Scaling Laws for the Welding Arc, Weld Penetration and Friction Stir Welding

This paper presents recent advances in the modeling of welding using scaling laws. Scaling laws based on the governing equations of transport phenomena provide closed form mathematical expressions that capture the essence of a welding process explicitly. The work focuses on the recent development of scaling laws for three distinct welding issues: characterization of the arc welding in GTAW, depth penetration in high current welding, and temperature and extent of shearing in FSW. These three processes involve multiple coupled physical phenomena, such that the determination of the dominant phenomena from the governing equations can involve up to several thousand iterations. For the arc diameter and the velocity of the plasma in the arc welding, a set of scaling laws will be presented and compared to numerical results for a variety of currents in argon and air. For depth penetration during high current arc welding, the corresponding scaling law will be compared to experiments in stainless steel, carbon steel, and two aluminum alloys. Finally, a set of scaling laws for the coupled thermomechanical problem of friction stir welding will be introduced and compared with published data. In all cases, the range of validity of the scaling laws will be established based on a rigorous description of the limits of the asymptotic regimes.