Analytical description of the surface temperature for the characterization of laser welding processes

The simplified model of a point source on the top surface of a plate with finite thickness is used to describe the temperature field outside the melt pool during the welding process with concentrated energy input (laser or electron beam welding). Two limit regions defined by Rosenthal (1946) depending on the distance to the source are analyzed by deriving explicit analytical expressions for the size of these regions on the plate surface. An important outcome is how a finite plate thickness influences the temperature field on the surface, which is representative of the heat transport of information from the inside to the surface. The simplified model is further used to characterize the temperature field of the top surface by geometrical quantities of the melt pool and quantities describing the temperature decay in the heat affected zone outside the melt pool. In the limit regions the values of these quantities are derived analytically. Their scaling behavior with the feed rate and the source power is confirmed in a typical process regime by experiments with thermographic imaging during a laser welding process.