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Keywords:

  • finite difference;
  • Grange–Kiefer approach;
  • hardenability;
  • mathematical modeling;
  • steel

In this research work an independent mathematical modeling approach has been adopted for determination of the hardenability of steels. In this model, at first, cooling curves were generated by solving transient heat transfer equation through discretization with pure explicit finite difference scheme coupled with MATLAB based programming considering effective constant thermo-physical properties of 1080 steel. Thereafter, Grange–Kiefer approach was extended for determination of 50% transformation nose of CCT diagram. The cooling curves were solved against 50% transformation nose of CCT diagram in order to predict hardening behavior of 1080 steel in terms of hardenability parameters (Grossmann critical diameter, DC; and ideal critical diameter, DI) and the variation of the unhardened core diameter (Du) to diameter of steel bar (D) ratio with diameter of the steel bar (D). The experiments were also performed to ascertain actual DC value of 1080 steel for still water quenching. The DC value obtained by the developed model was found to match the experimental DC value with only 8% deviation. Therefore, the model developed in the present work can be used for direct determination of DI, DC, and Du without resorting to any rigorous experimentation.