# Design and Assessment of an Austenitic Stainless Alloy for Laser Powder Bed Additive Manufacturing
## 2 Materials and Methods
### Criteria for Alloy Design
#### 2.1.1 Phase Stability: Targeting an Austenitic Structure  
To illustrate and demonstrate the method to design alloys that are specific to AM, we chose to propose austenitic stainless alloys, with the primary objective being the predominant presence of austenite (\(\gamma\), i.e., a face-centered cubic (FCC) solid solution) in the microstructure. Computational thermodynamics, with the calculation of phase diagrams (CALPHAD) method, can be employed to predict phase formation under equilibrium conditions. However, additive manufacturing generates out-of-equilibrium microstructures and CALPHAD may become inaccurate for such processes, somehow similar to welding. One possible solution is to use the Scheil-Gulliver model [28; 29] to predict the solidification tion sequence. This model, based on the CALPHAD method, assumes non-equilibrium conditions in which the solid phase forms instantaneously without diffusion, while the liquid phase stays fully homogeneous and in equilibrium with the last solid formed. It provides predictions of the composition and amount of each phase as the material cools and solidifies. However, this model is not well-suited for predicting the phase fractions after complete cooling. For instance, the Scheil-Gulliver model could predict the formation of \(\delta\) ferrite at very high temperature, whereas that phase could transform into austenite in solid state during subsequent cooling; similarly, austenite formed at high temperature may transform into \(\alpha\) ferrite or martensite upon cooling. In the present work, an empirical approach was preferred. Therefore, the prediction of phases resulting from AM was approached using an empirical diagram usually applied to welding [30]. This relies on the quantification of \(\gamma\)-stabilizing elements and of elements promoting body-centered cubic (BCC) ferrite phases (\(\alpha\), \(\delta\)), through quantities respectively named the \"nickel equivalent\" (Ni\({}_{\text{eq}}\)) and the \"chromium equivalent\" (Cr\({}_{\text{eq}}\)). One of the most frequently employed graphic representations for this purpose is the Schaeffler-Delong diagram [30; 31]. Yet, in our specific case, in order to account for the influence of as many alloying elements as possible, we consider the Hull equations and diagram which are an extension of the former [32], where contents are expressed in wt.%, as follows:  
\[\text{Cr}_{\text{eq}}=\text{Cr}+1.21\text{Mo}+0.48\text{Si}+2.27 \text{V}+0.72\text{W}+2.2\text{Ti}+0.14\text{Nb}+0.21\text{Ta}+2.48\text{Al}\] \[\text{Ni}_{\text{eq}}=\text{Ni}+0.11\text{Mn}-0.0086\text{Mn}^{2}+ 0.14\text{Co}+0.44\text{Cu}+18.4\text{N}+24.5\text{C}\]  
This approach can serve as a straightforward tool for estimating the phases that will be present after solidification and cooling to room temperature. It aids in a quick preliminary classification of compositions into two categories: potentially acceptable alloys (referred to as \"feasible\") and unacceptable ones (\"unfeasible\"). In Figure 1, the diagram illustrates the feasible space, defined with green dashed lines. The objective is to narrow down the search space to alloys that are characterized by a fully austenitic microstructure after solidification and cooling to room temperature. The feasible space is defined by two boundaries: one setting a limit on ferrite content and another on martensite content. Unlike martensite, which is to be completely avoided due to its britteness, there is a small margin of around 5% allowed for the boundary with ferrite. Indeed, it is generally agreed that alloys containing less than 5% ferrite exhibit properties that are undistinguishable from those of fully austenitic ones. Figure 1 displays the distribution of several existing alloys on the Hull diagram, with ferrite content ranging from 0% to 5%. These alloys include 304, 316, SSW2 [33], 316L-5 Mo-5 Ni [34] and the so-called Cantor alloy, an equimolar CoCrFeMnNi \"high entropy alloy\" (HEA) [35].