## 3 Results
### Verification of Constitutive Models  
The accuracy of constitutive Equations (18) and (19) to predict flow stress was evaluated by comparing predicted to experimental data. Figure 10a,b show graphical plots for the two equations obtained at different strain rates and temperatures. The graphs indicate a close correlation between the flow stresses (predicted and experimental) of these two steels investigated.  
Figure 10: Prediction of flow stress of mathematical models for (**a**) steel A and (**b**) steel B.  
The accuracy of the developed equations to predict flow stress was analysed using statistical parameters such as [PERSON]'s correlation coefficient, \(R\), in Equation (20) and average absolute relative error (AARE) in Equation (21) [62]. [PERSON]'s correlation coefficient, \(R\), ranges between 0 and 1 and is determined using Equation (20) [63]. The proximity of \(R\) to 1 signifies a higher capability for the model to predict flow stress and vice versa. The \(R\)-value obtained for steel A was 0.97, and that for steel B was 0.98. The \(R\)-value obtained for both materials indicated a good correlation and a higher ability of the models to predict flow stress. These values compare well with the reports of other authors, such as [PERSON] et al. [61] and [PERSON] et al. [21], with an \(R\)-value of 0.994.  
[PERSON]'s correlation coefficient, \(R\), is liable to bias towards greater or lower values, hence resulting in misrepresenting the accuracy of the model to predict flow stresses [61]. Using the average absolute relative error (AARE) complements [PERSON]'s correlation method and is less subject to bias [62]. AARE analyses errors for each predicted flow stress against the experimental value on a case-by-case basis. Therefore, AARE is applied for each deformation condition to ensure the statistical efficiency of the models developed. Therefore, AARE offers better reliability and presents unbiased statistical analysis [36]. Equation (21) provides means to calculate AARE as a percentage. A lower percentage value indicates a greater ability to predict flow stresses and vice versa. The AARE obtained for the steel A was 7.62%, and for heat-treated creep-exhausted steel it was 6.54%. Reports by other authors indicated marginally lower AARE findings for the hot deformation of P91. [PERSON] et al. [61] obtained an AARE of 2.999%, and [PERSON] et al. [21] had 5.27%. These variations are due to the differences in hot deformation parameters in the respective studies. The study by [PERSON] et al. [61] used a hot deformation temperature between 900 \({}^{\circ}\)C and 1200 \({}^{\circ}\)C and strain rates of 1 s\({}^{-1}\), 5 s\({}^{-1}\), 10 s\({}^{-1}\) and 15 s\({}^{-1}\). In [PERSON] et al. [21], the temperature for hot deformation was between 850 \({}^{\circ}\)C and 1100 \({}^{\circ}\)C and the strain rates were 0.001 s\({}^{-1}\), 0.1 s\({}^{-1}\) and 100 s\({}^{-1}\). Validation by both models thus signified satisfactory levels of confidence in the respective constitutive equations to predict flow stresses.  
\[R=\frac{\sum_{i=1}^{N}\left(P_{i}-P\right)(E_{i}-E)}{\sqrt{\sum_{i=1}^{N} \left(P_{i}-P\right)^{2}}\sqrt{\sum_{i=1}^{N}\left(E_{i}-E\right)^{2}}} \tag{20}\]  
\[AARE=\frac{1}{N}\underset{i=1}{\overset{N}{\underset{i=1}{\sum}}}\left|\frac {E_{i}-P_{i}}{E_{i}}\right|\times 100\% \tag{21}\]  
where \(E_{i}\) is the flow stress from the experiment, \(P_{i}\) is the flow stress predicted from constitutive equations, and \(E\) and \(P\) are the average flow stress values of experimental data and the predicted data, respectively. \(N\) is the sum of data points.