Computational Modeling and Sub-Grid Scale Stabilization of Incompressibility and Convection in the Numerical Simulation of Friction Stir Welding Processes

Abstract

This paper deals with the computational modeling and sub-grid scale stabilization of incompressibility and convection in the numerical simulation of the material flow around the probe tool in a Friction Stir Welding (FSW) process. Within the paradigmatic framework of the multiscale stabilization methods, suitable pressure and convective derivative of the temperature sub-grid scale stabilized coupled thermomechanical formulations have been developed using an Eulerian description. Norton-Hoff and Sheppard-Wright thermo-rigid-viscoplastic constitutive material models have been considered. Constitutive equations for the sub-grid scale models have been proposed and an approximation of the sub-grid scale variables has been given. In particular, Algebraic Sub-grid Scale (ASGS) and Orthogonal Sub-grid Scale (OSGS) methods for mixed velocity, pressure and temperature P1/P1/P1 linear elements have been considered. Furthermore, it has been shown that well known classical stabilized formulations, such as the Galerkin Least-Squares (GLS) for incompressible (or quasi-incompressible) problems or the Streamline Upwind/Petrov-Galerkin (SUPG) method for convection dominant problems, can be recovered as particular cases of the multiscale stabilization framework considered. Using a product formula algorithm for the solution of the coupled thermomechanical problem, the resulting algebraic system of equations has been solved using a staggered procedure in which a mechanical problem, defined by the linear momentum balance equation, under quasi-static conditions, and the incompressibility equation, is solved first at constant temperature. Then a thermal problem, defined by the energy balance equation, is solved keeping constant the mechanical variables, i.e. velocity and pressure. The computational model has been implemented in an enhanced version of the finite element software COMET, developed by the authors at the International Center for Numerical Methods in Engineering (CIMNE). Two numerical examples have been considered. The first one deals with the numerical simulation of a coupled thermomechanical flow in a 2D rectangular domain. Steady-state and transient

A Comparison of Different Finite Element Methods in the Thermal Analysis of Friction Stir Welding (FSW)

“…Agelet de Saracibar et al [106], Chiumenti et al [116], and Dialami et al [117][118][119] To model the plastic deformation and thermal analysis.…”

“…A finite element volume code has been employed by Askari et al [106] as an advection-diffusion solution for the energy balance equation. The elastic response has been considered and the temperature distribution, the strain and the strain rate predicted successfully.…”

“…By using a sub-grid scale stabilized mixed velocity, both the pressure and the temperature in different coupled thermo-rigid-plastic models, the thermal modelling of the FSW process was investigated by Agelet de Saracibar et al [106] Chiumenti et al [116], and Dialami et al [117][118][119]. In all models, the Eulerian and the Arbitrary Lagrangian Eulerian (ALE) approaches were employed.…”

3D numerical models of FSW processes with non-cylindrical pin

“…In this paper, the numerical results of the solid approach are compared with the already validated model based on the fluid approach (see [2,3,7,8]). In this example, the section of the pin is an equilateral triangle (Fig.…”

“…In spite of the important number of applications of FSW, the phenomena happening during welding are still not very well understood. Therefore, the investigations on this process and especially regarding numerical simulations are still very active [2,3,4,5,6,7,8]. The mechanical intermixing induces very high strains in the material in the neighbourhood of the tool.…”