## 3 Results and Discussion
### 3D Processing Maps Establishment  
Processing maps are important tools for analysing hot deformation parameters. They are based on the dynamic material model (DMM) [40] and usually established by combining two diagrams: power dissipation and flow instability [18; 23; 41]. According to DMM, the power dissipated consists of the content term \(G\) representing the power dissipated by \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{\(\varepsilon\)} & \multicolumn{3}{c}{**0.05 Sc**} & \multicolumn{3}{c}{**0.1 Sc**} & \multicolumn{3}{c}{**0.15 Sc**} & \multicolumn{3}{c}{**0.15 Sc**} \\ \cline{2-11}  & **Q. kJ-mol\({}^{-1}\)** & **ln(A)** & **n\({}_{2}\)** & **\(\alpha\)** & **Q. kJ-mol\({}^{-1}\)** & **ln(A)** & **n\({}_{2}\)** & **\(\alpha\)** & **Q. kJ-mol\({}^{-1}\)** & **ln(A)** & **n\({}_{2}\)** & **\(\alpha\)** \\ \hline
0.05 & 172 & 28.1 & 6.8 & 0.010 & 171 & 28.0 & 6.7 & 0.010 & 161 & 27.1 & 6.1 & 0.009 \\
0.1 & 175 & 29.3 & 6.4 & 0.010 & 176 & 29.4 & 6.4 & 0.009 & 169 & 28.9 & 6.0 & 0.009 \\
0.2 & 169 & 28.8 & 6.1 & 0.009 & 171 & 29.3 & 6.2 & 0.009 & 164 & 28.4 & 5.6 & 0.008 \\
0.3 & 165 & 28.7 & 6.0 & 0.008 & 172 & 30.1 & 6.2 & 0.008 & 164 & 28.7 & 5.5 & 0.008 \\
0.4 & 162 & 28.6 & 6.0 & 0.008 & 171 & 30.2 & 6.0 & 0.008 & 166 & 29.2 & 5.5 & 0.008 \\
0.5 & 167 & 29.5 & 6.1 & 0.008 & 174 & 30.9 & 6.1 & 0.008 & 169 & 29.9 & 5.5 & 0.008 \\
0.6 & 172 & 30.4 & 6.1 & 0.008 & 179 & 32.0 & 6.2 & 0.008 & 173 & 30.9 & 5.6 & 0.008 \\
0.7 & 180 & 31.9 & 6.2 & 0.008 & 186 & 33.6 & 6.3 & 0.007 & 179 & 32.3 & 5.6 & 0.008 \\
0.8 & 184 & 32.5 & 6.2 & 0.009 & 189 & 34.5 & 6.4 & 0.007 & 185 & 33.5 & 5.6 & 0.008 \\
0.9 & 186 & 32.8 & 6.2 & 0.009 & 192 & 35.1 & 6.4 & 0.007 & 183 & 33.0 & 5.3 & 0.008 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The materials constants for the alloy Al4.5 Zn4.5 Mg1 Cu0.12 Zr with different Sc contents. Figure 3: The comparison between experimental and calculated values of stress (**a**) and model validations using additional experiments at different temperature and strain rate conditions (**b**): alloy 0.05 Sc—375 \({}^{\circ}\)C and 0.05 s\({}^{-1}\); alloy 0.1 Sc—425 \({}^{\circ}\)C and 1.5 s\({}^{-1}\); alloy 0.15 Sc—325 \({}^{\circ}\)C and 0.8 s\({}^{-1}\). plastic work (most of it converted into heat), and the cocontent term \(J\) (consumed by the evolution of the material microstructure) [40]:  
\[P=\sigma\dot{\epsilon}=G+J=\int_{0}^{\dot{\epsilon}}\sigma d\dot{\epsilon}+\int_{ 0}^{\sigma}\dot{\epsilon}d\sigma \tag{6}\]  
If temperature and strain are constant, the flow stress is given by  
\[\sigma=K\dot{\epsilon}^{m} \tag{7}\]  
where \(K\) is the material constant and \(m\) is the strain rate sensitivity factor, which is related to \(G\) content and \(J\) cocontent [19,42]:  
\[m=\frac{\partial J}{\partial G}=\frac{\dot{\epsilon}\partial\sigma}{\sigma \partial\epsilon}=\frac{\partial ln\sigma}{\partial ln\dot{\epsilon}} \tag{8}\]  
\(J\) co-content can be written as  
\[J=\int_{0}^{\sigma}\dot{\epsilon}d\sigma=\frac{m}{m+1}\sigma\dot{\epsilon} \tag{9}\]  
The maximum possible dissipation is reached when \(m=1\), so the \(J\) co-content reaches a maximum, which implies \(J_{max}=(\sigma\dot{\epsilon})/2=P/2\). The power dissipation efficiency \(\eta\) can be calculated by as [18]:  
\[\eta=\frac{J}{J_{max}}=\frac{2m}{m+1} \tag{10}\]  
Optimal hot deformation parameters are characterised by higher a dissipation efficiency \(\eta\) and a flow stability \(\xi_{P}>0\), which is calculated by the following [42]:  
\[\xi_{P}=\frac{\partial\ln\bigl{(}\frac{m}{m+1}\bigr{)}}{\partial ln\dot{ \epsilon}}+m>0 \tag{11}\]  
Areas with negative \(\xi_{P}\leq 0\) are characterised by adiabatic shear bands, slip localisation [43] and crack formation based on grain boundary cavitation [32], dynamic strain ageing, kink bands, mechanical twinning and flow rotations [42]. Three-dimensional processing maps were established by combining power dissipation efficiency and flow stability diagrams at different strain values (Figure 4).