Microstructure evolution in metal additive manufacturing (AM) is a complex multi-physics and multi-scale problem. Understanding the impact of AM process conditions on the microstructure evolution and the resulting mechanical properties of the printed part is an active area of research. At the meltpool scale, the thermo-fluidic governing equations have been extensively modeled in the literature to understand the meltpool conditions and the thermal gradients in its vicinity. In many phenomena governed by partial differential equations, dimensional analysis and identification of important dimensionless numbers can provide significant insights into the process dynamics. In this context, a novel strategy using dimensional analysis and the method of linear least squares regression to numerically investigate the thermo-fluidic governing equations of the Laser Powder Bed Fusion AM process is presented in this work. First, the governing equations are solved using the Finite Element Method, and the model predictions are validated by comparing with experimentally estimated cooling rates, and with numerical results from the literature. Then, through dimensional analysis, an important dimensionless quantity - interpreted as a measure of heat ab- sorbed by the powdered material and the meltpool, is identified. This dimensionless measure of heat absorbed, along with classical dimensionless quantities such as Peclet, Marangoni, and Stefan numbers, is used to investigate advective transport in the meltpool for different alloys. Further, the framework is used to study the variations of thermal gradients and the solidification cooling rate. Important correlations linking meltpool morphology and microstructure evolution related variables with classical dimensionless numbers are the key contribution of this work.

Laser powder bed fusion (LPBF) is an additive manufacturing process employed in many industries, for example for aerospace, automotive and medical applications. In these sectors, mainly nickel-, aluminum- and titanium-based alloys are used. In contrast, the mechanical engineering industry is interested in more wear-resistant steel alloys with higher hardness, both of which can be achieved with a higher carbon content, like in high-speed steels. Since these steels are susceptible to cracking, preheating needs to be applied during processing by LPBF. In a previous study, we applied a base plate preheating temperature of 500 °C for HS6-5-3-8 with 1.3 % carbon content. We were able to manufacture dense (p > 99.9 %) and crack-free parts from HS6-5-3-8 with a hardness > 62 HRC (as built) by LPBF. In this study, we investigate the influence of preheating temperatures up to 600 °C on hardness and microstructure dependent on part height for HS6-5-3-8. The microstructure was studied by light optical microscopy (LOM), scanning electron microscopy (SEM) and electron backscatter diffraction (EBSD). The analysis of hardness and microstructure at different part heights is necessary because state-of-the-art preheating systems induce heat only into the base plate. Consequently, parts are subjected to temperature gradients and different heat treatment effects depending on part height during the LPBF process.