*3.3. How Different Alloying Elements Affect the Phase Transformation Start*

The alloying elements affect the phase transformation start via two main mechanisms. The chemical composition directly affects the effective activation energy of the transformation. Also, because the chemical composition can affect the grain growth and recovery of dislocation structures after deformation, the chemical composition can also affect the transformation start by changing the concentration of heterogenous nucleation sites. In order to obtain a useful measure which takes into account both of the effects, we analyzed the effect of different elements on the transformation start in the following way. First, the ideal TTT start diagram was calculated for the original steel composition, *τ*o(*T*). After this, the concentration of one alloying component was altered and the TTT start diagram was calculated for the altered composition, *τ*∗(*T*). By comparing the original TTT start diagram and the altered TTT start diagram, the extent to which the change in the alloying component affected the TTT start time could be observed. Figure 7 shows how changing the carbon concentration of the steel "TH16" [22] affected the transformation start time. The effect of alloying on the transformation start during constant cooling rate is given by Equations (1) and (2) [21], which formed the basis of our analysis.

Using the previously calculated incubation times *τ*<sup>∗</sup> and *τo*, we were able to calculate a useful measure to concisely describe both the effect of chemical composition on the transformation start as well as its effect on the number of nucleation sites. Since the effect of chemical composition on the thermal vibrations of the atoms is negligible, the fraction of the calculated transformation start times, Equation (16), gives a value that can be used to parameterize more detailed microstructure models. However, more information on the effect of chemical composition on the prior austenite microstructure and available nucleation sites is needed.

$$\frac{\pi\_\*}{\pi\_0} = \frac{C\_o}{C\_\*} \exp\left(\frac{E\_{A,\*}\left(T\right) - E\_{A,o}\left(T\right)}{RT}\right) \tag{16}$$

where *C*<sup>∗</sup> and *C*<sup>o</sup> are the concentrations of the nucleation sites corresponding to *τ*<sup>∗</sup> and *τ*o; and *EA*,∗(*T*) and *EA*,o(*T*) are the effective transformation activation energies at different temperatures. The fractions

of the transformation start times for elements that had non-negligible effects on the transformation start in the experimental analysis are shown in Figure 8 [21].

**Figure 7.** The start time of the original steel composition is compared to the compositions where the carbon wt % decreased/increased by 0.03%. The inset shows the change on a smaller scale near the ideal TTT "nose" in a logarithmic plot.

**Figure 8.** The effects of altering different alloying elements on the phase transformation start at different temperatures for fully recrystallized steel (deformation schedule a) is shown by calculating the fraction *τ*∗/*τ<sup>o</sup>* (see text). The plots were calculated from the difference in the ideal TTT start times for steel "TH16" shown in reference [22] (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 %).
