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Analysis of soft impingement in nonisothermal precipitation

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Abstract

The effects of soft impingement on precipitation are considered. A physically realistic analytical treatment of soft impingement has been developed for solid-state precipitation in a nonisothermal heating/cooling process following the basic assumptions (i.e., a two-stage transformation including site saturation of nucleation, isotropic growth and linear approximation for a concentration gradient in front of the precipitate/matrix interface). Furthermore, both one- and three-dimensional precipitations have been described using a compact expression which is analogous to Zener’s model but with a temperature-dependent growth coefficient. A detailed description for the model parameters has been given for the model application. Good agreement with published experimental data, for example, the decomposition of austenite in a 0.038–0.30wt%Mn plain carbon steel, has been achieved.

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References

  1. A. Deschamps, F. Bley, L. Lae, M. Dumont, and F. Perrard: Characterisation and modelling of non-isothermal precipitation in metallic systems. Adv. Eng. Mater. 8, 1236 (2006).

    Article  CAS  Google Scholar 

  2. J.W. Christian: The Theory of Transformations in Melts and Alloys (Pergamon Press, Oxford, UK, 2002), p. 486.

    Google Scholar 

  3. M.J. Starink and A.M. Zahra: Kinetics of isothermal and non-isothermal precipitation in an Al-6at.%Si alloy. Philos. Mag. 77.187 (1998).

    Article  Google Scholar 

  4. A.T.W. Kempen, F. Sommer, and E.J. Mittemeijer: Determination and interpretation of isothermal and non-isothermal transformation kinetics; The effective activation energies in terms of nucleation and growth. J. Mater. Sci. 37, 1321 (2002).

    Article  CAS  Google Scholar 

  5. I.N. Khan, M.J. Starink, and J.L. Yan: Determination of the precipitation kinetics of Ni3Al in the Ni–Al system using differential scanning calorimetry. Mater. Sci. Em.A, 472, 66 (2008).

    Article  Google Scholar 

  6. F. Liu, F. Sommer, and E.J. Mittemeijer: Determination of nucleation and growth mechanisms of the crystallization of amorphous alloys; Application to calorimetric data. Acta Mater. 52, 3207 (2004).

    Article  CAS  Google Scholar 

  7. J. Vazquez and P. Villares: Generalization of the Avrami equation for the analysis of non-isothermal transformation kinetics. Application to the crystallization of the Cu0.20As0.30Se0.50 alloy. J. Phys. Chem. Solids 61, 493 (2000).

    Article  CAS  Google Scholar 

  8. G. Ruitenberg, E. Woldt, and A.K. Petford-Long: Comparing the Johnson–Mehl–Avrami–Kolmogorov equations for isothermal and linear heating conditions. Thermochim. Acta 378, 97 (2001).

    Article  CAS  Google Scholar 

  9. F. Liu, F. Sommer, and E.J. Mittemeijer: Parameter determination of an analytical model for phase transformation kinetics: Application to crystallization of amorphous Mg-Ni alloys. J. Mater. Res. 19(9), 2586 (2004).

    Article  CAS  Google Scholar 

  10. J.W. Cahn: Transformation kinetics during continuous cooling. Acta Mater. 4, 572 (1956).

    Article  CAS  Google Scholar 

  11. H. Sieurin and R. Sandström: Sigma phase precipitation in duplex stainless steel 2205. Mater. Sci. Eng.A, 444, 271 (2007).

    Article  Google Scholar 

  12. Y.H. Wen, J.P. Simmons, C. Shen, C. Woodward, and Y. Wang: Phase-field modeling of bimodal particle size distributions during continuous cooling. Acta Mater. 51, 1123 (2003).

    Article  CAS  Google Scholar 

  13. R. Wagner and R. Kampmann: Materials Science and Technology: A Comprehensive Treatment (VCH, New York, 1991).

    Google Scholar 

  14. F. Liu, F. Sommer, C. Bos, and E.J. Mittemeijer: Analysis of solid-state phase transformation kinetics; Models and recipes. Int. Mater. Rev. 52, 193 (2007).

