A semi-analytical solution for the transient temperature field generated by a volumetric heat source developed for the simulation of friction stir welding

The accurate prediction of transient temperature fields, induced in alloy systems during advanced manufacturing processes, is critical. These fields influence the magnitude and distribution of residual stresses, the evolution of material microstructures, and material properties such as fracture toughness. Such predictions in the vicinity of a concentrated heat source require precise knowledge of the associated heat flux as a function of position and time. If the applied thermal load is time-dependent this can have a significant effect on the resulting temperature fields and microstructures. In this work a novel three-dimensional heat source is proposed to represent the friction stir welding process along with the semi-analytical solution for the temperature field. The volumetric heat source model has a nontrivial spatial distribution constructed from physical arguments and may account for complex mass transfer, and the associated thermal effects, without explicitly solving the flow equations. A method for incorporating a time-dependent heating scenario into analytical solutions generated by this heat source is also presented. Predicted temperatures are compared with those measured experimentally for two cases reported in the literature and good agreement is observed. Example solutions for various time-dependent heat inputs are also presented.