Interplay of Kinetics and Microstructure in the Recrystallization of Pure Copper: Comparing Mesoscopic Simulations and E
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INTRODUCTION
ALREADY some of the earliest works on mesoscopic microstructure simulation have treated the process of recrystallization in metals.[1–3] This can be understood as a consequence of the great technological importance of recrystallization and the recognition that the usually applied simple recrystallization models fail to describe correctly both the experimentally observed kinetics and the resulting microstructure. In particular, two experimental results could not yet be explained conclusively and, thus, give rise to enduring interest in recrystallization: First, the kinetics of (isothermal) recrystallization show a time dependence that cannot be explained with simple Johnson–Mehl– Avrami–Kolmogorov (JMAK) models[4–6] based on a constant growth rate of recrystallized grains:[7] In so-called double-logarithmic plots of lnð lnð1 fÞÞ vs lnðtÞ; with f being the fraction recrystallized and t being the time elapsed since the start of the recrystallization, a straight line results if the recrystallization can be ERIC A. JA¨GLE, formerly PhD Student at the Max Planck Institute for Intelligent Systems (formerly Max Planck Institute for Metals Research), 70569 Stuttgart, Germany, is now a Post-doctoral Researcher with the Max-Planck-Institut fu¨r Eisenforschung, 40237 Du¨sseldorf, Germany. Contact e-mail: [email protected] ERIC J. MITTEMEIJER, Director, is with the Max Planck Institute for Intelligent Systems (formerly Max Planck Institute for Metals Research), and is also a Full Professor with the Institute for Materials Science at the University of Stuttgart, Heisenbergstrasse 3, 70569 Stuttgart, Germany. Manuscript submitted July 20, 2011. Article published online March 20, 2012 2534—VOLUME 43A, JULY 2012
described by the classical JMAK model (for a discussion of JMAK[-like] models, see Reference 8). The frequently observed deviation from a straight line toward the end of the recrystallization has been interpreted as a result of a decreasing growth rate of recrystallized grains.[9,10] Second, the grain-size distributions of the microstructures generated by physically conceivable models considered in computer simulations are (so far) consistently and distinctly narrower than the ones observed experimentally.[11,12] Even though broad grain-size distributions can, of course, always be generated by devising arbitrary nucleation and growth models in computer simulations,[2,13] the question arises what the physical background of such nucleation and growth models could be, if there is any. In more recent recrystallization models, the nucleation and growth rates are defined depending on the deformed microstructure at the onset of recrystallization (see, e.g., References 9, 12, 14,15). The reason for the decreasing growth rate is believed to originate from the inhomogeneity of the deformed microstructure, in which, during the annealing, new nuclei are forming and into which the recrystallizing grains are growing. In recrystallization simulations departing from an inhomogeneous, deformed microstructure, it is important
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