## 3 Results
### Activation Energy and Stress Exponent  
Table 2 summarises the material constants \(n^{\prime}\), \(\beta\), \(n\), and \(S\), and the activation energy, \(Q\), for the two steels. The stress exponent and activation energy are termed as apparent values. The term apparent implies that the constitutive equation does not consider the internal microstructure changes that occur during deformation, thus assuming constant metal flow behaviour [53; 54]. The stress exponent, \(n\), and apparent activation energy, \(Q\), indicate the deformation mechanisms that control the deformation process [45]. The activation energy shows the plastic workability of the material during the deformation process [55]. The difference between the apparent and self-diffusion activation energy of Fe in austenite provides information on the dominant softening mechanisms during forging [55]. [PERSON] and [PERSON] [56] reported that the apparent activation energy is 20% higher than the self-diffusion activation energy when DRX is the dominant mechanism. The presence of precipitates, solutes, inclusions, or reinforcements causes the activation energy to be 50% greater than the activation energy for self-diffusion. For high-stacking fault energy materials, the apparent activation energy is equivalent to or close to the activation energy for self-diffusion [41]. The results of this study show that the apparent activation energy for the two steels was 473.08 kJ/mol (steel A) and 564.48 kJ/mol (steel B). In comparison, \(Q\)-value for the steel A was 65% greater than the self-diffusion activation energy of Fe in austenite (284 kJ/mol), while rejuvenated creep-exhauset steel was 98% higher. These results show that the two steels exhibited low plastic deformability.  
The \(Q\)-values of the two steels show that the rejuvenated creep-exhauset steel has a higher resistance to deformation. The reason for this might be an incomplete dissolution of carbides during deformation. The presence of carbides impedes the deformation process by hindering dislocation movement and increases the stress exponent, \(n\)[57; 52]. The stress exponent obtained for steel B was 6.67 and for steel A was 5.76. The stress exponent is significantly affected by an increase in flow stress. Steel B had higher flow stresses than steel A, and therefore had higher activation energy.  
The stress exponent also shows the dynamic softening mechanisms Involved during forming [45]. [PERSON] et al. [58] reported that when dislocation climb controls deformation, the stress exponent is 5, compared to 3 for dislocation glide mechanism-controlled deformation. Dislocation climb and glide are dynamic softening mechanisms, showing that DRV occurred during deformation [59]. In this study, the flow stress-strain curves did not exhibit a clear flow stress peak. However, the flow curves exhibited a steady-state condition at higher strain, as shown in Figures 5 and 6. Lower \(n\)-values (<5) show that DRX was the dominant softening mechanism [48]. The stress exponent values shown in Table 1 indicate that both WH and DRV controlled the deformation process. This deformation behaviour occurs in materials with a high stacking fault energy, such as creep-resistant steel [60]. The difference between the steels may be due to the deformation conditions and steel chemistry. Higher \(n\)-values may be due to precipitates in the matrix, improving solid solution strengthening by pinning dislocation movement [2].  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**P91** & \(\hat{\eta}\) & \(\beta\) & \(\eta\) & \(a\) & \(S\) & \(Q\) [k]mol\({}^{-1}\)) & _ln A_ \\ \hline Steel A & 7.79 & 0.054 & 5.76 & 0.0069 & 9.89 & 473.08 & \(9.98\times 10^{18}\) \\ Steel B & 9.03 & 0.058 & 6.67 & 0.0065 & 10.18 & 564.48 & \(9.58\times 10^{22}\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Material constants and activation energy for steel A and steel B.