Semi-Analytical Thermal Modelling of Laser Powder Bed Fusion Process: Influence of Laser Source shapes on Defects studied through Process Maps

Abstract

Laser Powder Bed Fusion (L-PBF) is a metal additive manufacturing process in which localized melting and rapid solidification govern the formation of successive layers. The focused and transient nature of the laser–material interaction makes the thermal history and melt-pool geometry highly sensitive to parameters such as laser power, scan velocity, and spatial energy distribution. Most thermal models represent the laser as a Gaussian heat source, which captures energy concentration near the beam center, but often overestimates temperature gradients and underestimate uniform heating regions. Alternative non-Gaussian profiles, such as square or top-hat intensity distributions, offer a more uniform power density that can reduce peak temperatures, limit keyhole instability, and promote consistent melt-pool formation. However, the quantitative influence of these beam-shape variations on melt-pool morphology, thermal stability, and defect formation remains inadequately characterized, underscoring the need for systematic modeling of non-Gaussian source effects in L-PBF.
In this study, a semi-analytical thermal model is utilized to investigate the influence of different laser source shapes on the melt-pool geometry and thermal history during single-track scanning of Ti-6Al-4V. The model simulates the temperature evolution by representing the moving laser spot as a finite set of heat sources. The temperature field is obtained by superimposing analytical solutions for heat sources in a semi-infinite medium. To accurately account for boundary effects, a finite-difference correction field is superimposed on the analytical solution. The analytical temperature field for different source shapes is obtained by convolving the laser intensity distribution with the Green’s function solution of the transient heat conduction equation. The model computes three-dimensional temperature transients and extracts melt-pool width and depth based on the isotherm corresponding to the alloy’s melting temperature. A parametric computational study across a wide range of laser powers and scan velocities is performed to construct Power–Velocity (PV) process maps, identifying regimes of conduction, lack-of-fusion, and keyholing. Results show that non-Gaussian profiles, such as top-hat beams, significantly expand the defect-free window by promoting uniform melt-pool geometry and reducing thermal gradients. The proposed framework offers a physically consistent and computationally efficient approach for predicting temperature fields and defect formation, enabling process optimization and laser beam design in advanced L-PBF systems.