaufenden Mechanismen vollständig verschieden sind. Die Wachstumsgeschwindigkeit ist umgekehrt proportional zur Subkorngröβe und proportional der Kriechbeweglichkeit und der Linienspannung für Versetzungen. Für zweiphasige Legierungen erscheint ein Faktor, der den Reibungseinfluβ der Partikel auf die Subkorngrenzen berücksichtigt. Bei festen Lösungen vermindert die Wechselwirkungsenergie ΔE zwischen Lösungsatomen und Versetzungen die Wachstumsgeschwindigkeit, wenn ΔE hinreichend groβ ist. Vergleiche mit Experimenten finden sich in einer späteren Arbeit.
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