## 2 Materials and TTs  
Inconel 718 material (HAYNES(r)718; Haynes International) (hereafter, Inco718) was used. The material (1.645 mm thick) was supplied in a solution annealed state. Its chemical composition is shown in Table 1.  
According to the supplier, Inco718 has a Young's modulus of 200 GPa, with a yielding stress value of 419 MPa and ultimate stress value (real stress at \(\sigma_{\text{u}}\)) of 871 MPa. The material has a ductility (elongation) of 46% at the point of necking, a grain size of 6-8 ASTM and hardness of 92.4 HRB.  
Figure 1 shows the difference in the material in its AR state and PSTT state (i.e., after deformation and annealing) in a simple tensile test.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Al** & **B** & **C** & **Co** & **Cr** & **Cu** & **Fe** & **Mn** & **Mo** \\ \hline
0.65 & 0.004 & 0.049 & 0.37 & 18.10 & 0.04 & 18.6 & 0.22 & 3.07 \\ Ni & P & S & Si & Ti & Ta & Bi & Pb & Ag \\
52.9 & \textless{}0.005 & \textless{}0.002 & 0.08 & 1.04 & \textless{}0.05 & \textless{}0.00003 & \textless{}0.0005 & \textless{}0.0002 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Chemical composition of the Inco718 material (wt.%).  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Elastic Modulus** & \(\sigma_{y}\) **(MPa)** & \(\sigma_{u}\) **(MPa)** & **Elongation (\%)** & **Hardness** (HRB)** & **ASTM** \\ \hline
200 & 419 & 871 & 46 & 92.4 & 6-8 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Material specifications provided by the material supplier.  
The standard test corresponds to the AR condition, whereas the PSTT condition corresponds to the material after it had been stretched by up to 50% of its total elongation capability (50% of Rm elongation) and subsequently annealed. In the intermediate annealing process, the holding time was 6 min under 980 \({}^{\circ}\)C, followed by air-cooling at room temperature. As the material had an elongation to Rm of about 46% of plastic strain, a limit of 22% of plastic strain was taken as the pre-stretch for the PSTT samples.  
To evaluate whether the intermediate annealing process changed the microstructure beyond the relaxation of the dislocations, a microstructural analysis of the material under three different conditions was conducted. Figure 2 shows representative SEM-ETD images of the samples under the various conditions.  
The averaged grain size of the samples remains on the 5 ASTM with a deviation of 1 ASTM. On the one hand, this is on the boundary of the supplier specifications, and on the other hand, this denotes that neither the TT and the pre-strain has deformed excessively the grain size.  
Figure 1: Difference between the as-received (AR) state and post-stretching thermal treatment (PSTT) state shown as a post-TT test.  
Figure 2: SEM-ETD images of the microstructure of the material under three different conditions. (**a**) AR condition, (**b**) after stretching the material to 50% of its stretching capacity and (**c**) after the intermediate annealing process (PSTT condition). The images were taken in the RD&ND direction (on the section plane between the rolling direction and the normal direction).  
Based on these observations, there were no obvious microstructural changes in the samples under the different conditions, suggesting that no critical microstructural changes were introduced during the annealing process. The results also indicated that only the dislocation density played a role in the elasto-plastic behaviour of the material. These results were expected as the holding time and temperature specifications used in this study were taken from an aeronautical handbook. Thus, these variables were not expected to modify the microstructure beyond stress relaxation.  
Next, we investigated the changes in the behaviour in the elasto-plastic strain-stress state.