Upper bound analysis of friction stir spot welding of 6061-T6 aluminum alloys

Most of the research on friction stir spot welding (FSSW) process has been conducted experimentally. Finite element method (FEM) has been also used to analyze the process, which typically requires large computation time because of mesh. Therefore, in this study, the FSSW process was analyzed using the upper bound method to save computation time. In the upper bound analysis, the velocity fields of the torsional backward extrusion process were modified using a dual-stream function, which reduces the number of unknowns while satisfying the incompressibility condition. For comparison, FEM was also used to analyze the FSSW process. The forming load was calculated at various tool rotational speeds, and the temperatures predicted by the upper bound method and the FEM were compared with the thermocouple measurements. The computation time of the upper bound analysis was only 1.4% of the FEM. The temperatures predicted by the upper bound analysis were slightly higher than those of the FEM and the experimental results, but a similar trend was obtained.