*3.4. Effect of Strain Hardening on the Phase Transformation Start*

The microstructure of the steel and the phase transformation start are affected by the final rolling temperature and the time spent at elevated temperature prior to cooling. If the steel is rolled above the recrystallization limit temperature and kept at a high temperature prior to cooling, the mechanically-deformed grains have adequate time to recrystallize. In contrast, if the metal is additionally rolled at or below the temperature where no significant recrystallization occurs, the austeninte grains do not have time to recrystallize prior to cooling and are in a more unstable state. This causes the ferrite transformation to start earlier for strain hardened austenite. A comparison of

numerical simulation studies to experimental data showed that deformation affects transformation mainly via reduction in the undercooling required for nucleation [38].

The original reference [21] that we used for calculating the transformation start temperatures and critical cooling rates via Equations (1) and (2), also provided the regression constants for strain hardened metal. It is therefore straightforward to calculate the same quantities for the strain hardened steel that were calculated for the fully recrystallized steel. The effects of different alloying elements on the transformation start of the strain hardened material are shown in Figure 9. By comparing the results, we can analyze the effect of strain hardening on the transformation onset.

**Figure 9.** The effects of altering different alloying elements to the phase transformation start at different temperatures for strain hardened steel (deformation schedule b) is shown by calculating the fraction *τ*∗/*τ<sup>o</sup>* (see text). The plots are 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 %).

We calculated the original ideal TTT transformation start time for the fully recrystallized steel, *τ*r, and the strain hardened steel, *τ*h, at different temperatures (Figure 10a). To quantitatively analyze the effect of strain hardening versus fully recrystallized steel, we also calculated the fraction *τ*h/*τ*<sup>r</sup> by applying Equation (16). The result is shown in Figure 10b. The steel composition used in the calculation was 0.096 C, 0.150 Si, 1.204 Mn, 0.018 P, 0.006 S, 0.008 N, 0.032 Al, and 0.036 Nb (wt %).

**Figure 10.** Comparison of the calculated ideal TTT curves of work hardened versus fully recrystallized austenite: (**a**) plots of the TTT curves; (**b**) the time required to start the transformation for strain hardened material divided by the corresponding time for fully recrystallized material.
