Physics guided heat source for quantitative prediction of IN718 laser additive manufacturing processes

Additive manufacturing (AM) processes such as laser powder bed fusion (LPBF), selective laser melting (SLM), and directed energy deposition (DED) for metal alloys enable complex, lightweight parts but face qualification and certification challenges due to process variability and resulting defects. Government-led benchmarks (NIST/AFRL AM Bench 2018, 2020, 2022) have provided high-quality experimental datasets to drive predictive modeling capabilities. This study targets NIST AM Bench 2022 Challenge 3, which explored the effects of laser power, scan speed, and spot diameter on single and multi-track scans on IN718 bare plates, with in-situ process monitoring of liquid/solid cooling rates and time above melting and ex-situ melt pool geometry and microstructure. The research problem is to develop computationally efficient yet quantitatively accurate models to predict melt pool geometry and thermal metrics (solid/liquid cooling rates, time above melt) across a wide operating envelope without resorting to prohibitively expensive full-physics simulations. The work investigates simplified, calibrated cylindrical laser heat source models integrated in a thermal-fluid solver and proposes physics-guided parameterizations linked to volumetric energy density and keyhole scaling to improve predictions, especially at higher energy densities.

Modeling approaches for LPBF range from pure heat conduction to fully coupled thermal-fluid models incorporating Marangoni convection and vaporization. Pure conduction models are computationally efficient but cannot capture melt pool convection and tend to overestimate melt pool depth. Introducing effective conductivities can partially compensate but lacks fidelity. Thermal-fluid models that include Marangoni flow better predict melt pool dimensions; neglecting Marangoni flow overestimates depth. Vaporization physics is critical for accurate cooling rate prediction and width; ignoring it leads to overestimated temperatures and cooling rates. At high volumetric energy density (VED), keyhole formation dominates and requires accounting for surface evolution, multiple reflections, dynamic heat input, and attenuation through vapor plumes (e.g., Beer–Lambert law). However, full-physics part-scale simulations are computationally prohibitive, motivating model reduction and calibration. Recent reduced-order strategies (e.g., HOPGD-based surrogates) have been applied to calibrate heat source parameters effectively. A universal keyhole scaling (Keyhole number, Ke) has been proposed to capture keyhole stability and porosity, offering a pathway to inform heat source parameterization when keyholes are present. Literature melt pool data for IN718 have been used for calibration and validation, showing that simple volumetric sources perform well at lower VED but underpredict depth at higher VED where keyholing becomes important.

Experiments: NIST AM Bench 2022 Challenge 3 used IN718 bare plates (no powder) on the AMMT platform. Single-track experiments spanned seven process conditions by varying power, scan speed, and spot diameter; multi-track (pad) scans used base settings. In-situ measurements: time-resolved laser coupling, liquid and solid cooling rates, and time above melting; ex-situ: cross-sectional melt pool geometry and microstructure. Base laser: 285 W, 960 mm/s, Gaussian spot diameter 67 μm.

Computational framework: An in-house C++ finite volume method (FVM) CFD code (AM-CFD) solves a transient 3D thermal-fluid model with Marangoni-driven melt flow and a calibrated cylindrical volumetric heat source. The governing equations include mass conservation, Navier–Stokes with buoyancy and mushy-zone resistance, and energy conservation with temperature-dependent properties and latent heat via an enthalpy method. Surface boundary conditions include radiative, convective, and evaporative heat losses; the top surface enforces Marangoni shear stresses. The melt pool region is defined using liquid fraction derived from solidus/liquidus temperatures.