    Article  CAS  Google Scholar 

  15. F. Liu, F. Sommer, and E.J. Mittemeijer: An analytical model for isothermal and isochronal phase transformation kinetics. J. Mater. Sci. 39, 1621 (2004).

    Article  CAS  Google Scholar 

  16. M. Avrami: Kinetics of phase change. I: General theory. J. Chem. Phys. 7, 1103 (1939).

    Article  CAS  Google Scholar 

  17. M. Avrami: Kinetics of phase change. II: Transformation-time relations for random distribution of nuclei. J. Chem. Phys. 8, 212 (1940).

    Article  CAS  Google Scholar 

  18. M. Avrami: Kinetics of phase change. III: Cranulation, phase change, and microstructure. J. Chem. Phys. 9, 177 (1941).

    Article  CAS  Google Scholar 

  19. G. Yu, Y.K.L. Lai, and W. Zhang: Kinetics of transformation with nucleation and growth mechanism: Diffusion-controlled reactions. J. Appl. Phys. 82, 4270 (1997).

    Article  CAS  Google Scholar 

  20. J. Crank: The Mathematics of Diffusion, 2nd ed. (Clarendon Press, Oxford, UK, 1975).

    Google Scholar 

  21. C. Zener: Theory of growth of spherical precipitates from solid solution. J. Appl. Phys. 20, 950 (1949).

    Article  CAS  Google Scholar 

  22. E.A. Brandes and G.B. Brook: Smithells Metals Reference Book (Butterworths, London, 1992).

    Google Scholar 

  23. P. Shewmon: Diffusion in Solids, 2nd ed. (The Minerals, Metals & Materials Society, Warrendale, PA, 1989).

    Google Scholar 

  24. B.A. Howard, D. Fainstein, and R. Gerald: Diffusion-limited phase transformation: A comparison and critical evaluation of the mathematical approximations. J. Appl. Phys. 41, 4404 (1970).

    Article  Google Scholar 

  25. K. Fan, F. Liu, G.C. Yang, and Y.H. Zhou: Modeling of isothermal solid-state precipitation using an analytical treatment of soft impingement. Acta Mater. 56, 4309 (2008).

    Article  CAS  Google Scholar 

  26. M. Militzer, R. Pandi, and E.B. Hawbolt: Ferrite nucleation and growth during continuous cooling. Metall. Mater. Trans. A 27, 1547 (1996).

    Article  Google Scholar 

  27. García de C. Andres, Capdevila C.F.G. Caballero, and H.K.D. BhadeshiaH.: Modeling of isothermal ferrite formation using an analytical treatment of soft impingement in 0.37C-0.45Mn-0.11V microalloyed steel. Scr. Mater. 39, 853 (1998).

    Article  Google Scholar 

  28. G.P. Krielaart and Van der S. Zwaag: Kinetics of γ-α phase transformations in Fe-Mn alloys containing low manganese. Mater. Sci. Technol. 14, 10 (1998).

    Article  CAS  Google Scholar 

  29. R.A. Vandermeer: Modeling diffusional growth during austenite decomposition to ferrite in polycrystalline Fe-C alloys. Acta Mater. 38, 2461 (1990).

    Article  CAS  Google Scholar 

  30. A.T.W. Kempen, F. Sommer, and E.J. Mittemeijer: The kinetics of the austenite-ferrite phase transformation of Fe-Mn: Differential thermal analysis during cooling. Acta Mater. 50, 3207 (2002).

    Google Scholar 

  31. E.J. Mittemeijer: Analysis of the kinetics of phase transformations. J. Mater. Sci. 27, 3977 (1992).

    Article  CAS  Google Scholar 

  32. M. Abramowitz and I.A. Stegun: Handbook of Mathematical Functions (Dover Publication Inc., New York, 1965).

    Google Scholar 

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Fan, K., Liu, F., Wei, Y. et al. Analysis of soft impingement in nonisothermal precipitation. Journal of Materials Research 24, 3664–3673 (2009). https://doi.org/10.1557/jmr.2009.0434

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