*2.1. Calculation of CCT Start Time for Different Steel Compositions*

An estimate for the phase transformation start point in CCT diagrams for different steel compositions can be calculated with Equations (1) and (2) which were presented in reference [21]. As described in the original works, the equations were obtained by linear regression analyses on the effect of alloying elements on the CCT diagrams, considering the following elements: C, Si, Mn, Cr, Cu, Ni, Mo, V, Ti, B, Nb. The experimental results were obtained with 34 different steel compositions by cooling specimens after thermomechanical treatments relevant to industrial hot rolling and cooling processes.

$$T\_{\rm s,ext}(\mathbf{K}) = \underbrace{273.15 + B\_0 + \sum\_{i} B\_i c\_i + B\_1 \text{arcsinh}(t\_{85} - t\_{85, \mathbf{k}})}\_{T\_{\rm N}} \tag{1}$$

$$\log\_{10}(t\_{85,k}) = A\_0 + \sum\_{i} A\_i c\_i \tag{2}$$

where *T*s,cct(*K*) is the start temperature (in degrees Kelvin) for the phase transformation occurring with a constant cooling rate; *ci* are the concentrations of different elements in the steel composition in weight %; *Ai* and *Bi* are the constants obtained from the regression analysis; *t*<sup>85</sup> is the time elapsed while cooling the specimen from 800 ◦C to 500 ◦C; and *t*85,k corresponds to the critical cooling rate, which is the slowest cooling rate that does not produce a measurable phase transformation. *T*<sup>N</sup> is used to denote 273.15 + *B*<sup>0</sup> + ∑*<sup>i</sup> Bici*. Prior to cooling, the steel sample was subjected to a mechanical deformation schedule consisting of either (a) two 20% strain deformations above the recrystallization limit temperature, or (b) the same as (a) but with an additional 30% deformation below the non-recrystallization temperature. The different deformation schedules (a and b) yielded different CCT start curves and regression constants. The regression constants for ferrite transformation for both deformation schedules were given in reference [21] and are reproduced in Table 1.


**Table 1.** The regression constants given in [21], which were used in Equations (1) and (2). The constants are given for two different deformation schedules, (a) and (b) (see text).

The composition limits (in wt %) for the experimental data used in the regression analysis are shown in Table 2 [21,27].


**Table 2.** The composition limits (in wt %) of the model.

A comparison with the experimental results showed that the functional form of Equation (1) represents the transformation to ferrite near the critical cooling rate (or *t*85,k) well. For some steels whose CCT diagrams indicate a transformation start near the equlibrium *A*e3 temperature, the functional form gives a slightly higher value for the transformation temperature near the equlibrium temperature than that observed experimentally. When the transformation temperature described by Equation (1) of the steel is well below the equilibrium temperature, the functional form represents the transformation temperatures for the whole experimental range, *t*<sup>85</sup> ∈ *t*85,k...1000 s, well.

At a constant cooling rate, ˙ *θ* = (300 K)/*t*85, the temperature of the specimen can be expressed as *<sup>T</sup>* <sup>=</sup> *<sup>A</sup>*e3 <sup>−</sup> ˙ *θt*, where *A*e3 is the equilibrium ferrite formation temperature, and *t* is the time spent below the *A*e3 temperature. By applying Equations (1) and (2), the time required for phase transformation to start during cooling, *t*s,cct is given by Equation (3):

$$t\_{\rm s,cct} = \frac{A\rm e3 - T\_{\rm s,cct}}{300} t\_{\rm 85} = \frac{A\rm e3 - T\_{\rm s,cct}}{300} \left[ \sinh\left(\frac{T\_{\rm s,cct} - T\_{\rm N}}{B\_{\rm t}}\right) + t\_{\rm 85,k} \right]. \tag{3}$$

Equation (3) is valid for the temperatures where Equations (1) and (2) represent the experimental results well (see discussion above) and can be used to calculate *t*s,cct for different temperatures, *T*s,cct. The coordinates (*t*s,cct(*T*s,cct), *T*s,cct) then represent the CCT diagram in time-temperature coordinates. Following [28], we used Equation (4) to describe the *A*e3 temperature (in degrees Kelvin):

*<sup>A</sup>*e3(K)=(<sup>1184</sup> <sup>−</sup> <sup>29</sup>*Mn* <sup>+</sup> <sup>70</sup>*Si* <sup>−</sup> <sup>10</sup>*Cr*) <sup>−</sup> (<sup>418</sup> <sup>−</sup> <sup>32</sup>*Mn* <sup>+</sup> <sup>86</sup>*Si* <sup>+</sup> <sup>1</sup>*Cr*)*<sup>C</sup>* <sup>+</sup> <sup>232</sup>*C*<sup>2</sup> (4)

where the element symbols refer to their concentrations (in wt %). The equation includes the effects of C, Mn, Si and Cr. The effect of small amounts of microalloying with other elements is neglected for the equilibrium temperature calculation [28].

The CCT start curve was calculated using Equations (1)–(3) and is shown in Figure 1 with the critical cooling rate, which is the slowest cooling rate that does not produce the phase transformation. The plot was calculated for a steel composition of 0.09 C, 0.28 Si, 1.53 Mn, 0.012 P, 0.005 S, 0.03 Al, 0.05 Cr, 0.05 Cu, 0.035 Nb, 0.04 Ni, 0.02 Ti and 0.05 V (wt %) (named "TH16" in reference [22]) which was subjected to mechanical deformation but allowed time to recrystallize prior to cooling. To describe the "nose" of the CCT diagram without discontinuities in the temperature derivative, a piecewise polynomial was used for smooth transition from the CCT curve to the critical cooling rate curve (see Figure 1).

**Figure 1.** The continuous cooling transformation (CCT) diagram for the given steel composition can be calculated with the parameters reported in [21]. To describe the CCT "nose" without discontinuities in the derivative, a spline was fitted between the calculated CCT curve and the critical cooling rate.
