# Process Parameter Optimisation in Laser Powder Bed Fusion of Duplex Stainless Steel 2205
## 4 Optimization Procedure  
Once the tensile tests were completed, the collected data were processed to represent the engineering stress-strain curve for each test from the experimental matrix in Table 4. Figure 2 shows the two typical behaviors that were observed during tests and depicts the most characteristic broken specimen sections. On the one hand, some specimens have suffered brittle fractures, such as specimens 5 and 7, and on the other hand, others displayed more ductile behavior, such as specimens 2 and 13. The brittle behavior observed is characterized by low fracture strain, implying that the necking of the specimen is practically non-existent, and thus the reduction of the area is very small. In contrast, in ductile behavior, the fracture strain and reduction of area are high, and necking occurs in the fracture zone. As can be seen in the fracture surfaces of the micrographs, the ductility of the material is directly related to the reduction of the area of the specimen at failure and to the necking of the specimen. Specimen 7 shows that the laser beam has not been able to completely weld the steel, leaving more pores and reducing the relative density of the material, while specimen 2 shows a more homogeneous and compact matrix. The most representative specimens for the ductile and brittle behaviors are specimens 2 and 7, whose fracture surfaces have been analyzed with the scanning electron microscope (SEM). Comparing Figures 3 and 4, the differences in the ductile behavior are very remarkable. However, specimen 2 still has big pores as it does not have the optimal process parameters. In Figure 3, it can be clearly observed how the specimen has experienced necking in the fracture zone, considerably reducing its initial diameter. Conversely, in Figure 4, it is evident that the fracture occurred without necking in the fracture zone. The detail in Figure 4 clearly shows the lack of powder fusion due to the low energy per unit volume provided by the laser during the manufacturing process. \begin{table}
\begin{tabular}{c c c c c c c c} \hline  & \multicolumn{3}{c}{Experimental Matrix} & \multicolumn{3}{c}{Experiment Plan} \\ \hline NUM. & \(\mathbf{P^{*}}\) & \(\mathbf{S^{*}}\) & \(\mathbf{H^{*}}\) & \(\mathbf{P[M]}\) & \(\mathbf{S[mm/s]}\) & \(\mathbf{H[mm]}\) & \(\mathbf{VED[J/mm^{3}]}\) \\ \hline  
\end{tabular}
\end{table} 
Table 4: Proposal for the design of experiments. For every test from Table 4, the values for all the analyzed properties (D, \(\sigma_{0,2}\), \(\sigma_{\text{us}}\), \(\varepsilon_{\text{r}}\), and A) have been obtained, and these are depicted in Table 5. Using the calculated responses and with the aid of the Design Expert software, a mathematical model based on a quadratic function was applied to generate the response surfaces for each of them and the corresponding coefficients of determination (R\({}^{2}\)). These surfaces are characterized by Expressions (4-8). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline Test & D (\%) & \(\sigma_{0,2}\) (MPa) & \(\sigma_{\text{uts}}\) (MPa) & \(\varepsilon_{\text{r}}\) (\%) & A (\%) \\ \hline  
\hline \end{tabular}
\end{table} 
Table 5: Values of the mechanical properties analyzed for DSS-2205 in the design of experiments. Figure 2: Engineering stress–strain curve of the tested samples. Figure 3: The fracture surface of specimen 2: (**a**) magnitude 15\(\times\), (**b**) magnitude 50\(\times\). Figure 4: The fracture surface of specimen 7: (**a**) magnitude \(16\times\), (**b**) magnitude \(50\times\). \[ \begin{split}\text{D}\,f(\text{P}^{*},\,\text{S}^{*},\,\text{H}^{*})& =97.866+1.295\cdot\text{P}^{*}-0.683\cdot\text{S}^{*}-0.607\cdot\text{H}^{*}+ \\ +0.593\cdot\text{P}^{*}\cdot\text{H}^{*}+\,0.806\cdot\text{P}^{*} \cdot\text{S}^{*}-0.856\cdot\text{S}^{*}\cdot\text{H}^{*}\\ \text{R}^{2}&=0.764\end{split}  \tag{4}\]  
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