Modeling Grain Boundary Motion and Dynamic Recrystallization in Pure Metals
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INTRODUCTION
DURING the high-temperature deformation process of metals, the energy from the plastic deformation is dissipated by heat, and a fraction is stored in the material in the form of dislocations. These dislocations can disappear either by recovery (i.e., mutual annihilation) or by the generation of new grains. The second process is called dynamic recrystallization (DRX).[1–3] This phenomenon can lead to a significant grain refinement and is found to be a powerful method to enhance the mechanical properties by grain boundary strengthening. Discontinuous DRX is a mechanism occurring during the hot working of a wide range of metals with a low to intermediate stacking-fault energy[4,5] and proceeds by nucleation and growth of new grains in the material. Because discontinuous DRX reaches a steady state at large strain (e > 0.5), the microstructure becomes independent of the strain and depends only on the deformation conditions. As a consequence, the smart selection of process conditions can enable a significant control of the grain size and consequently of the mechanical properties of the worked material. JULIEN FAVRE, Researcher, is with the INSA-Lyon, MATEIS CNRS UMR5510, Universite´ de Lyon, 25 avenue Jean Capelle, 69621 Villeurbanne, France, and also with the Centre SMS, CNRS UMR 5146, Ecole Nationale Supe´rieure des Mines de Saint-E´tienne, 158 Cours Fauriel, 42023 Saint-E´tienne Cedex 2, France. Contact e-mail: [email protected] DAMIEN FABRE´GUE, Associate Professor, and ERIC MAIRE, Research Director, are with the INSA-Lyon, MATEIS CNRS UMR5510, Universite´ de Lyon. DAVID PIOT, Researcher, is with the Centre SMS, CNRS UMR 5146, Ecole Nationale Supe´rieure des Mines de Saint-E´tienne. NING TANG, Researcher, YUICHIRO KOIZUMI, Associate Professor, and AKIHIKO CHIBA, Professor, are with the Institute for Materials Research, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai, 980-8577 Japan. Manuscript submitted January 15, 2013. Article published online August 20, 2013 METALLURGICAL AND MATERIALS TRANSACTIONS A
The microstructure design through DRX is possible only if the relationship between processing parameters and the grain size is determined. This can be achieved by empirical fit of experimental data[6] or by physical modeling.[4,5] Modeling has the advantage to provide a better understanding of the mechanisms at stake, and leads to a better prediction of microstructure evolution in the case of untested processing conditions. For instance, recent work on pure copper enabled the prediction of the resulting mean grain size[7] and the grain size distribution[4] after hot deformation. DRX modeling usually includes three main elements: a plasticity law determined from experimental stress–strain curves, a nucleation criterion, and a grain growth equation. While determining the constitutive equation of plasticity that can be achieved by the Kocks–Mecking model,[8] the determination of grain boundary motion and nucleation remains a major issue in a general case. In the case of pure copper, nucleation is determined by
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