Modeling the physics and the mechanics of a friction stir welding process (FSWP) is very challenging because of the intrinsic coupling between thermal and mechanical phenomena and the occurrence of extremely large deformations. Mathematically, the analysis of a FSWP requires studying a three-dimensional (3-D) convection-diffusion-reaction problem under appropriate initial and complex boundary conditions. The multi-physics interaction results in complex flow patterns which make the FSWP useful in engineering applications. We note that the material deformation and flow in a FSWP is shear dominated with significant heat flux generated at the boundaries and from the energy dissipated during plastic deformations. Accordingly, key features of the process can be delineated by studying simple shearing deformations of a thermo-elasto-viscoplastic material with both the tangential velocity and the heat flux prescribed at the boundaries as was done in [1] to analyze the localization of deformation near the boundaries. It was found that the prescribed heat flux at the boundaries makes the deformations inhomogeneous and introduces a nucleation site for the deformations to localize [1]. Subsequently, recognizing the severe deformations, even melting, caused by the sustained thermal softening, a fluid mechanics based lubrication approach was developed [2] and the results were compared with those available in the literature. The effect of the heat flux input on the flow pattern, such as the thickness of the localized flow zone, were revealed.
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