## 3 Results
### Constitutive Equation and Material Constants  
Constitutive equations relate the flow stress and hot deformation parameters (strain rate, strain, deformation temperature) during the hot working process. Various equations have been proposed to predict the flow stress behaviour of alloys and metals during hot deformation. Some examples include the Johnson-Cook equation, the Zerilli-Armstrong equation, the Hensel-Spittel equation and the Arrhenius-type equation. These equations have varying accuracy in predicting the flow stress and deformation conditions [44, 45]. The Arrhenius type equation (Equation (2)) has wide-ranging applications in analysing the metal flow behaviour during deformation. Therefore, in this study, this model was used to compare the flow stress behaviour of the two steels [41, 46, 47, 22]. The Zener-Hollomon parameter (Z) in Equation (2) was also used to represent the effect of temperature and strain rate [48]. \[\dot{\epsilon}=Af(\sigma)\text{exp}\left(\frac{-Q}{RT}\right) \tag{2}\]  
Figure 6: Flow stress–strain curves of steel B.  
\[Z=\dot{\epsilon}\text{exp}\bigg{(}\frac{Q}{RT}\bigg{)} \tag{3}\]  
where \(\sigma\) is the flow stress, \(\dot{\epsilon}\) is the strain rate, \(T\) is the absolute temperature (K), \(Q\) is the activation energy for hot deformation (kJ/mol), \(A\) is a material constant and \(R\) is the universal gas constant (8.314 Jmol\({}^{-1}\) K\({}^{-1}\)). \[Z=\dot{\epsilon}\text{exp}\bigg{(}\frac{Q}{RT}\bigg{)}=f(\sigma)=A\sigma^{n^{ \prime}} \tag{4}\]  
\[Z=\dot{\epsilon}\text{exp}\bigg{(}\frac{Q}{RT}\bigg{)}=f(\sigma)=A\text{exp}( \beta\sigma) \tag{5}\]  
\[Z=\dot{\epsilon}\text{exp}\bigg{(}\frac{Q}{RT}\bigg{)}=f(\sigma)=A[sinh( \alpha\sigma)]^{n} \tag{6}\]  
The relationship between the Zener-Hollomon parameter and flow stress is expressed by Equations (4) to (6) [49]. The terms in these equations--\(n^{\prime}\), \(\beta\), \(n\), and \(\alpha\)--are material constants. Equation (4) is the power law applied for low stresses (\(\alpha\sigma<0.8\)), as it breaks down at higher flow stress. Equation (5) is the exponential law used for higher stress (\(\alpha\sigma>1.2\)) and breaks down at a strain rate under 1 s\({}^{-1}\) and high temperature [50]. Equation (6) is a hyperbolic sine function equation developed by [PERSON] and [PERSON] [51] to be applicable to a wide range of stresses (both high and low). Equations (4)-(6) can also give Equations (7) and (9) [25]:  
\[\dot{\epsilon}=A\sigma^{n^{\prime}}\text{exp}\bigg{(}\frac{-Q}{RT}\bigg{)} \tag{7}\]  
\[\dot{\epsilon}=A\text{exp}(\beta\sigma)\bigg{(}\frac{-Q}{RT}\bigg{)} \tag{8}\]  
\[\dot{\epsilon}=A[\text{sinh}(\textit{ff}\alpha)]^{n}exp\bigg{(}\frac{-Q}{RT} \bigg{)} \tag{9}\]  
The constants \(n^{\prime}\) and \(\beta\) are determined by taking logarithms on both sides of Equations (7) and (8) [46]. These are presented as Equations (10) and (11) [22]. The plots of ln \(\dot{\epsilon}\) versus ln \(\sigma\) (Equation (10)) and ln \(\dot{\epsilon}\) versus \(\sigma\) (Equation (11)) are used to calculate the material constants \(n^{\prime}\) and \(\beta\) shown in Figure 7a,b [22]. \[\ln\dot{\epsilon}=\ln A+n^{\prime}\ln\sigma-\frac{Q}{RT} \tag{10}\]  
Figure 6:0  
The stress multiplier \(\alpha\) is an adjustable constant. This \(\alpha\)-value is obtained from: \(\alpha=\beta/n\)[50]. The stress exponent, n, and activation energy, Q, are determined by taking logarithms on both sides of Equation (9), which gives Equations (12) and (13) [50]. These equations are plotted as ln \(\dot{\epsilon}\) versus ln (sinh (\(\alpha\alpha\))) and ln (sinh (\(\alpha\alpha\))) versus (1000)/T, as shown in Figure 8a,b. The average value of the slopes obtained in these plots provides n and S values for calculating the activation energy Q [25]. Figure 6:1Figure 6:2  
The relationship between the flow stress and the Zener-Holloman parameter is given in Equation (6). The structure factor (A) is determined by taking logarithms on both sides of Equation (6), as in Equation (14) [21].