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

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Abstract

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.

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Acknowledgements

This material is based upon work supported by the US Department of Energy’s Office of Energy Efficiency and Renewable Energy (EERE) under the Advanced Manufacturing Office Award Number DE-EE0009100. This report was prepared as an account of work sponsored by an agency of the US Government. Neither the US Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the US Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the US Government or any agency thereof. B.J.W and P.V.B thank Mr. Nicholas Wu for insightful comments on the manuscript.

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Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, University of Virginia, Charlottesville, VA, 22904, USA

    Brendan J. Whalen & Prasanna V. Balachandran

  2. Department of Materials Science and Engineering, University of Virginia, Charlottesville, VA, 22904, USA

    Ji Ma & Prasanna V. Balachandran

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  1. Brendan J. Whalen
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Correspondence to Prasanna V. Balachandran.

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Whalen, B.J., Ma, J. & Balachandran, P.V. A Bayesian Approach to the Eagar–Tsai Model for Melt Pool Geometry Prediction with Implications in Additive Manufacturing of Metals. Integr Mater Manuf Innov 10, 597–609 (2021). https://doi.org/10.1007/s40192-021-00238-z

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