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The friction stir welding (FSW) process consists essentially of a rotating tool, which travels along the joint of two restricted plates. The union results from the frictional heating induced by the tool, which leads to a viscoplastic material flow between the joined plates. A complete analysis of the FSW process requires the solution of a thermo-mechanical coupled problem. Due to the considerably large plastic deformation involved, an Eulerian viscoplastic flow formulation on a fixed domain is usually employed to mathematically describe the prob- lem. Nevertheless, when the details of the tool must be taken into account the symmetry of the problem about the rotation axis of the pin is definitively lost. In this regard, an effective strat- egy to deal with this difficulty is to attach a rotating domain to the pin. Moreover, an arbitrary Lagrangian-Eulerian (ALE) formulation is used for irregular tool geometries, considering a convenient rotating domain to precisely track the details of the tool surface. The purpose of this work is to implement a domain decomposition technique in order to ex- ploit the advantages of both formulations. Hence, the whole domain is decomposed into two non-overlapping sub-domains in accordance with the particularities of each region. Con- sequently, a rotating region close to the tool is adopted while a fixed domain surrounding it is considered to appropriately take into account the inlet and outlet boundary conditions. Thereby, a coupling problem on the common boundary to both sub-domains must be solved. In this work a coupling strategy based on an iterative GMRES technique in its matrix free form is adopted. The application of this methodology allows to determine the material flow and temperature field considering the specific details of the tool and welding plates geometries in an efficient and easy to implement manner.

THERMO-MECHANICAL MODELING OF FRICTION STIR WELDING PROCESS VIA AN ITERATIVE MATRIX FREE GMRES DOMAIN DECOMPOSITION TECHNIQUE