2.2.2. Construction of the Ideal TTT Diagram from (*t*s,cct(*T*s,cct), *T*s,cct) type CCT Diagram

The numerical value of the isothermal start time can also be obtained from the (*t*s,cct(*T*s,cct), *T*s,cct) type constant cooling rate CCT diagram, where *t*s,cct and *T*s,cct are the time and temperature coordinates of the CCT curve and *T*start is the cooling start temperature temperature, by using the difference approximation described in Section 2.2.1. Since the constant cooling rate is ˙ *θ*<sup>c</sup> = (*T*start − *T*s,cct)/*t*s,cct(*T*s,cct), Equation (8) describes the ideal isothermal start time as a function of temperature.

$$\begin{split} \tau \left( T\_{\text{s,cct}} \right) &\approx -\frac{\Delta T\_{\text{s,cct}}}{\Delta \theta\_{\text{c}} \left( T\_{\text{s,cct}} \right)} \\ &= \frac{h}{\frac{T\_{\text{start}} - \left( T\_{\text{s,cct}} - h/2 \right)}{t\_{\text{s,cct}} \left( T\_{\text{s,cct}} - h/2 \right)} - \frac{T\_{\text{start}} - \left( T\_{\text{s,cct}} + h/2 \right)}{t\_{\text{s,cct}} \left( T\_{\text{s,cct}} + h/2 \right)} \end{split} \tag{8}$$

where *t*s,cct(*T*s,cct ± *h*/2) represent the function values of *t*s,cct(*T*) at *T* = *T*s,cct ± *h*/2. Equation (8) can be used to calculate the ideal isothermal transformation start, *τ*(*T*), when the constant cooling CCT curve (*t*s,cct(*T*s,cct), *T*s,cct) is known.
