## 3 Results and Discussion
### Hot Deformation Behaviour Modelling  
The typical true stress true strain curves of the investigated alloys after compression under different conditions are presented in Figure 2. It can be observed that with an increase in temperature (Figure 2a,c,e), the level of flow stress decreased, and with an increase in strain rate, it increased. Nevertheless, with an increase in the deformation rate, the difference in the level of flow stress decreased (Figure 2b,c,f), which was caused by destruction of the specimens with the accumulation of the degree of strain at a strain rate of 15 s\({}^{-1}\). Moreover, in addition to the characteristic stage of stress growth due to strain hardening (SH), the flow curves generally lacked the region characteristic for dynamic recrystallisation (DRX) with softening, and reached the steady-state stage of deformation. This means that the main controlling process of structural evolution during the growth of deformation was dynamic recovery (DRV).  
Figure 1: SEM-image of the alloy 0.15 Sc as cast (**a**) and after the heat treatment (**b**). The images show the characteristic emissions of the alloying elements into the selected zone (the red rectangle on the microstructure) and TEM-image with secondary phases of T and Al\({}_{3}\)(Sc,Zr).  
The correlation between the flow stress, strain rate and temperature of hot plastic deformation is described by the Zener-Hollomon parameter \(Z\)[33]:  
\[Z=\dot{\varepsilon}e^{\frac{Q}{RT}} \tag{1}\]  
where \(\dot{\varepsilon}\) is the strain rate (s\({}^{-1}\)), \(Q\) is the effective activation energy of hot deformation (J-mol\({}^{-1}\)) and \(R\) is the universal gas constant (8.314 J\(\cdot\)mol\({}^{-1}\cdot\)K\({}^{-1}\)). The relation between \(Z\) and flow stress is usually described by the power function (2) for low stresses, an exponential function (3) for high levels of stress, and a hyperbolic sinus function (4) for all ranges of stress [21; 34; 35]:  
\[Z=A_{1}\sigma^{n_{1}} \tag{2}\]  
\[Z=A_{2}e^{\beta\sigma} \tag{3}\]  
\[Z=A_{3}[sinh(\alpha\sigma)]^{n_{2}} \tag{4}\]  
Figure 2: True stress true strain curves of the alloys 0.05 Sc (**a,b**), 0.1 Sc (**c,d**) and 0.15 Sc (**e,f**) at different temperatures and a strain rate of 1 s\({}^{-1}\) (**a,c,e**), and different strain rates and a temperature of 400 \({}^{\circ}\)C (**b,d,f**).  
where \(A_{1}\), \(A_{2}\), \(A_{3}\), \(n_{1}\), \(n_{2}\) and \(\beta\) are experimentally-determined parameters. The value of \(\alpha\) can be determined as:  
\[\alpha\approx\frac{\beta}{n_{1}} \tag{5}\]  
The materials constants are presented in Table 2 for the alloys with different Sc content and different strain values. The values of the effective activation energy were in the range of 161-192 kJ-mol\({}^{-1}\) for all compositions, which is consistent with the values obtained previously for Al-5.8 Zn-2.3 Mg-1.5 Cu-0.21 Cr (168.08 kJ-mol\({}^{-1}\)) [36], Al-7.3 Zn-2.3 Mg-0.6 Cu-0.3 Mn-0.11 Er-0.12 Zr (189.67 kJ-mol\({}^{-1}\)) [37] and Al-6.2 Zn-0.70 Mg-0.30 Mn-0.17 Zr (181-189.5 kJ-mol\({}^{-1}\)) [38].  
The comparison between experimental and calculated values of stress is shown in Figure 3a. As one can see, the dispersion of the stress values was significantly higher at high values. The accuracy of the strain-compensated model was quantified by additional experiments for the alloys with different Sc content at different temperature-strain rate conditions: 0.05 Sc--375 \({}^{\circ}\)C and 0.05 s\({}^{-1}\); 0.1 Sc--425 \({}^{\circ}\)C and 1.5 s\({}^{-1}\); 0.15 Sc--325 \({}^{\circ}\)C and 0.8 s\({}^{-1}\). The average absolute relative error (AARE) determined accordingly [39] was 5.0% (Figure 3b).