• Governing physics: Navier–Stokes momentum with viscosity, gravity/buoyancy; energy equation with conduction and source terms; enthalpy formulation includes sensible heat and latent heat of fusion; mushy-zone momentum sink based on permeability approximation; surface losses modeled via Stefan–Boltzmann radiation, convection coefficient, and evaporation flux dependent on latent heat of vaporization and evaporation coefficient. Marangoni stresses are applied using temperature-dependent surface tension (negative Marangoni coefficient). Liquid fraction defines mushy and liquid regions.
• Adaptive meshing: Bias-controlled structured control volumes with a moving, high-resolution subdomain that tracks the laser; state variables are transferred between time steps via linear interpolation. This reduces cost while maintaining accuracy in the melt pool region.
• Material properties: Temperature-dependent properties for IN718 compiled from literature (e.g., solid/liquid densities, solidus 1533 K and liquidus 1609 K, Cp, thermal conductivities, latent heat of fusion, viscosity, thermal expansion, surface tension, Marangoni coefficient).

Heat source modeling and calibration: A cylindrical Gaussian volumetric heat source represents laser heating. Process parameters (power P, scan speed V, spot radius r0) and an absorptivity η determine the source; residual heat factor (RHF) accounts for preheating from prior tracks in pads (RHF=1 for single tracks). Calibration employs a surrogate HOPGD model to minimize discrepancies between predicted and measured melt pool width and depth using literature datasets (e.g., Balbaa et al.). Three parameterization schemes are developed:

• Heuristic heat source parameterization: d, η, and beam radius rb scale with sqrt(P/(V η RHF^2)); volumetric source is Gaussian radially and truncated at depth d. Parameters P1–P3 are identified by minimizing an objective function over melt pool width/depth against literature data via HOPGD.
• Scaling law-based parameterization: Uses the keyhole number Ke to inform depth d=p1(Ke(p2) − 1.4), absorptivity η=max{0.7[1−exp(−0.6Ke(p2))], p2}, and rb=P3 L (normalized diffusion length). Intended for regimes with active keyholing.
• Physics-guided parameterization: Correlates volumetric energy density (VED) to heat source depth, aspect ratio, and energy input: d=P1√(Vo)RHF^2/2; η=max(P2√(Vo), 1); rb=P3(√(Vo)/2)RHF^2. This modification captures melt pool geometry trends at higher VED and links to aspect ratio.

Simulation protocol: For each NIST case, preliminary runs established time to steady-state melt pool length (~1–3 ms, corresponding to 1–3 mm scan distance at 960 mm/s), enabling reduced computational domains. Thermal histories at steady state were used to calculate cooling rates and time above melting following NIST definitions: solid cooling rate via linear fit between 1260 °C and 1150 °C; liquid cooling rate via linear fit between 1400 °C and 1336 °C; time above melt as time above midpoint temperature (1298 °C) from temperature–time curves mapped from spatial midline profiles using scan speed. Multi-track predictions included overlap width/depth and thermal metrics at specified pad locations (P2, P3).

• The cylindrical heat source calibrated with a HOPGD surrogate against literature IN718 melt pool data predicts melt pool width and depth well at low VED (< ~70 J/mm³), but underestimates depth at higher VED due to missing keyhole/surface-evolution physics.
• For NIST single-track cases, steady state is reached rapidly (~1 ms for low VED and ~3 ms for high VED), allowing reduced domains without sacrificing accuracy.
• Solid cooling rates: Heuristic calibration overestimates solid cooling rates at higher VED due to non-physical peak temperatures from missing vaporization and keyhole energy losses. Scaling-law calibration underestimates slightly. The physics-guided scheme yields much more comparable solid cooling rates across cases, improving agreement with experiments.
• Liquid cooling rates show similar trends: better agreement at lower VED, overestimation at higher VED for heuristic calibration; physics-guided calibration improves predictions, though some limitations remain (e.g., case 2.2).
• Time above melting (TTAM): Differences between prediction and experiment are smaller than for cooling rates because heat source calibration is tied to melt pool geometry; physics-guided calibration reduces TTAM error to below 20% across cases.
• Melt pool geometry (single-track): Physics-guided calibration brings predictions within about 5% of experimental values for width and depth across all seven process conditions; aspect ratio trends versus VED are captured better by the physics-guided scheme than by heuristic or scaling-law schemes.
• Multi-track (pad) cases: Predicted melt pool dimensions and thermal metrics generally agree within ~10% of experiments. However, melt pool morphology and overlap metrics can deviate substantially (overlap depth/width differences up to ~55%) due to omission of surface evolution and gas flow effects; alternating melt pool depths along Y-scan direction suggest unmodeled gas flow influence.
• Relative error analysis (Table 2 in paper) shows the physics-guided heat source consistently yields the lowest errors for melt pool dimensions compared to heuristic and scaling-law schemes, while cooling rate errors are significantly reduced but not eliminated at higher VED.
• Overall, linking heat source parameterization to VED and aspect ratio and incorporating keyhole-informed scaling markedly improves quantitative prediction without the cost of full keyhole/resolved surface models.

