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 requires 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 so-
lutions 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.