## 3 Characterization of Mechanical Properties of the Material
### Friction Characterization  
Apart from material behaviour, friction between the die and sheet also plays a key aspect in drawing operations. According to previous research, this friction was highly dependent on the lubricant, sheet, die surface roughness and material, as well as on contact pressure, sliding velocity and temperature [7]. In this study, the die material used was F-522T. The dies were polished in a toolmaker partner to give a final surface quality of 0.22 \(\upmu\)m Ra and 1.34 \(\upmu\)m Rz. In a strip drawing test, the dies were used in conjunction with strips of the Inco718 material under different pressures ranging from 1 MPa to 40 MPa at a constant speed of 10 mm/s at room temperature. Prior to the strip drawing test, surface strips of each sample covering an area of \(3250\times 3040\)\(\upmu\)m\({}^{2}\) was analysed using a Sensofar S Neos with a \(20\times\) objective, sampling of 0.65 \(\upmu\)m and vertical resolution of 8 nm. Figure 8 shows the topographical analysis of the surfaces of the samples. Figure 8a,c shows the values for the AR sample, and Figure 8b,d depicts the values for the PSTT sample. Figure 7: FLC of the Inco718 material. The continuous lines show the FLC of the AR necking limit, and the dashed lines denote the PSTT necking limit. To evaluate differences between the surfaces, the Sq (the root mean square value of ordinate values) and Sdr (the developed interfacial area ratio) values of the surfaces were calculated. The results are shown in Table 6.  
Pre-strain of the sample and subsequent TT modified the surface roughness, increasing the Sq value from 0.38 to 0.79 and the Sdr value from 0.48 to 1.01. The increase in these values could affect the friction and wear behaviour of the material. To evaluate the impact of changes in the values on friction behaviour, strip drawing tests were conducted. In the strip drawing tests, G-Start graphite spray and Condat Vicafil TFH4002 lubricant, which is commonly used in material drawing operations, were used. During the test, a strip of the sheet material under analysis is pressed between two square flat dies in order to apply the desired contact pressure. Once the pressure is achieved, the strip is pulled, and a relative displacement between the dies and the sheet is generated in which both forces--the puling force and the normal force--are measured in order to calculate the existing friction coefficient on the tribological system. Further details \begin{table}
\begin{tabular}{c c c} \hline \hline
**State** & **Sq (\(\mu\)m)** & **Sdr (\(\mu\)m)** \\ \hline AR & 0.38 \(\pm\) 0.04 & 0.48 \(\pm\) 0.02 \\ PSTT & 0.79 \(\pm\) 0.02 & 1.01 \(\pm\) 0.06 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Quantitative comparison of the surface of the AR material and that of the PSTT material after 7% pre-strain. Figure 8: Topographic view of the material surface. (**a**,**c**) 3D and 2D representations of the surface of the AR material, respectively. (**b**,**d**) 3D and 2D representations of the surface of the PSTT material, respectively. of the system can be found in [21]. The friction coefficient values obtained in the strip drawing tests are shown in Table 7.  
As shown in Table 7, even with an increase in surface roughness, the differences in the friction coefficient values of both material states (AR and PSTT) were negligible. Furthermore, the friction coefficient value obtained for the combination of materials and lubricant was low (\(<\)0.08). Changes in the coefficient of friction are shown in Figure 9.  
As shown in Figure 9, the friction coefficient rapidly decreased in the first 8 MPa, followed by saturation at a value of around 0.01. In the figure, the slight increase starting at 20 MPa may have been due to lubricant slippage. The high viscosity of the used lubricant usually creates a lubricant film, preventing contact between both surfaces. Therefore, in the first range of pressures (from 0 MPa to 20 MPa) the interaction behaviour is related to the behaviour of the lubricant under different pressures.