A semi-empirical model of the temperature field in the AISI 304 laser welding

The present paper is addressed to the modelling of the temperature field in a 304 stainless steel workpiece welded by a CW CO2 laser with a multimode power distribution. The proposed model is based on the well known Rosenthal solution, representing the laser beam action as a linear heat source delivering a constant heat rate along the workpiece thickness. In order to obtain a more realistic description of the temperature field, the hypothesis of a constant heat rate along the thickness is removed and replaced by a generic unknown function, to be determined from experimental data. Thanks to the superimposition principle, the solution for the above mentioned problem is obtained once that the unknown heat rate function is described in the frequency domain as a cosine series. A first experimental phase, extended to the whole processing window of the 304 stainless steel, was carried out and the correspondent bead profiles in the cross-section were measured. Then, by the application of the inverse thermal model, the coefficients of the cosine series were evaluated from the bead profiles measurements. At least, a synthetic formulation obtained by multiple regression technique was used to relate the coefficients of the cosine series to the significant process parameters, yielding a model that describes the temperature field as a function of laser process parameters. Starting from the temperature field, this model can be used to predict some related entities, such as the bead profile or the thermal stresses.