2.2.3. High Temperature Extrapolation of the TTT Start Time

For ferrite formation, we used the following high temperature extrapolation of the calculated ideal TTT start time. The function describing the isothermal transformation start time can be expressed by Equation (9) [20]

$$
\tau = K \exp(\frac{\mathcal{Q}}{RT}) \Delta T^{-m} \tag{9}
$$

where *K* and *m* are constants; *R* is the ideal gas constant; *T* is the absolute temperature; Δ*T* = *A*e3 − *T* is the amount of undercooling; and *Q* is the activation energy to facilitate carbon mobility in the austenite–ferrite transformation.

Taking the logarithm of both sides of the Equation (9) and differentiating yields,

$$\frac{d\ln\tau}{dT} = -\frac{Q}{RT^2} + \frac{m}{A\text{e3} - T} \tag{10}$$

Since near the equilibrium, *<sup>A</sup>*e3, the temperature is *<sup>m</sup> <sup>A</sup>*e3−*<sup>T</sup>* >> *<sup>Q</sup> RT*<sup>2</sup> , we approximate *<sup>d</sup>*ln*<sup>τ</sup> dT* <sup>≈</sup> *<sup>m</sup> <sup>A</sup>*e3−*<sup>T</sup>* . This allows us to use Equation (11) for high temperature extrapolation of the transformation start time:

$$
\Delta \ln \tau \approx \ln B - m \ln \left( A \mathbf{e3} - T \right) \Leftrightarrow \tau \approx B \Delta T^{-m} \tag{11}
$$

where the constants *B* and *m* are determined from the conditions under which the functions ln*τ* and *d*ln*τ*/*dT* are continuous. The ideal TTT curve calculated from the CCT diagram as well as the high temperature extrapolation are shown in Figure 2.

**Figure 2.** The high temperature extrapolation of the ideal temperature–time transformation (TTT curve), calculated using Equation (11), shown together with the ideal TTT start diagram calculated directly from the experimentally fitted CCT curve using Equation (8).
