Self-Consistent Model for Planar Ferrite Growth in Fe-C-X Alloys

Abstract

A self-consistent model for non-partitioning planar ferrite growth from alloyed austenite is presented. The model captures the evolution with time of interfacial contact conditions for substitutional and interstitial solutes. Substitutional element solute drag is evaluated in terms of the dissipation of free energy within the interface, and an estimate is provided for the rate of buildup of the alloying element “spike” in austenite. The transport of the alloying elements within the interface region is modeled using a discrete-jump model, while the bulk diffusion of C is treated using a standard continuum treatment. The model is validated against ferrite precipitation and decarburization kinetics in the Fe-Ni-C, Fe-Mn-C, and Fe-Mo-C systems.

Appendix

The phase equilibria between ferrite and austenite in the Fe-Mn system were experimentally investigated by Triano and McGuire,[42] Hillert,[43] and Srivastava and Kirkaldy.[44] The last authors reported the 95 pct confidence interval of their measurements as ±3 pct. The experimental data are summarized in Figure 12 along with the thermodynamic model due to Huang,[45] which is the basis of the TCFE2 database of ThermoCalc. It is clear from the comparison that the pioneering treatment of Huang[45] systematically underestimates the solubility of Mn in ferrite at high temperatures. The discrepancy is, arguably, insignificant for most applications. In the present case, however, the difference between the experiments and model predictions at 1095 K (822 °C) is sufficient to change the interpretation of the decarburization data at 1098 K (825 °C); PE is predicted if the description of Reference 45 is used, while LENP would be predicted if one modified the description to fit the experimental data of Srivastava and Kirkaldy[44] at 1095 K (822 °C). We have, therefore, modified the description of Reference 45 in order to produce a better fit of the experimental data as shown by the dashed curves in Figure 12. The modifications were limited to one parameter, namely

$$ L\left( {{\text{bcc, Fe,Mn:Va}};0} \right) = 4007.8-4.44 \, T\left( {\text{k}} \right)\,{\text{J/mol}} $$

Fig. 12

A portion of the Fe-Mn-C phase diagram. Experimental data point along with the calculated phase boundaries using thermodynamic models by Huang,[45] Srivastava and Kirkaldy[44] and the modified version of Huang’s description

This description was used for all calculations on the Fe-Mn-C system in this contribution. A more thorough examination of the thermodynamics, including new experimental data between 1095 K and 1173 K (822 °C and 900 °C), seems necessary in order to reach definitive conclusions as to the operating interfacial conditions during decarburization at high temperatures.