Equilibrium Phase Fractions
In several of the phase transformation models in COMSOL Multiphysics, a model parameter is the equilibrium phase fraction of the destination (forming) phase, . When a hypoeutectoid steel is cooled from an austenitic state, ferrite begins to form when the temperature falls below Ae3.
Figure 3-6: A schematic Fe–C diagram and the points involved in calculating the equilibrium phase fraction of ferrite.
In an Fe–C diagram (Figure 3-6), the equilibrium phase fraction of ferrite in this austenite–ferrite two-phase region can be extracted using a simple lever rule as
Note that in using the lever rule, the ferrite region above the eutectoid temperature Ae1 is taken to be a line from to the ferrite carbon solubility, , at Ae1.
The formation of free ferrite below the eutectoid temperature Ae1 during quenching can be included. COMSOL Multiphysics provides two models of the equilibrium phase fraction of ferrite below the eutectoid temperature, see Hippchen and others (Ref. 18) for a description. In one model, the equilibrium phase fraction of ferrite is taken to be constant below Ae1, and equal to the equilibrium phase fraction at Ae1, see Figure 3-7.
Figure 3-7: A schematic Fe–C diagram showing how the lever rule is used above and below eutectoid temperature. On the left, a constant equilibrium phase fraction of ferrite below the eutectoid. On the right, the Hultgren extrapolation is used.
In the other model, the equilibrium phase fraction of ferrite is computed by considering a modified Fe–C diagram. The Acm line in the Fe–C diagram is extrapolated according to Hultgren (Ref. 19). The lever rule is employed using this extrapolated line to compute the equilibrium phase fraction, see Figure 3-7. The equilibrium phase fraction of ferrite below the eutectoid temperature in the two models can be expressed as
Note that in using the lever rule, the ferrite region below the eutectoid temperature Ae1 is taken to be a line from to the ferrite carbon solubility, , at Ae1.
To model the formation of pearlite and bainite below the eutectoid temperature, the corresponding equilibrium phase fractions are taken to be