Powder bed fusion with electron beam: The interplay of sintering, porosity, and coordination number in modelling the powder thermal conductivity through a novel tortuosity formulation

For the powder bed fusion with electron beam (PBF-EB) additive manufacturing, properties such as the thermal conductivity of the material surrounding the melting area are critical. Thermal conductivity is influenced by the extremely high temperature reached in a short time and distributed in the building area. This fast temperature growth produces sintering phenomena and the creation of a neck between the particles. Because of this sintering, measuring the thermal conductivity at the process conditions is challenging. This paper proposes an analytical formulation for estimating the effective powder bed thermal conductivity at the PBF-EB conditions, introducing a novel modelling strategy for the tortuosity factor. In a changing net of sintered powder particles, the proposed model for the tortuosity factor considers the neck evolution and the complexity of the heat transfer due to the several heat paths possible through the particle net. To show the effectiveness of the proposed model, the thermal conductivity is evaluated for three 3D structures characterised by an increasing number of powder particles and heat path complexity: a simple cubic, a body centred cubic and a portion of a powder bed. It is shown that thermal conductivity strongly depends on the arrangement of the particles in 3D space, the structure density and the complexity of the heat diffusion path (tortuosity). Also, the numerical results from the proposed model show good agreement when compared with finite element analysis and experimental literature data.