A Geometric Framework for Mesoscale Models of Recrystallization
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INTRODUCTION
MODELING tools for the prediction of microstructure evolution are needed to optimize thermomechanical processes, i.e., to obtain desirable mechanical properties and to reduce both process design time and manufacturing cost. The usual method, based on the so-called Avrami or Johnson-Mehl-Avrami-Kolmogorov (JMAK) formulation, has been applied with some success for a number of years. In particular, its implementation in finite-element-method (FEM) subroutines, requiring minimal additional computational power, has provided a very useful tool for manufacturers.[1] However, such models become increasingly phenomenological as their domain of application is extended over wider ranges of temperature, strain, and strain rate, and for complex sequences of dynamic, metadynamic, and static recrystallization, as illustrated in Reference 2. As long as dynamic recrystallization can be neglected or represented using reasonable approximations, it is possible to integrate a number of mechanisms and couple them inside the framework of an Avrami formulation.[3] However, the Avrami approach poses a number of limitations related to its lack of a true physical basis outside the context of classical static evolution. For example, it is incapable of properly J.P. THOMAS, Visiting Scientist, Air Force Research Laboratory, AFRL/MLLMP, is with the Universal Technology Corporation, Dayton, OH 45432. F. MONTHEILLET, CNRS Senior Scientist, is with the Ecole Nationale Supe´rieure des Mines, Centre SMS, CNRS UMR 5146, 42023 Saint-Etienne Cedex 2, France. S.L. SEMIATIN, Senior Scientist, Materials Processing/Processing Science is with the Air Force Research Laboratory, Materials and Manufacturing Directorate, AFRL/MLLMP, Wright-Patterson Air Force Base, OH 45433. Contact e-mail: [email protected] Manuscript submitted October 19, 2006. Article published online July 25, 2007. METALLURGICAL AND MATERIALS TRANSACTIONS A
incorporating the influence of precipitates on dynamic recrystallization,[4] and its extension to deal with partial waves of dynamic or metadynamic recrystallization is questionable.[5] Geometric and texture effects are also rarely included in such instances. A more fundamental weakness of this phenomenological approach, even when focusing on a specific alloy, relates to the extensive and, hence, expensive experimentation required to characterize microstructure evolution over the full range of temperature, strain rate, and history variables and, thus, to fit such models. Furthermore, it is usually not possible to extend Avrami relations derived for one material to another, even in the same alloy class, because the model parameters have limited physical meaning. Models of microstructure evolution based on the Monte-Carlo[6] and cellular-automata[7,8] techniques also have their own advantages and limitations. They provide an enhanced representation of the physics of evolution. Nevertheless, they require substantial computational power, thus preventing their application at every node of an FEM mesh. In such cases, analysis
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