Modeling C-Curves for the Growth Rate of Widmanstätten and Bainitic Ferrite in Fe-C Alloys
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When Zener formulated his maximum growth rate criterion for predicting the coarseness of various metallographic objects, he simplified the growth rate equations and predicted that the optimum coarseness should be twice the critical value for which all the driving force would be absorbed by interfacial energy. It is now emphasized that a composition dependence of the diffusion coefficient has a considerable influence and can result in a ratio much larger than two. Various approximations have now been removed from the growth rate equation. When applied to acicular ferrite in the Fe-C system, a C-curve for the growth rate is obtained that resembles the unusually wide C-curve obtained experimentally when information on Widmanstätten ferrite and bainite is combined. It is not necessary to explain that shape as a combination of separate curves for Widmanstätten ferrite and bainite. The main reason for the wide C-curve is the direct effect of the composition dependence of the diffusivity of carbon in austenite.
KeywordsFerrite Austenite Bainite Interfacial Energy Effective Diffusion Coefficient
The authors wish to acknowledge the financial support rendered by VINNOVA, the Swedish Governmental Agency for Innovation Systems, Swedish industry and KTH Royal Institute of technology. The work has been performed within the VINN Excellence Centre Hero-m.
- 1.M. Hillert: Report, Swedish Inst. Metal Res., 1960: Thermodynamics and Phase Transformations, The Selected Works of Mats Hillert, Introduction to “The Growth of Ferrite, Bainite and Martensite, J. Ågren, Y. Bréchet, C. Hutchinson, J. Philibert, and G Purdy, eds., EPD Sci., Les Ulis Cedex, 2006, pp. 111–158Google Scholar
- 2.C. Wells, W. Batz and R. F. Mehl, Trans. AIME, 1950, vol. 188, pp. 553–60.Google Scholar
- 3.C. Zener, Trans. AIME, 1946, vol. 167, pp. 550–95.Google Scholar
- 4.M. Hillert, Jernkont, Ann., 1957, vol. 141, pp. 757–89.Google Scholar
- 5.L. Kaufman, S. V. Radcliffe and M. Cohen: Decomposition of Austenite by Diffusional Processes, Eds. pp. 313–52, Interscience Publ., New York, 1962Google Scholar
- 8.G. P. Ivantsov, Dokl Nauk SSSR, 1947, vol. 58, pp. 567–69.Google Scholar
- 19.H.I. Aaronson: Decomposition of Austenite by Diffusional Processes, Eds. pp. 387-545, Interscience Publ., New York, 1962Google Scholar
- 20.R.D. Townsend and J.S. Kirkaldy, Trans. ASM, 1968, vol. 61, pp. 605–19.Google Scholar
- 21.M.J. Hawkins and J. Barford, J. Iron Steel Inst., 1972, vol. 210, pp. 97–105.Google Scholar
- 22.G.R. Speich and M. Cohen, Trans. Metall. Soc. AIME, 1960, vol. 218, pp. 1050–59.Google Scholar