Journal of Materials Science

, Volume 43, Issue 4, pp 1334–1339 | Cite as

An alternative to the JMAK equation for a better description of phase transformation kinetics

  • Jan KohoutEmail author


The kinetics of phase transformations is usually described by the Johnson–Mehl–Avrami–Kolmogorov (JMAK) equation. The article shows that this equation cannot give a sufficiently general description of austenitization kinetics of ferritic nodular cast iron. Therefore, another kinetics equation is proposed which catches the main circumstances and substance of austenitization more accurately than the JMAK equation does. It shows that the crucial phenomena in the transformation are not only the processes of the creation and growth of new austenite grains but also the change in specific volume and the chemical liquation of alloying additives, which retard the subsequent conversion. The proposed equation together with the Arrhenius equation allows describing simultaneously the temporal and temperature dependence of austenitization conversion including the partial transformation at insufficiently high overheating of transformed iron. It is verified by successful regression of experimental data, whose results allow drawing predictive curves for temperatures from the experimental temperature region or from its near vicinity, for which the conversion was not determined.


Ferrite Austenite Specific Volume Arrhenius Equation Nodular Cast Iron 



Financial support of the Ministry of Defence of the Czech Republic within research project MO0 FVT0000404 is gratefully acknowledged. Moreover, the author is grateful to Prof. Herfurth (see [16]), whose original experimental results were used in author’s calculations.


  1. 1.
    Keough JR (1995) Foundry Manage Technol 123(11):27Google Scholar
  2. 2.
    Nath SK, Ray S, Mathur VNS, Kapoor ML (1994) ISIJ Int 34:191CrossRefGoogle Scholar
  3. 3.
    Zhang W, Elmer JW, Debroy T (2002) Mater Sci Eng A 333:320CrossRefGoogle Scholar
  4. 4.
    Elmer JW, Palmer TA, Zhang W, Wood B, Debroy T (2003) Acta Mater 51:3333CrossRefGoogle Scholar
  5. 5.
    Elmer JW, Palmer TA, Babu SS, Zhang W, Debroy T (2004) Weld J 83:224SGoogle Scholar
  6. 6.
    Kumar A, Mishra S, Elmer JW, Debroy T (2005) Metal Mater Trans A 36:15CrossRefGoogle Scholar
  7. 7.
    Johnson WA, Mehl RF (1939) Trans AIME 135:416Google Scholar
  8. 8.
    Avrami M (1939) J Chem Phys 7:1103CrossRefGoogle Scholar
  9. 9.
    Kolmogorov AN (1937) Izv Akad Nauk SSSR, Ser Matem 3:355Google Scholar
  10. 10.
    Todinov MT (2000) Acta Mater 48:4217CrossRefGoogle Scholar
  11. 11.
    Levine LE, Narayan KL, Kelton KF (1997) J Mater Res 12:124CrossRefGoogle Scholar
  12. 12.
    Starink MJ, Zahra AM (1998) Philos Mag A 77:187CrossRefGoogle Scholar
  13. 13.
    Schmidt U, Schmidt B (2000) Mater Sci Forum 331–333:889CrossRefGoogle Scholar
  14. 14.
    Starink MJ (2001) J Mater Sci 36:4433CrossRefGoogle Scholar
  15. 15.
    Starink MJ (2004) Int Mater Rev 49:191CrossRefGoogle Scholar
  16. 16.
    Herfurth K, Giesserei-Praxis (2003) 99Google Scholar
  17. 17.
    Kohout J (1999) J Mater Sci 34:843CrossRefGoogle Scholar
  18. 18.
    Kohout J (2004) J Phys IV 120:191Google Scholar
  19. 19.
    Kohout J (2007) Mater Sci Eng A 462:159CrossRefGoogle Scholar
  20. 20.
    Dorazil E (1991) High strength austempered ductile cast iron. Horwood, LondonGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Department of Mathematics and Physics, Military Technology FacultyUniversity of DefenceBrnoCzech Republic

Personalised recommendations