Semi-analytical modeling columnar-to-equiaxed transition during metal powder bed fusion

Columnar-to-equiaxed transition (CET) is crucial to the microstructure design and mechanical performance optimization of metallic parts via powder bed fusion (PBF). It is essential to effectively understand the CET behavior under various process conditions. However, the straightforward relation between process parameters, porosity, and CET of PBF-built alloys remains unclear. To address this, this paper develops an integrated semi-analytical modeling framework to efficiently characterize the CET behavior of multicomponent alloys under various process settings. The thermal behavior of multicomponent alloys during PBF is first predicted based on the differential quadrature method combined with the rule of the mixture. Subsequently, the thermal-induced porosity, element diffusion, rapid solidification, undercooling, and nucleation distributions are comprehensively formulated to analytically capture the CET in PBF-built multicomponent alloys. The predicted model is validated by the comparisons with the reported CET behaviors of five typical multicomponent alloys during PBF. Additionally, the crucial process parameters on the thermal-induced CET during metal PBF are demonstrated, including the energy density, preheating temperature, heat source dimension, part dimension, and compositional content. The results show that the ratio of process-related thermal gradient and solidification velocity plays a dominant role in the CET during metal PBF. When higher energy density or lower preheating temperature is used, the growth of equiaxed grains is significantly suppressed during solidification. In contrast, due to the reduction in thermal gradient, the growth of equiaxed grains is promoted with the increasing length-to-thickness ratio of as-built parts and heat source dimensions. In addition, the addition of ceramic particles can promote CET in the consolidation process of metal PBF. The findings can serve as a guideline for the design and printing of multicomponent alloys with desired mechanical properties.