SIM-AM 2023

Mathematically consistent representation of interface fluxes for finite-element-based melt pool modeling in metal additive manufacturing

  • Much, Nils (Technical University of Munich)
  • Schreter, Magdalena (Technical University of Munich)
  • Munch, Peter (University of Augsburg)
  • Kronbichler, Martin (University of Augsburg)
  • Wall, Wolfgang A (Technical University of Munich)
  • Meier, Christoph (Technical University of Munich)

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In powder bed fusion (PBF) additive manufacturing (AM), thin layers of metal powder are selectively molten by a laser beam to form the cross-sections of the final part. Because it is a comparatively young technology, the interplay between process parameters and part quality is not yet fully understood. In particular, the complex melt pool and vapor dynamics arising from typical process conditions may entail quality-degrading defects, such as evaporation-induced pores, spatter, and lack of fusion. State-of-the-art melt pool models showed that surface tension, Marangoni convection and evaporation-induced recoil pressure are the mayor driving forces having a significant influence on the melt pool shape. While most existing models assume spatially fixed powder particles, in our recent contribution also coupled fluid-powder dynamics have been considered. In the present work, a new high-fidelity model for the melt pool thermo-hydrodynamics processes is presented. The focus lies on a mathematically consistent description of the underlying multi-phase flow problem, employing a conservative level-set approach to track the diffuse phase interfaces. The two-phase flow system melt/gas is governed by extreme interface forces due to temperature-dependent surface tension and evaporation-induced recoil pressure, which are particularly challenging from a numerical point of view. Thus, to improve the robustness of the computational model in presence of steep gradients in material properties and strongly localized forces across the interface, we discuss the usage of parameter-scaled interface Delta-functions in the context of continuum interface flux modeling. The model is discretized in space using the finite element method and employs implicit time stepping. Adaptive meshing schemes are applied to guarantee a high spatial mesh resolution in the interface region. In combination with highly efficient matrix-free solvers based on sum-factorization techniques, the resulting modeling framework is capable of capturing practically relevant scales.