A Model for Static Recrystallization with Simultaneous Precipitation and Solute Drag
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INTRODUCTION
DURING thermo-mechanical processing of crystalline materials, the growth velocity of recrystallizing grains can strongly be affected by the presence of precipitates and solute atoms. Precipitates interact with the moving grain boundaries via the well-known Zener pinning effect,[1] which acts as a retarding force on the velocity of boundary movement. The magnitude of the Zener pressure is mainly determined by the precipitate phase fraction and size, which are commonly evolving in the course of thermo-mechanical treatment. In case of micro-alloyed steel, this effect is experimentally well analyzed for the case of carbo-nitrides forming with minor additions of Al, V, Ti, and Nb.[2] In addition to Zener pinning, the grain boundary mobility can also be drastically influenced by the solute drag effect.[3] In this case, elements that are segregated into the grain boundary must be ‘‘dragged along’’ with the moving boundary, thus exerting a retarding effect on the movement. The absolute value of the solute drag effect is mainly determined by the nominal concentration of the solute drag elements and their binding energy to the grain boundary. Detailed experiments in steel[4] show that V, Mo, Ti, and Nb are probably the most practically relevant elements with regard to solute drag in austenite of Fe-based alloys. A proper consideration of both effects, Zener drag and solute drag, is therefore essential for a successful simulation of recrystallization kinetics. In literature, two types of simulation approaches exist for a description of these effects in micro-alloyed steel: phenomenological and physically based models. On one
HEINRICH BUKEN, PhD Student, is with the Institute of Materials Science and Technology, TU Wien, Getreidemarkt 9, 1060 Vienna, Austria. Contact e-mail: [email protected] ERNST KOZESCHNIK, Professor, is with the Institute of Materials Science and Technology, TU Wien, and also with MatCalc Engineering GmbH, Getreidemarkt 9, 1060 Vienna, Austria. Manuscript submitted December 15, 2015. METALLURGICAL AND MATERIALS TRANSACTIONS A
hand, Medina and co-workers[2,5] utilize a phenomenological approach based on the Avrami model.[6] In this approach, the impact of precipitation on recrystallization is described by means of two coupled Avrami equations. The fast reaction term reproduces recrystallization kinetics in the regime before the Zener pressure exceeds the driving pressure for recrystallization. As soon as precipitation starts to control the grain boundary mobility, the slower Avrami kinetics becomes dominant. By interconnecting both solutions (slow and fast kinetics), Medina et al. are able to describe the evolution of the recrystallized fraction for a large amount of precipitation-controlled recrystallization experiments. The additional effect of solute atoms on grain boundary mobility is taken into account indirectly by an empiric formula, which accounts for the nominal chemical composition of the steel with a composition-dependent activation energy for recrystallization. In contrast, Zuro
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