Analytical solutions for rapid prediction of transient temperature field in powder-fed laser directed energy deposition based on different heat source models

The present paper aims to develop an effective analytical solution for laser directed energy deposition through powder feeding (LDED-PF). Three heat source models are introduced and compared to analytically describe the transient temperature field in the process. These models are known as point (1D) heat source, circular (2D) heat source, and semi-spherical (3D) heat source. For the validation tests, single-track deposition of Ti-5Al-5 V-5Mo-3Cr powder on Ti-6Al-4 V substrate is conducted at different laser powers, scanning speeds, and powder feed rates. The temperature field is validated using the measurement of melt-pool/deposit geometry. In order to improve the model fidelity, the enhanced thermal diffusivity and heat source radius are calibrated in terms of linear functions. It is found that the 2D Gaussian heat source model, which is in agreement with the underlying physics of the process, establishes a better match between the predicted and experimental data. The developed model only needs the basic information from the LDED-PF setup and material thermal properties to predict the thermal history and melt-pool geometry at different processing parameters.