Radiative transfer, absorption, and reflection by metal powder beds in laser powder-bed processing

Laser powder-bed processing is widely employed in 3D printing. The technological processes strongly depend on such effective radiative-transfer properties of powder beds as the absorptance and the radiation penetration depth. However, it is still not completely clear what are the principal factors influencing these properties and what are the possible ranges of their variation. For theoretical investigation of the radiative transfer, a ray-tracing method is developed where the effective properties of powder beds are expanded in series of the reflectance of the solid-phase surface. Once the coefficients of the power series are calculated, they can be used for any combination wavelength/material thus facilitating parametric analysis. Powder beds are modeled by equal spheres packed in regular cubic-symmetry structures of various density. The calculated radiation penetration depth can vary from few particle diameters for close-packed structures with moderate solid-phase absorptance to few tens of particle diameters for less dense power beds of a highly reflecting material. The effective absorptance of the powder bed is revealed to decrease significantly with the packing density. The calculated dependence of the powder-bed absorptance versus the solid-phase absorptance and the density is validated by the known experimental data. The calculated angular distribution of the radiation reflected by a powder bed slightly deviates from the cosine-like distribution corresponding to the diffuse reflection law. It is validated by the known experimental data. A modified model of equivalent medium is proposed to approximate the obtained ray tracing results by analytic expressions. (C) 2020 Elsevier Ltd. All rights reserved.