A Computational Model for the Numerical Simulation of FSW Processes

Arch Computat Methods Eng

et al. 2016

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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 essential 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 de…ning the problem 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 induced by the visco-plastic response, a mixed …nite 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 …elds, respectively. The same stabilization strategy is adopted to tackle the instabilities of the temperature …eld, inherent characteristic of convective dominated problems (thermal analysis in ALE/Eulerian kinematic framework).At global level, the material behavior is characterized by a thermo-elasto-viscoplastic constitutive model. The analysis at local level is characterized by a rigid thermovisco-plastic constitutive model. Di¤erent thermally coupled (non-Newtonian) ‡uidlike models as Norton-Ho¤, Carreau or Sheppard-Wright, among others are tested.To better understand the material ‡ow pattern in the stirring zone, a (Lagrangian based) particle tracing is carried out while post-processing FSW results.A coupling strategy between the analysis of the process zone nearby the pin-tool (local level analysis) and the simulation carried out for the entire structure to be welded (global level analysis) is implemented to accurately predict the temperature histories and, thereby, the residual stresses in FSW.

Section: Kinematic Frameworkmentioning

confidence: 99%

Challenges in Thermo-mechanical Analysis of Friction Stir Welding Processes

Dialami

Arch Computat Methods Eng

et al. 2016

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“…Furthermore, for some of those applications the plastic strains and plastic strain rates are extremely high and Eulerian or Arbitrary Lagrangian-Eulerian (ALE) formalisms, instead of a Lagrangian one, are far more convenient from the numerical point of view. Those situations arise, for instance, in the numerical simulation of Friction Stir Welding (FSW) processes [6,7,8,33,34].…”

Section: Introduction Motivation and Goalsmentioning

confidence: 99%

“…Agelet de Saracibar et al (2010) [6,7], Agelet de Saracibar et al (2011) [8], Chiumenti et al (2012) [33], and Dialami et al (2012) [52] used a sub-grid scale finite element stabilized mixed velocity/pressure/ temperature formulation for coupled thermo-rigid-plastic models, using Eulerian and Arbitrary Lagrangian Eulerian (ALE) formalisms, for the numerical simulation of Friction Stir Welding (FSW) processes. They used ASGS and OSGS methods and quasi-static sub-grid scales, neglecting the sub-grid scale pressure and using the finite element component of the velocity in the convective term of the energy balance equation.…”

Section: Introduction Motivation and Goalsmentioning

confidence: 99%

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

Saracibar

Arch Computat Methods Eng

et al. 2014

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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

“…The Arbitrary Lagrangian Eulerian (ALE) formalisms have been proposed to deal with non-cylindrical pin shapes (see [1][2][3][4][5][6][7][8][9]). A mixed stabilized sub-grid scale finite technology has been adopted to solve coupled thermo-mechanical problems with a rigidviscoplastic constitutive behavior [4].…”

mentioning

confidence: 99%

Local–global strategy for the prediction of residual stresses in FSW processes

Dialami

Int J Adv Manuf Technol

et al. 2016

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The final publication is available at Springer via http://dx.doi.org/10.1007/s00170-016-9016-3This work describes the local–global strategy proposed for the computation of residual stresses in friction stir welding (FSW) processes. A coupling strategy between the analysis of the process zone nearby the pin tool (local level analysis) and the simulation carried out for the entire structure to be welded (global level analysis) is implemented to accurately predict the temperature histories and, thereby, the residual stresses in FSW. As a first step, the local problem solves the material stirring as well as the heat generation induced by the pin and shoulder rotation at the heat affected zone. The Arbitrary Lagrangian Eulerian (ALE) formulation is adopted to deal with the rotation of complex pin shapes. A thermo-rigid-viscoplastic constitutive law is employed to characterize the viscous flow of the material, driven by the high-strain rates induced by the FSW process. A mixed temperature–velocity–pressure finite element technology is used to deal with the isochoric nature of the strains. The output of this local analysis is the heat generated either by plastic dissipation or by friction, and it is used as the power input for the welding analysis at structural (global) level. The global problem is tackled within the Lagrangian framework together with a thermo-elasto-viscoplastic constitutive model. In addition, in this case, the mixed temperature–displacement–pressure format is introduced to deal with the deviatoric nature of the plastic strains. The outcomes of this analysis are the distortions and the residual stresses after welding. The material used in this work is stainless steel 304 L; however, the methodology presented is applicable to a wide range of materials. The proposed numerical strategy is validated by the experimental evidence.Peer ReviewedPostprint (author's final draft