Simplified Two-Dimensional Analytical Model for Friction Stir Welding Heat Transfer

A two-dimensional heat transfer problem pertaining to friction stir welding is developed by converting various pin tool configurations of interest to a simplified pin only configuration by assigning an equivalent heat flux to the pin surface. Mechanical dissipation heating, responsible for the welding, is modeled by means of a thermal boundary condition at the pin surface. A series solution is developed for the temperature distributions in the workpiece (assumed to be infinite) and these distributions are analyzed at various radial and circumferential locations. It is found that the closed form solutions developed are not influenced greatly by the truncation numbers of this series. Maximum reduced temperatures pertinent to configurations available in literature are estimated from the series and one term solutions developed and compared with those observed. Furthermore, the applicability of one term solution of this series is tested for various parametric combinations based on models available in literature. It is found that the one term solution can be applied to within a reasonable range of the process governing parameters.