The study addresses the challenge of quantitatively predicting melt pool geometry and thermal histories across diverse LPBF process conditions with manageable computational cost. By calibrating a simplified cylindrical heat source via surrogate modeling and guiding parameterization with measurable quantities (VED, aspect ratio) and keyhole scaling, the approach captures the dominant effects of laser–material interaction needed for accurate melt pool width/depth and acceptable thermal metrics. The findings demonstrate that errors in cooling rates at high VED largely stem from neglected physics (vaporization, dynamic absorptivity, multiple reflections, plume attenuation, surface evolution). Incorporating these effects implicitly through physics-guided parameterization significantly mitigates overprediction while preserving efficiency. The improved agreement in TTAM and melt pool aspect ratio indicates that tying the heat source depth and energy deposition to VED-based scaling aligns the model with experimental observables across regimes from conduction to transitional/keyhole. Multi-track results highlight that while global dimensions are well captured, detailed morphology and overlap are sensitive to surface dynamics and gas flow, suggesting where additional physics would most benefit future predictions. The work underscores that careful heat source parameterization is crucial for reliable part-scale predictions when full-physics models are computationally infeasible.

Three cylindrical heat source calibration schemes were developed and assessed against NIST AM Bench 2022 Challenge 3 for IN718 single- and multi-track LPBF on bare plates. The initial heuristic scheme performs adequately at low VED but degrades at higher VED. A scaling law-based scheme informed by the keyhole number improves predictions in keyhole regimes. A physics-guided scheme that relates VED to heat source depth, radius, energy input, and melt pool aspect ratio provides the best overall accuracy: single-track melt pool dimensions within ~5% of experiments, TTAM differences below ~20%, and multi-track dimensions within ~10%. The approach enables quantitative predictions while avoiding the cost of explicitly modeling surface evolution and multiple reflections. Future work should integrate or better approximate missing physics—surface evolution, dynamic absorptivity and plume attenuation, vaporization-driven recoil pressure, and shielding gas flow effects—to further improve cooling rate predictions and melt pool morphology/overlap accuracy, and extend to multi-layer, part-scale simulations.

• The model omits explicit surface evolution, multiple reflections, and Beer–Lambert attenuation through the vapor plume; consequently, dynamic changes in heat input are not resolved, leading to overestimated peak temperatures and cooling rates at high VED when calibrated heuristically.
• Vaporization physics is included as a surface loss but detailed keyhole dynamics (recoil pressure-driven cavity, free surface deformation) are not modeled; depth underprediction at high VED occurs without physics-guided parameterization.
• Gas flow effects (shielding flow direction/magnitude) are not included; multi-track Y-scan depth alternation and overlap differences suggest sensitivity to unmodeled gas flow.
• Morphology and overlap predictions can deviate substantially (overlap depth/width differences up to ~55%) despite good agreement in global dimensions.
• Some parameterizations (e.g., scaling law-based) perform poorly outside their intended regime (low VED, no keyhole).
• Material properties are compiled from literature; uncertainties in temperature dependence can affect predictions.
• Publication provides incomplete affiliations for some authors; not relevant to method but noted in metadata.