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            <title xml:lang="en">A 3D numerical simulation of different phases of friction stir welding</title>
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                <title xml:lang="en">A 3D numerical simulation of different phases of friction stir welding</title>
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                <term xml:lang="en">Aluminium alloys</term>
                <term xml:lang="en">models</term>
                <term xml:lang="en">mechanics</term>
                <term xml:lang="en">recovery</term>
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              <p>An adaptive arbitrary Lagrangian-Eulerian formulation is developed to compute the material flow and the temperature evolution during the three phases of the friction stir welding (FSW) process. It follows a splitting approach: after the calculations of the velocity/pressure and temperature fields, the mesh velocity is derived from the domain boundary evolution and from an adaptive refinement criterion provided by error estimation, and finally state variables are remapped. In this way, the unilateral contact conditions between the plate and the tool are accurately taken into account, so allowing one to model various instabilities that may occur during the process, such as the role played by the plunge depth of the tool on the formations of flashes, the possible appearance of non-steady voids or tunnel holes and the influence of the threads on the material flow, the temperature field and the welding efforts. This formulation is implemented in the 3D Forge3 FE software with automatic remeshing. The non-steady phases of FSW can so be simulated, as well as the steady welding phase. The study of different process conditions shows that the main phenomena taking place during FSW can be simulated with the right sensitivities.</p>
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