A numerical investigation of dimensionless numbers characterizing meltpool morphology of the laser powder bed fusion process

TL;DR

This paper introduces a numerical and dimensional analysis approach to identify key dimensionless numbers influencing meltpool morphology in laser powder bed fusion, enhancing understanding of process dynamics and microstructure evolution.

Contribution

The work presents a novel strategy combining dimensional analysis and finite element modeling to identify and analyze critical dimensionless numbers in laser powder bed fusion.

Findings

Identified a key dimensionless quantity related to heat absorption in the meltpool.

Established correlations between meltpool morphology and classical dimensionless numbers.

Validated model predictions with experimental cooling rates and literature results.

Abstract

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 absorbed 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.