## 4 Discussion
The increase in grain size with MDF temperature can be explained using a Zener factor [46]. The L1\({}_{2}\) -phase dispersoids prevent the intense grain coarsening due to the Zener pinning effect. The dispersoids exhibited a mean size of -10 nm. Taking into account that all atoms of Sc and Zr precipitated from the solid solution and formed an Al\({}_{3}\)(Sc,Zr) phase, the dispersoid volume fraction \(f\) is approximately -0.005. The Zener factor allows for calculating the particles' contribution to the grain growth suppression [46; 74]:  
\[Z_{H}=\frac{3 fd}{4r} \tag{20}\]  
where \(d\) is the mean grain size. The grain size after MDF at 150 \({}^{\circ}\)C was \(\sim\)1.2 \(\upmu\)m and at 250-350 \({}^{\circ}\)C it was \(\sim\)2.0-2.1 \(\upmu\)m. The corresponding Zener factor value was equal to 0.9 at 150 \({}^{\circ}\)C and \(\sim\)1.5 at 250-350 \({}^{\circ}\)C. The Z = 1 is a threshold value above which the static grain growth is suppressed [74; 75]. The Zener parameter value Z > 1 after MDF at both 250 and 350 \({}^{\circ}\)C. The threshold grain size value above which the grain growth is considered suppressed is \(\sim\)1.3 \(\upmu\)m. While the Zener factor does not consider the strain-induced grain growth, an insignificant difference in the grain size after MDF at 250 and 350 \({}^{\circ}\)C is most obviously associated with the Zener effect. The fine-grained structure of the alloy after MDF and the Zener pinning effect provided a near superplastic behavior in a temperature range of 460-500 \({}^{\circ}\)C. The dynamic strengthening observed in the stress-strain curves is associated with dynamic grain growth that occurs at elevated temperatures [6]. This explains a decrease of elongation with increasing temperature during hot deformation. A hyperbolic Arrhenius constitutive model [76; 77; 78] is successfully constructed to estimate the flow stress behavior of this alloy in the studied temperature and strain rate range. The developed model demonstrated high predictability accuracy with the maximum error AARE of 6.6%. The as-forged alloy demonstrated improved mechanical properties. The same level of mechanical characteristics was observed in the alloy with similar composition but increased Sc after thermomechanical treatment included hot and cold rolling [43]. The as-rolled and further annealed sheets with Sc exhibited a non-recrystallized structure that contributes significantly to strength due to dislocation strengthening mechanism [79; 80]. Moreover, Sc and Zr provide for a high precipitation contribution to strength (Orowan strengthening) due to L1\({}_{2}\) dispersoids [81]. In the present study, the alloy contains low Sc of 0.1% and exhibits a recrystallized structure, whereas the strength was maintained at a similar level Shat was achieved through both grain refinement Hall-Petch mechanism and Zener pinning effect. A near-superplastic behavior and high strength observed in the bulk samples offers additional opportunities for industrial application of the studied alloy and MDF technique. The Arrhenius type constitutive model based on the experimental stress-strain results was constructed to model the hot flow behavior of this alloy. The constants of the Arrhenius type constitutive model were illustrated on the dependance of the deformation level. The stress exponent \(n\) is commonly employed in order to determine the primary mechanism governing the hot deformation process. Hence, the diverse methods of superplastic deformation can be correlated with independent values of \(n\). Based on the findings of previous studies [82; 83], it has been observed that the grain boundary sliding and the dislocation glide mechanism can result in values of \(n\) that are approximately two and three, respectively. On the other hand, processes associated with \(n\) values ranging from four to six are attributed to dislocation climb.