*2.3. Calculation of the Phase Transformation Start for an Arbitrary Cooling Path*

Once the ideal isothermal transformation time has been constructed, it can be used to calculate the transformation start time for an arbitrary cooling path using Scheil's additivity principle. The transformation is assumed to start when the sum of the fractional transformation times equals one, as shown in Equation (12) [18–20,30].

$$\sum\_{i=1}^{n} \frac{t\_i}{\tau\_i(T)} = 1\tag{12}$$

where *ti* is the time spent at temperature *T*, and *τi*(*T*) is the time required to produce a measurable transformation at that temperature.

To check that the computational method gave the correct result, the CCT diagram, which was obtained using the regression Equations (1) and (2), was recalculated using the obtained ideal TTT diagram and Scheil's additivity principle, as shown in Equation (12). We also compared the results to the experimental data presented in reference [22] for steel "TH16". The comparison is shown in Figures 3 and 4. The agreement between the original CCT diagram obtained by the regression formulas and the recalculated CCT diagram is excellent. Also, the comparison with the experimental data [22] shows a good agreement, although the difference between the experimental result and the CCT curve calculated with the regression equations is slightly higher for the temperatures near the CCT "nose" for this steel, as shown in the logarithmic plot in the inset of Figure 4. In any case, at temperatures above 993 K (720 ◦C), the experimental values also agree well with the computed values.

**Figure 3.** Ideal (or true) isothermal transformation diagram calculated with Equation (8), the original CCT diagram calculated with Equation (3), and the CCT diagram which was recalculated by applying the Scheil's additivity principle in Equation (12).

**Figure 4.** To validate the model, the CCT diagram was recalculated from the ideal (or true) TTT curve using Scheil's additivity rule. The result shows excellent agreement between the original CCT curve calculated from Equations (1) and (2) and the recalculated CCT curve. The results were also compared to the experimental data given in [22]. Note that the original CCT curve and the recalculated curve almost overlap.
