Quasi-steady modeling of friction stir welding heat transfer

Friction Stir Welding (FSW) has been an area of concentrated research for the past few years owing to its many advantages over conventional forms of welding. The primary objective of the current study was to formulate quasi-steady models of FSW heat transfer. For this, the mechanical dissipation heating responsible for the weld was treated as a function of the workpiece yield stress and melting temperature and was modeled as a thermal boundary condition on the pin tool surfaces. Subsequently, governing equations are developed for three pertinent configurations and closed form solutions (in the form of series solutions) were derived for heat transfer around a cylindrical source in a 2D infinite domain using a simplified "pin only" FSW configuration. The solutions were compared with numerical results and it was found that the maximum error was around 1% at the pin surface. It was also shown that the one term solution was applicable to within a reasonable range of the governing FSW parameters.;Numerical models of quasi-steady heat transfer (infinite length models) were developed for three pertinent FSW configurations using FLUENT and it was shown that the partial and full penetration models predict similar maximum temperatures, while the self-reacting model predicts a higher value (for the same heating). The numerical formulation was later extended to typical models available in literature and it was shown that, in general, the quasi-steady formulation replicates the reference data both qualitatively and quantitatively. Further, FSW heat transfer was shown to be quasi-steady from the pin tool point of view by studying the temperature distributions at the pin surface for varying locations in finite domains representative of actual FSW configurations. It was found that the temperature distributions were independent of the tool location. It was concluded that this formulation due to its simplicity and minimal usage of computational resources can be used to predict FSW temperatures accurately without resorting to unsteady models.