Laser powder bed fusion 3D printing requires a great deal of effort to make sure that quality parts are being produced – and there are a lot of things that can go wrong with metal prints, such as porosity and residual stress, which causes distortion and part failure. Therefore, it is important to optimize the machine parameters as much as possible. In a paper entitled “3-Dimensional heat transfer modeling for laser powder-bed fusion additive manufacturing with volumetric heat sources based on varied thermal conductivity and absorptivity,” eight 3D heat sources used for simulating laser powder bed fusion are compared, and new equations for varied thermal conductivity and laser absorptivity are proposed.

The schematic of the heat source models, (a) cylindrical shape; (b) semi-spherical shape; (c) semi-ellipsoidal shape; (d) conical shape, (e) radiation transfer method; (f) ray-tracing method; (g) linearly decaying method; (h) exponentially decaying method.

“The physical phenomena associated in a melt pool are highly complicated, mainly controlled by mass and heat transfer,” the researchers explain. “The heating and cooling rates are extremely high due to the fast-moving laser irradiation on the powder particles. In addition, the dynamic melt pool development beneath the powder-bed, phase change dynamics from liquid to vapor and plasma, and powder particles drawn by high-speed metal vapor flux and capillary effects exist in the melt pool. Therefore, fine-scale numerical models, which included several details, such as laser-ray tracing in randomly distributed particles and thermal fluid dynamics, have been built in order to simulate several complex melt pool behaviors. However, the computational cost for such simulations is extremely high.”

Therefore, the researchers propose effective simulation models with certain approximations and assumptions to predict the dimensions of melt pools, in order to reduce the computational time.

Experiments were carried out on an EOS M 290 machine. A 3D heat transfer finite element model for laser powder bed fusion was developed for accurately predicting melt pool dimensions and surface features.

Temperature-dependent thermal material properties (a) density of SS17-4PH; (b) thermal conductivity of SS17-4PH; (c) heat capacity of SS17-4PH; (d) material properties of mild carbon steel.

“Based on the literature review, eight heat source models are used for the numerical modeling of LPBF and can be categorized as 1) geometrically modified group (GMG); and, 2) absorptivity profile group (APG),” the researchers state. “Experiments were carried out to validate the simulation results. All the eight heat source models lead to over 40% shallower melt pools compared with the experiments.”

Stainless steel powder particles

To improve the model performance, a mathematical model with varied anisotropically enhanced thermal conductivity and varied absorptivity was proposed and applied to the heat transfer simulation with the exponentially decaying heat source.

The researchers came to two main conclusions:

“The expressions of varied anisotropically enhanced thermal conductivity and varied absorptivity were linear algebraic equations,” they state. “Good agreement between the simulation and the experimental results was derived. The averaged error of melt pool width and depth are 2.9% and 7.3%, respectively.

“The proposed heat transfer model has been further validated by the surface features, track stability and ripple angle. For the track stability, the predicted results are in good agreement with the experimental results. In addition, the simulated ripple angles are within the range of experimental results.”

They also concluded that the heat source expressions can be linear while causing the simulation results to be in better agreement with both experimental melt pool dimensions and track surface morphology.

Authors of the paper include Zhidong Zhang, Yuze Huang, Adhitan Rani Kasinathan, Shahriar Imani Shahabad, Usman Ali, Yahya Mahmoodkhani, and Ehsan Toyserkani.

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