Prediction and analytical description of the single laser track geometry in direct laser fabrication from process parameters and energy balance reasoning

Direct laser fabrication (DLF) is a process for the manufacture of functional parts directly from powder injected in a laser beam. Deposition of 316L stainless steel powder on a steel substrate is carried out using a 700 W fiber laser for one module. One problem for this process is the control of the building structure dimensions. In this study a mathematical model implemented in the software Mathematica 8© is used to predict the clad cross-section dimensions and obtain an analytical description of the clad geometry. We experimentally notice that the cross-section shape is a disk due to the surface tension forces. Analytical relationships are established between the radius and the center of the disk in one hand and the process parameters in the other hand. This way we show that we can reproduce the laser track geometry in all the area experimentally explored. A number of laser tracks are deposited using a varying process parameter combination in order to compare with our calculation results. This analytical description of the clad geometry could be used in order to improve the calculation quickness of the thermal field induced by the process.

► A mathematical modeling is proposed to predict the shape and the cross section characteristics of a single laser track.
► Solution is obtained solving a geometrical balance equation between the powder mass deposited and the volume of the laser clad.
► Powder efficiency Pe and width W are needed to entirely determinate the clad geometry.
► Firstly, parametric relationships are used to determinate Pe and W from the process parameters.
► Secondly, an analytical thermal modeling is proposed to determinate the clad width.
► Confrontations between the mathematical modeling results and the experimental ones are very convincing.