Local and global approaches to friction stir welding

This paper deals with the numerical simulation of Friction Stir Welding (FSW) processes. FSW techniques are used in many industrial applications and particularly in the aeronautic and aerospace industries, where the quality of the joining is of es- sential importance. The analysis is focused either at global level, considering the full component to be jointed, or locally, studying more in detail the heat a¤ected zone (HAZ). The analysis at global (structural component) level is performed defining the prob- lem in the Lagrangian setting while, at local level, an apropos kinematic framework which makes use of an e¢ cient combination of Lagrangian (pin), Eulerian (metal sheet) and ALE (stirring zone) descriptions for the di¤erent computational sub-domains is introduced for the numerical modeling. As a result, the analysis can deal with complex (non-cylindrical) pin-shapes and the extremely large deformation of the material at the HAZ without requiring any remeshing or remapping tools. A fully coupled thermo-mechanical framework is proposed for the computational modeling of the FSW processes proposed both at local and global level. A staggered algorithm based on an isothermal fractional step method is introduced. To account for the isochoric behavior of the material when the temperature range is close to the melting point or due to the predominant deviatoric deformations in- duced by the visco-plastic response, a mixed finite element technology is introduced. The Variational Multi Scale (VMS) method is used to circumvent the LBB stability condition allowing the use of linear/linear P1/P1 interpolations for displacement (or velocity, ALE/Eulerian formulation) and pressure fields, respectively. The same stabi- lization strategy is adopted to tackle the instabilities of the temperature field, inherent characteristic of convective dominated problems (thermal analysis in ALE/Eulerian kinematic framework).