# Design and Assessment of an Austenitic Stainless Alloy for Laser Powder Bed Additive Manufacturing
## 2 Materials and Methods
### Criteria for Alloy Design
#### 2.1.3 Melt Pool Composition and Stability  
AM processes involve the use of liquid metal, making it imperative to examine various properties of materials in this state. Among these properties, surface tension (ST) plays a critical role and significantly impacts the wetting conditions of the previously deposited solid phase by the liquid phase. The value of ST influences the ability of the melt pool to form a continuous and stable seam. At high scanning speeds and with low deposited energy, the length of the melt pool increases relative to its diameter, leading to the phenomenon known as the \"balling effect\" [2]. This happens when the melt zone, which can be roughly seen as a \"cylinder\", becomes unstable and splits into beads for a given ratio of its diameter over its length. The melt cylinder is attached to the solid substrate by a contact band; however, the physical phenomenon can be compared with some extent to a free-falling liquid jet and the resulting stability criterion differs only of a constant geometric factor [46; 47]. A material-dependent criterion can be determined by considering the stability of a free-falling jet over time. Equation (1) [48] provides the expression of the characteristic time \(\tau\) for the breakup of a fluid jet into drops:  
\[\tau\propto\sqrt{\frac{\rho R^{3}}{\gamma}} \tag{1}\]  
where R denotes the jet radius, \(\rho\) signifies fluid density and \(\gamma\) stands for the surface tension value. It can be inferred that, reducing the ST value would result in an extended breakup time, potentially longer than the solidification time, thus mitigating the balling effect. This decrease in ST would, overall, enhance the geometric stability of the seam. Due to the absence of a reliable physical model with which to predict the surface tension of metallic alloys as a function of composition, a general machine learning (ML) approach was employed. The model relies on a Bayesian algorithm, specifically Gaussian process regression (GPR); the method and the assessment of the model are detailed elsewhere [49]. Another phenomenon contributing to melt pool instability is vaporization. As reported by [PERSON] et al. [50], the vaporization of the melt can lead to the occurrence of keyholing. This may result in the formation of pores if gas bubbles become trapped [51]. Reducing the risks associated with such instabilities can be achieved by lowering the vaporization flux of the elements. Additionally, selective vaporization may induce significant composition changes as shown by [PERSON] et al. [52]. To assess the risks related to instabilities arising from vaporization and composition changes, the vaporization flux of each element is estimated. Equation (2) shows the Langmuir expression for the vaporization flux (\(\rm{J_{i}}\)) of element \(\rm{i}\)[53]:  
\[J_{i}=\lambda_{c}\frac{P_{i}}{\sqrt{2\pi M_{i}T}} \tag{2}\]  
where \(\rm{P_{i}}\) and \(\rm{M_{i}}\) are the equilibrium vapor pressure and molecular weight of element \(\rm{i}\), respectively, T is the temperature and \(\rm{\lambda_{c}}\) is a positive constant that accounts for the condensation, typically assigned a value of 1 under vacuum conditions. Estimating \(\rm{J_{i}}\) for individual elements requires the determination of their respective vapor pressure values. One approach to achieve this is by estimating it at a specific temperature using Alcock equations [54] in the form of a polynomial, as follows:  
\[\log P_{i}=A_{i}+\frac{B_{i}}{T}+C_{i}\text{log}T+\frac{D_{i}}{T^{3}} \tag{3}\]  
where \(\text{A}_{i}\), \(\text{B}_{i}\), \(\text{C}_{i}\) and \(\text{D}_{i}\) are coefficients specific to the i-th element, with commonly used values sourced from [54]. Equation (3) is applicable within the indicated temperature range and the fitted coefficients depend on the state of the material (solid or liquid). Yet, coefficients are often available over only a limited temperature range, and sometimes for the solid or liquid state only, the latter being the one needed.