Phase Field Modeling of Cyclic Austenite-Ferrite Transformations in Fe-C-Mn Alloys
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E transformations in steels have been studied for more than a century due to their practical importance in steel design and production, and various aspects of these phase transformations were discussed thoroughly in the literature.[1–3] Recently, the specific topic of alloying element effects on migrating interfaces (ALEMI) in steels has attracted significant attention from the phase transformation community, and much effort has been made to improve the understanding of this topic.[4,5] Two classical models, i.e., paraequilibrium (PE)[6,7] and local equilibrium (LE),[8–10] have been proposed to describe the interface condition during the austenite-ferrite transformation in Fe-C-X alloys, where X is a substitutional alloying element, e.g., Mn, Cr, Ni, or Mo. PE is a constrained equilibrium where it is assumed that the chemical potential of C is constant across the interface while there is no redistribution of X during the phase transformation in Fe-C-X alloys. Therefore, the PE model predicts that the transformation is purely controlled by carbon diffusion. On the other hand, the LE model adopts full local equilibrium, in which the chemical potential of both C and X is HAO CHEN, Assistant professor, is with the Key Laboratory for Advanced Materials of Ministry of Education, School of Materials Science and Engineering, Tsinghua University, Beijing, China. Contact e-mail: [email protected] BENQIANG ZHU, Ph.D. Student, and MATTHIAS MILITZER, Professor, are with the Centre for Metallurgical Process Engineering, The University of British Columbia, Vancouver, V6T 1Z4, Canada. Manuscript submitted December 11, 2015. METALLURGICAL AND MATERIALS TRANSACTIONS A
assumed to be constant across the interface. Based on this assumption, the transformation rate is determined either by C diffusion or X diffusion. Due to the large difference in diffusivities of C and X, there are two different partitioning modes of X during the phase transformations. In the first mode, the kinetics of interface migration is controlled by carbon diffusion, and the concentration of X in the growing phase is the same as that in the parent phase. However, due to LE conditions, a ‘‘spike’’ of X is moving ahead of the interface. This mode has been termed ‘‘local equilibrium with negligible partitioning’’ (LE-NP). In the second mode, the carbon concentration gradient in the parent phase is almost negligible while that of X is large. Hence, the transformation rate is slow and controlled by diffusion of X. This mode has been termed ‘‘local equilibrium with partitioning’’ (LE-P). In order to explore the transition among PE, LE-NP, and LE-P, several phenomenological models have been developed[11–16] where also the effect of X segregation at the interface on transformation kinetics is taken into account using Cahn’s solute drag[17] or Hillert’s Gibbs energy dissipation theory,[18] respectively. The solute drag theory suggests that the segregation of X leads to a drag pressure on the migrating interface, and the magnitude of the drag pressure depends on the interface
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