Dependence of carbon concentration in austenite on the temperature during newly developed Quench and Partitioning (Q&P) process has been mentioned by several authors.
x(austenite) = x(ferrite) *exp((76,789 -43.8T-(16,905 - 120.4T)x(austenite))/RT) where x(austenite), x(ferrite) are mole fraction of carbon in austenite and ferrite, respectively and T is the absolute temperature. Is this relation valid in the intercritical range of annealing also? If not, what is the what is the empirical relation between x(austenite) and T in the intercritical range?
In the intercritical range ferrite and austenite are in equilibrium. The volume fraction of the phases and their composition depend on the intercritical annealing temperature and the composition of the steel. One should be able to calculate the carbon content in austenite, which depends on the exact compositiion of the steel (Mn, Si, etc.). A software program, like Thermo-Calc, is suitable for this calculation. However, if equilibrium is not established in the intercritical range, for example if the holding time is too short, then the carbon content should be calculated by a diffusion software, like DICTRA. Since the carbon content of austenite depends on the composition of the steel, any empirical relationship in the literature, like the one you cited in the question, has limited validity only for the specific composition, on which it was based.
Also it also need consider the time effect , time should be long enough to allow to be close to equilibrium. If the holding time is too short, then the carbon content is more sensitivable to many process forctor and there are more variables in no stable state
You should actually consider the partitioning of heavier elements such as Mn in carbon steels. According to DICTRA, the partitioning of carbon occurs very fast in seconds. In your case, you may assume that the mole fraction of carbon in austenite or ferrite should be at equilibrium.
When you hold steel in intercritical range, temperature just determines fraction amount of ferrite and austenite. Since solubility of carbon in ferrite is very low, most of carbon is used to enrich austenite. When other elements are not considered you can calculate enrichment in plain Fe-C with rule of mixtures. If you consider other elements then your formula changes a bit.
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