# Design and Assessment of an Austenitic Stainless Alloy for Laser Powder Bed Additive Manufacturing
## 2 Materials and Methods
### Criteria for Alloy Design
#### 2.1.2 Solidification Cracking  
The issue of solidification cracking has been extensively investigated in conventional manufacturing techniques such as casting and welding, but it also occurs in the specific case of LPBF process [36]. One of the key factors influencing the susceptibility of an alloy to cracking is its solidification temperature range. Therefore, calculating this value serves as a means to quantify the cracking susceptibility of an alloy [18]. More specifically, it is crucial to consider the critical temperature range (CTR) [37; 38]. Lowering this range in the mushy zone during solidification minimizes shrinkage, reduces liquid suction in the interdendritic spacing and ultimately lowers the risk of void and crack formation. Definitions vary across sources, but, generally, the CTR is defined as the difference between temperatures at which certain fractions of solids have formed. This study adopts the definition corresponding to fractions of solids between 95% (T\({}_{1}\)) and 99% (T\({}_{2}\)), as these values are commonly reported [13; 23; 24]. To predict the solidification range and associated phases, including their order and the evolution of their fractions, the classical Scheil model from Thermo-Calc is employed. This computational tool enables the calculation of the complete solidification range. This model is only applied to alloys predicted by the Hull diagram to be austenitic, whereas alloys judged unsatisfactory by the Hull criterion are excluded from the Scheil calculation in order to limit computation time. When considering processes with high solidification rates, various studies have demonstrated that the primary formation of ferrite from the liquid can significantly reduce the susceptibility to solidification cracking compared with the primary formation of austenite. Such a beneficial effect is observed when solidification produces ferrite only (F mode) or ferrite then austenite (FA mode) compared with the production of austenite only (A mode) or austenite then ferrite (AF mode) [39; 40; 41; 42]. An important factor contributing to this effect is the higher solubility of harmful impurities (S, P...) in ferrite compared with that in austenite. This results in less segregation during the primary ferrite solidification. The cracking behavior of several austenitic stainless steels is influenced by the impurity content of S and P, as well as the Cr\({}_{\text{eq}}\)/Ni\({}_{\text{eq}}\) ratio [43]. [PERSON] et al. [44] noted that, as the Cr\({}_{\text{eq}}\)/Ni\({}_{\text{eq}}\) ratio approaches 1.48, the impurity content of S and P, which leads to cracking, becomes significantly higher. Beyond this value (~1.48), cracking becomes rare, even with somewhat elevated impurity contents (>0.2 wt.%). This value of Cr\({}_{\text{eq}}\)/Ni\({}_{\text{eq}}\) corresponds to the range where the solidification mode changes from A or AF to FA. To ensure that the solidification  
Figure 1: Hull diagram with a definition of the feasible search space defined in our study. A stands for austenite, F for ferrite and M for martensite. mode is FA or F, it would be possible to use a minimum value of the \(\rm{Cr_{eq}}/\rm{Ni_{eq}}\) ratio as a design constraint. Instead, our choice was to impose the first phase formed during solidification as predicted by Thermo-Calc, which is set to \(\delta\)-ferrite. Moreover, using Thermo-Calc with the Scheil model makes it possible to estimate the fraction of ferrite formed, unlike the \(\rm{Cr_{eq}}/\rm{Ni_{eq}}\) ratio alone. As a precaution, a minimum of 10% \(\delta\)-ferrite formation is specified to reduce the risk of cracking [45]. However, with the ultimate desired microstructure being austenitic, it is also useful to establish an upper limit on the fraction of \(\delta\)-ferrite formed during solidification, in addition to the Hull diagram criterion, to avoid an incomplete transformation of ferrite into austenite during cooling.