Understanding the structure and dynamics of local powder packing density variations in metal additive manufacturing using set Voronoi analysis

In powder bed fusion (PBF), the global packing density is an important property used to quantify the bulk behaviour of the powder. However, packing density can be highly non-uniform across the PBF system. In some cases global packing density is even ill-defined, such as in the case of spread powder layers which are typically only 1-2 particles thick and packed across a complex surface. However, an accurate calculation of the local packing density down to the resolution of individual particles can allow us to go beyond bulk descriptions and spatially quantify local powder packing density variations. In this paper, we present Set Voronoi tessellation as a precise method for calculating the local packing fraction of non-spherical particles across arbitrary boundaries. Using the Discrete Element Method (DEM) for a calibrated Ti-6Al-4 V powder model, we study the local packing variation in three critical sections of the PBF system. First, we analyse a discharging Hall flowmeter, a common apparatus used to benchmark the flowability of PBF feedstock. Second, we analyse the powder spreading process to understand how particle densities and velocities influence deposition. Lastly, we analyse the local packing variation across a realistic AM powder layer to demonstrate how layers can be digitally qualified to inform subsequent laser melting. Our work provides a novel technique to study the variations in the local packing structure of powders in dynamic PBF systems and to understand the mechanisms through which key process parameters influence final part quality.