A Buckingham-Pi dimensionless analysis for melt pool stability and defect prediction in additive manufacturing

Melt pool instabilities limit the reliability of additive manufacturing. Here, we demonstrate that a minimal Buckingham-π framework, supplemented by a normalized enthalpy (NE) metric, consolidates process outcomes across heat source settings (power, speed, spot) and material properties. IN738LC was processed on an EOS M290; single-track and bulk responses, melt pool geometric features, part relative density (ρ∗), and areal roughness parameters Sa and Sz, were quantified and subsequently mapped onto compact NE-dimensionless number spaces after the normalized-enthalpy metric had been calibrated using an effective absorptivity inferred from the measured melt pool depth. The recoil number cleanly delineates modes: Recoil≲2 (conduction→stable keyhole) maintains ρ∗≳99% with low Sa, whereas Recoil≳4–5 marks an unstable keyhole with spatter and porosity. Within this map, favorable transport balances are Re≲100, We<1, small Ca and not-too-small Oh, and Fo>0.1; external convection remains negligible (Nu≪1). Rather than VED, we advocate working directly in Π-space (NE,Recoil,Re,We,Ca,Oh,Fo,Nu)—to define, compare, and transfer qualifiable process windows across machines and alloys.