A Bayesian Approach to the Eagar–Tsai Model for Melt Pool Geometry Prediction with Implications in Additive Manufacturing of Metals

This paper focuses on improving the melt pool geometry predictions and quantifying uncertainties using an adapted version of the Eagar–Tsai (E–T) model that incorporates temperature-dependent properties of the material as well as powder conditions. Additionally, Bayesian inference is employed to predict distributions for the E–T model input parameters of laser absorptivity and powder bed porosity by incorporating experimental results into the analysis. Monte Carlo uncertainty propagation is then used with these parameter distributions to estimate the melt pool depth and associated uncertainty. Our results for the 316L stainless steel suggest that both the absorptivity and powder bed porosity are strongly influenced by the laser power. In contrast, the scanning speed has only a marginal effect on both the absorptivity and powder bed porosity. We constructed a printability map using the Bayesian E–T model based on power-dependent input parameter values to demonstrate the merit of the approach. The Bayesian approach improved the accuracy in predicting the keyhole regions in the laser power-scan speed parameter space for the 316L stainless steel. Although applied to a specific adaptation of the E–T model, the method put forth can be extended to quantify uncertainties in other numerical models as well as in the estimation of unknown parameters.