K. Tello, U. Duman, P. F. Mendez, Colorado School of Mines, Golden, CO
This paper presents exciting 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. Their simplicity and accuracy makes them especially suitable for process control. Scaling is a proven technique for the synthesis, generalization, and extrapolation of knowledge across systems in physics, applied mathematics, and many engineering disciplines. Judging by the impact of scaling on those other disciplines, their application to the field of welding holds enormous potential. Paradoxically, scaling techniques are not frequently applied in the welding field, and the results in those cases not always find widespread acceptance. This paper will focus on the recent development of scaling laws for three distinct welding questions: arc diameter and temperature in GTAW, 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 temperature, a set of scaling laws will be presented and compared to numerical results for a variety of currents in argon and air. For penetration during high current arc welding, the corresponding scaling law will be compared to experiments in stainless steel, carbon steel, and two aluminum alloys. Contrary to normal expectations, penetration in this case is not significantly influenced by surface active elements. 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.
Summary: This paper presents exciting recent advances in the modeling of welding using scaling laws. Modeling efforts to capture arc properties, weld penetration, and friction stir welding behavior will be described and compared to numerical models and experiments. The range of validity of the scaling laws is presented.
