Abstract
Powder bed fusion (PBF) additive manufacturing (AM) technology has greatly matured in recent years driven by numerous industrial applications. However, lack-of-fusion (LoF) porosity is a significant challenge during PBF, and LoF pores can form even when processing with optimized deposition parameters. This paper proposes an analytical approach for simulating LoF porosity during PBF AM on the basis of a semi-elliptical model of the melt pool cross-section. Melted area, reference area, and LoF area fraction calculations are developed for the case where only one layer melts the reference area because of a shallow melt pool. In more complex cases where two layers melt a portion of the initial layer, the melted volume, reference volume, and LoF volume fraction calculations are developed using a change of coordinate system and integration. Finally, the model is extended to an arbitrary number of layers by assuming LoF porosity exponentially decays as the number of interacting layers increases. The analytical model predicts LoF porosity for both identical and variable melt pools and enables uncertainty analysis for LoF porosity calculations through the rapid sampling of a large number of experimentally-determined melt pool geometries. The model is used to calculate porosity fraction across the melt pool depth, melt pool width, hatch spacing, and layer thickness processing space. The accuracy of the model is demonstrated through comparisons with experimental data, and the effect of melt pool geometric uncertainty on the PBF process window is demonstrated through experimental comparisons. A new LoF porosity criterion for variable melt pools is proposed that simplifies to a previously defined, widely used LoF porosity criterion in the case of identical melt pools. Overall, the new approach presented provides a straightforward, low computational cost method for calculating LoF porosity that incorporates uncertainty for PBF AM processing.