# Design and Assessment of an Austenitic Stainless Alloy for Laser Powder Bed Additive Manufacturing
## 3 Results  
### Selection of a Specific Alloy  
The distribution of compositions for the optimized population of alloys is illustrated in Figure 2 using a violin plot. Cr content ranges between 15% and 31 wt.%, while Ni falls within the range of 11% to 22 wt.%. Mn exhibits a broader range, spanning from 0% to 24 wt.%. Notably, a significant amount of Co, ranging from 5% to 20 wt.%, is prevalent in most of the alloys. This elevated cobalt content is likely a result of the criterion for enhancing solid solution hardening and stabilizing the austenitic structure. The content of other elements is generally limited to a few percent: Mo and Al do not exceed 3% and 4 wt.%, respectively. On the other hand, elements like Nb, Ti and W have average values well below a fraction of a percent and are considered negligible, despite their potentially high solid solution hardening capability. It seems possible that the strong tendency of these three elements towards primary segregation conflicts with the objective of minimizing the CTR value. Furthermore, these three elements act as ferrite stabilizers, ultimately raising the Cr\({}_{\text{eq}}\) value and rendering their inclusion unfavorable. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Criteria** & **Constraint** & **Objective** & **Method of Calculation** \\ \hline \multirow{4}{*}{Austenitic structure} & (a) Belongs to feasible space on & (f) Maximize distance from & \\  & Hull diagram & boundaries & Hull diagram \\ \cline{2-4}  & (b) \(\delta\) \(<\) 50\% & & \\ \cline{2-4}  & (c) \(\delta\) \(+\) \(\gamma\) \(>\) 99\% at the end of & & Scheil model \\  & solidification & & \\ \hline \multirow{2}{*}{Solidification cracking} & (d) Solidification mode = FA & (g) Minimize CTR & \\ \cline{2-4}  & (e) \(\delta\) \(>\) 10\% & & Scheil model \\ \hline \multirow{2}{*}{Melt pool stability and balling} & & (h) Minimize ST & GPR-ML model \\ \cline{2-4}  & Thermal strains and & (i) Minimize \(\alpha_{\text{CTE}}\) & Rules of mixtures \\ \cline{2-4}  & residual stresses & & \\ \hline Strength & & (j) Maximize SSH & Labusch SSH model \\ \hline \multirow{2}{*}{Porosity} & (k) Minimize total vaporization flux & Vaporization flux \\ \cline{2-4}  & (l) Minimize variance of & \\ \cline{2-4}  & vaporization flux & Vaporization flux \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Summary of the different objective functions and constraints. After optimization, all the alloys in the population belong to a Pareto front. Selecting a single optimal alloy is challenging as each performs better in some specific criteria. To determine the best overall option, we ranked the alloys by their average performance across all objectives. The preference ranking organization method for enrichment evaluation (PROMETHEE) method [68], a multi-criteria decision tool, was used to select the best alloys based on expressed preferences. The detailed methodology is explained elsewhere [69] but, to summarize, the user expresses the relative importance of each objective (or property), using a so-called preference function whose parameters are specific to each objective. This allows, based on said preferences, to establish a global ranking of alloys that are, by design in the present case, incomparable as they are all Pareto optimal, i.e., each alloy outperforms all the others on at least one objective. This results in a shortlist of alloys. At this stage, selecting an alloy remains challenging because all materials of the shortlist display rather close characteristics. To aid in selection, we introduced an additional criterion: the temperature range for austenite stability at equilibrium, predicted by Thermo-Calc. Although not initially included in the multi-objective optimization due to computational costs, it is essential for avoiding unwanted phase transformations during post-AM heat treatments. This criterion helped differentiate between otherwise equivalent alloys based on other factors. From the best performing alloys on the shortlist, one composition was selected based on this additional criterion.