A Novel Approach to Model Static Recrystallization of Austenite During Hot Rolling of Nb Microalloyed Steel. Part I: Pre
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I.
INTRODUCTION
MICROALLOYED steels owe much of their attractive properties to their fine grain size and high number density of nanoscale carbo-nitrides. The microstructure of these steels is manipulated through thermo-mechanical processing which offers considerable energy savings over rolled and heat-treated routes.[1] The optimization of thermo-mechanical processing schedules requires robust models of the microstructure evolution during hot rolling. Over the last three decades, great progress has been made toward the modeling of thermo-mechanical processing of microalloyed steels.[1–10] The key to modeling the microstructure evolution during the hot rolling of microalloyed steels is to capture the processes of recovery, recrystallization, and precipitation as well as their interactions. The most widely implemented model for recrystallization is based on the seminal works of Johnson and Mehl, Avrami, and Kolmogorov and is often referred to as the JMAK model.[11] In the simplest case, the experimental data are fitted to an equation of the form X ¼ 1 exp( Ktn Þ
½1
where X is the recrystallized fraction and t is time. The parameters K and n are assumed to be constant at a given temperature. The fitted values of K and n are then analyzed to gain an insight into the nucleation and the growth processes. Earlier work on this topic has led to the development of powerful semi-empirical relationships that describe the interactions between recovery, precipitation, and recrystallization with great accuracy.[3,7,10,12–15]
MD. KASHIF REHMAN, Ph.D. Candidate, and HATEM S. ZUROB, Associate Professor, are with the Department of Material Science and Engineering, John Hodgings Engineering Building, McMaster University, 1280 Main Street West, Hamilton, ON L8S4L8, Canada. Contact e-mail: [email protected] Manuscript submitted February 8, 2012. METALLURGICAL AND MATERIALS TRANSACTIONS A
These semi-empirical models work well within the domain for which they were developed and validated, but often lack the predictive ability which is needed to guide the development of new alloys and processes. For this reason, there has been much effort in recent years to develop physically based models that have the potential to predict trends over a wide range of processing conditions including ones that are difficulty to access in the laboratory.[9,15–17] In physically based models, the driving force, nucleation rate, and number of nucleation sites enter explicitly into the model. The effect of recovery on recrystallization is captured through the evolution of the driving force with time, leading to the so-called relaxed JMAK models.[9,17–19] The effect of particle pinning has often been captured by reducing the driving force for recrystallization by an amount equal to the Zener pinning term.[20–23] In addition, the effect of solutes on boundary migration is captured through a solute drag treatment of the type proposed by Cahn[24] and Hillert and Sundman.[25] The above modifications greatly improve the way in which the physically based models capture
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