Growth Kinetics of Proeutectoid Ferrite in Fe-0.1C-1.5Mn-1Si Quaternary and Fe-0.1C-1.5Mn-1Si-0.2Al Quinary Alloys
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INTRODUCTION
DRIVEN by the scientific and industrial importance of ferrite transformations, its diffusional growth in steels has been the focus of considerable research during the past several decades. Of the variety of morphologies the ferrite can adopt when forming from austenite, the grain boundary allotriomorph is the most representative microstructure. In theoretical treatments of allotriomorphic ferrite growth in the binary Fe-C system, it is often assumed that the free energy dissipated by the finite mobility of interface is negligible and the problem is treated as a diffusion-controlled process. Consequently, predictions of ferrite growth kinetics reduce to solving the flux balance equation for carbon at the austenite– ferrite interface subjected to an appropriate interfacial condition. A local equilibrium (LE) interfacial condition proposed first by Zener[1] is usually chosen so that no chemical potential gradients exist for C or Fe across the migrating interface. Thus, for an isothermal transformation in Fe-C alloy, the compositions at the interface are given by the ends of a tie-line that pass through the bulk alloy composition in the equilibrium phase diagram. Some experimental results of the ferrite growth kinetics in the binary Fe-C system indicate that these assumptions are indeed reasonable.[2,3] The situation immediately becomes complicated when a substitutional alloying element (e.g., X = Mn, Si, Ni, Al, Cr, etc.) is added to the Fe-C system. Because of the large differences in the diffusivities of C and X in G.H. ZHANG, Postdoctoral Fellow, and D.W. SUH, Assistant Professor, are with the Graduate Institute of Ferrous Technology, Pohang University of Science and Technology, Pohang 790-784, Republic of Korea. Contact e-mail: [email protected] R. WEI, Graduate Student, and M. ENOMOTO, Professor, are with the Department of Materials Science and Engineering, Ibaraki University, Hitachi 316-8511, Japan. Manuscript submitted July 13, 2011. Article published online November 18, 2011 METALLURGICAL AND MATERIALS TRANSACTIONS A
austenite at the temperatures of interest, it is not possible to simultaneously satisfy the flux balance equations for both C and X with interface compositions given by the tie-line passing through the bulk alloy composition in c + a two-phase region. To satisfy the flux balance equations simultaneously and yet maintain the local equilibrium at the interface, another tie-line that deviates from the bulk composition must be considered. This leads to two cases.[4–9] In the first case, the tie-line is chosen so that the carbon activity gradient in austenite near the c/a interface is almost to zero as illustrated in Figure 1(a); then the driving force for carbon diffusion in austenite will be greatly reduced and the slow diffusion of alloying element can keep pace with carbon diffusion. Because the concentration of alloying element in ferrite differs significantly from that in the bulk, it will be partitioned between austenite and ferrite. This growth mode is, therefore, called partitioning local eq
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