Scaling of coupled heat transfer and plastic deformation around the pin in friction stir welding

This paper presents a coupled phenomenological model of heat transfer and plastic flow around the pin in friction stir welding (FSW). The approach is analogous to the boundary layer analysis in fluid mechanics, and is based on the methodology of scaling. The results are a set of novel closed-form expressions for the maximum temperature reached in the process, the thickness of the shear layer, the shear stress around the pin, the torque and the thermal effect of the shoulder. The model presented focuses on the most common conditions encountered in the practice of FSW, which involve relatively slow translation velocities, relatively high rotation velocities and thin shear layers. The ultimate purpose of this model is to provide simple and accurate expressions useful for providing a temperature and strain rate context for metallurgical analysis of FSW and for the selection of process parameters when using FSW to join novel alloys.