Analytical Thermal Modeling of Powder Bed Metal Additive Manufacturing Considering Powder Size Variation and Packing.

This work presents a computationally efficient predictive model based on solid heat transfer for temperature profiles in powder bed metal additive manufacturing (PBMAM) considering the heat transfer boundary condition and powder material properties. A point moving heat source model is used for the three-dimensional temperature prediction in an absolute coordinate. The heat loss from convection and radiation is calculated using a heat sink solution with a mathematically discretized boundary considering non-uniform temperatures and heat loss at the boundary. Powder material properties are calculated considering powder size statistical distribution and powder packing. The spatially uniform and temperature-independent material properties are employed in the temperature prediction. The presented model was tested in PBMAM of AlSi10Mg under different process conditions. The calculations of material properties are needed for AlSi10Mg because of the significant difference in thermal conductivity between powder form and solid bulk form. Close agreement is observed upon experimental validation on the molten pool dimensions.

Analytical Thermal Modeling of Metal Additive Manufacturing by Heat Sink Solution.

Metal additive manufacturing can produce geometrically complex parts with effective cost. The high thermal gradients due to the repeatedly rapid heat and solidification cause defects in the produced parts, such as cracks, porosity, undesired residual stress, and part distortion. Different techniques were employed for temperature investigation. Experimental measurement and finite element method-based numerical models are limited by the restricted accessibility and expensive computational cost, respectively. The available physics-based analytical model has promising short computational efficiency without resorting to finite element method or any iteration-based simulations. However, the heat transfer boundary condition cannot be considered without the involvement of finite element method or iteration-based simulations, which significantly reduces the computational efficiency, and thus the usefulness of the developed model. This work presents an explicit and closed-form solution, namely heat sink solution, to consider the heat transfer boundary condition. The heat sink solution was developed from the moving point heat source solution based on heat transfer of convection and radiation. The part boundary is mathematically discretized into many heats sinks due to the non-uniform temperature distribution, which causes non-uniform heat loss. The temperature profiles, thermal gradients, and temperature-affected material properties are calculated and presented. Good agreements were observed upon validation against experimental molten pool measurements.

Analytical Modeling of In-Process Temperature in Powder Bed Additive Manufacturing Considering Laser Power Absorption, Latent Heat, Scanning Strategy, and Powder Packing.

Temperature distribution gradient in metal powder bed additive manufacturing (MPBAM) directly controls the mechanical properties and dimensional accuracy of the build part. Experimental approach and numerical modeling approach for temperature in MPBAM are limited by the restricted accessibility and high computational cost, respectively. Analytical models were reported with high computational efficiency, but the developed models employed a moving coordinate and semi-infinite medium assumption, which neglected the part dimensions, and thus reduced their usefulness in real applications. This paper investigates the in-process temperature in MPBAM through analytical modeling using a stationary coordinate with an origin at the part boundary (absolute coordinate). Analytical solutions are developed for temperature prediction of single-track scan and multi-track scans considering scanning strategy. Inconel 625 is chosen to test the proposed model. Laser power absorption is inversely identified with the prediction of molten pool dimensions. Latent heat is considered using the heat integration method. The molten pool evolution is investigated with respect to scanning time. The stabilized temperatures in the single-track scan and bidirectional scans are predicted under various process conditions. Close agreements are observed upon validation to the experimental values in the literature. Furthermore, a positive relationship between molten pool dimensions and powder packing porosity was observed through sensitivity analysis. With benefits of the absolute coordinate, and high computational efficiency, the presented model can predict the temperature for a dimensional part during MPBAM, which can be used to further investigate residual stress and distortion in real applications.