THERMO-ELASTO-VISCO-PLASTIC MODELLING OF FRICTION STIR WELDING IN AN EULERIAN REFERENCE FRAME

Two sets of stabilized, Galerkin finite element formulations for modeling elastovisco-plastic material response of quasi-steady state processes in Eulerian frames are presented. One set is based on the rate equilibrium equation, and the other set is based on the true equilibrium equation. The rate equilibrium formulation couples the velocity (V), stress (σ), deformation gradient (F) and internal variable (s) together. While, the true equilibrium formulation solves the velocity (V), deformation gradient (F), viscoplastic part of deformation gradient (F) and internal variable (s) simultaneously. The streamline upwind Petrov-Galerkin (SUPG) method is introduced to eliminate spurious oscillations which may be caused by the convection of stress, deformation gradient, viscoplastic deformation gradient and internal variable evolution. A progressively stiffening solution strategy is proposed to improve the convergence of the Newton-Raphson solution procedure. These formulations have been implemented in a 4 node quadrilateral element. Three numerical examples (radial flow, strip drawing and gas metal arc welding) have been modeled to verify the accuracy of these Eulerian methods. ii A coupled 2-dimensional Eulerian thermo-elasto-visco-plastic model has been developed for modeling the Friction Stir Welding process. First, a coupled thermo-viscoplastic analysis is performed to determine the temperature distribution in the full domain and the incompressible material flow around the spinning tool. Next, an elasto-viscoplastic analysis based on the true equilibrium is performed outside the visco-plastic region to comput the residual stress. Both frictional heat and plastic deformation heat generation are considered in the model. Furthermore, this is the only known model computing residual stress accounting for plasticity caused by both thermal expansion and mechanical deformation due to material spinning. The computed residual stress is verified by comparing to experimentally measured data.

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