Self-Consistent Model for Planar Ferrite Growth in Fe-C-X Alloys
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THE influence of alloying elements on the kinetics of ferrite growth in steel has been the subject of investigation and debate for over a century. The roots of the problem lie almost entirely in the differences in mobilities of the substitutional and interstitial solutes (e.g., Mn and C) in steel. In the binary Fe-C system, the relaxation times of ferrite growth are necessarily related to the diffusion of carbon, either in austenite or in ferrite or in the interface joining them. Thus, for example, in the isothermal growth of planar grain boundary ferrite from supersaturated austenite, one finds that a local equilibrium model of the kind initially proposed by Zener[1] gives an adequate first order representation of the thickening kinetics. In contrast, it has been recognized for more than half a century that the simple extension of the Zener model to the thickening of grain boundary ferrite allotriomorphs in ternary and higher order iron alloys is not so straightforward. The instinctive choice of tie-line which includes the bulk composition does not yield a satisfactory solution, as the two solute mass balances cannot be simultaneously satisfied. The selection of the appropriate interfacial tieline then becomes a part of the solution of the growth problem, as pointed out for example by Kirkaldy[2] and Hillert,[3] who examined solutions of the three component diffusion equations under the assumption of full interfacial local equilibrium. Indeed, the interfacial tie-line that does satisfy both solute mass balances is one that permits negligible partitioning of the substitutional solute (X) and H.S. ZUROB, Associate Professor, D. PANAHI, Graduate Student, and G.R. PURDY, Professor, are with the Department of Materials Science and Engineering, McMaster University, Hamilton, ON, Canada. Contact e-mail: [email protected] C.R. HUTCHINSON, Associate Professor, is with the Department of Materials Engineering, Monash University, Clayton, 3800 VIC, Australia. Y. BRECHET, Professor, is with the SIMAP, Institute National Polytechnique de Grenoble, St Martin D’He`res 38402, Grenoble, France. Manuscript submitted June 30, 2012. Article published online October 24, 2012 3456—VOLUME 44A, AUGUST 2013
which therefore forms unpartitioned ferrite of the bulk composition, as shown in Figure 1. On this reasoning, one expects that ferrite growth will be fast and limited only by the diffusion of carbon. The same argument holds for all initial austenite compositions within the ‘‘Local equilibrium, negligible-partition’’ (LE-NP) boundary. A similar approach to the selection of the local equilibrium interfacial tie-line for bulk austenite compositions above the LE-NP boundary dictates that the transformation product should be accompanied by the long-range redistribution of the substitutional solute, X; the rates of growth would then be dictated by the rate of diffusion of this component and would then be much slower than those within the envelope. This argument has been expressed in a different language by Hillert,[3] Purdy et al.,[4] and Coa
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