Analytical estimation of fusion zone dimensions and cooling rates in part scale laser powder bed fusion

The laser powder bed fusion process is increasingly used for the building of metallic parts by melting and solidification of alloy powders under a fast-moving finely focussed laser beam. A quick estimation of the resulting temperature field, fusion zone dimensions, and cooling rates is needed to ensure the manufacture of dimensionally accurate parts with minimum defects. A novel three-dimensional analytical heat transfer model with a volumetric heat source that can simulate the laser powder bed fusion process in part scale quickly and reliably is proposed here. The volumetric heat source term is constructed to analytically simulate the evolution of melt pools with a fair range of depth to width ratio. The proposed analytical model can simulate the building of multiple tracks and layers in part scale dimensions significantly faster than all the numerical models reported in the literature. The computed results of fusion zone shapes and sizes and cooling rates are found to be in good agreement with the experimentally reported results in builds of three commonly used alloys with diverse materials properties, SS316L, Ti6Al4V, and AlSi10Mg. Based on the analytically computed results, a set of easy-touse process maps is presented to estimate multiple process conditions to obtain a set of target fusion zone dimensions without trial-and-error testing.