Abstract

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 affected zone (HAZ). The analysis at global (structural component) level is performed defining the problem in the Lagrangian setting while, at local level, an apropos kinematic framework which makes use of an efficient combination of Lagrangian (pin), Eulerian (metal sheet) and ALE (stirring zone) descriptions for the different 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 finite element technology is introduced. The Variational Multi Scale 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 stabilization strategy is adopted to tackle the instabilities of the temperature field, 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 thermo–visco-plastic constitutive model. Different thermally coupled (non-Newtonian) fluid-like models as Norton–Hoff, Carreau or Sheppard–Wright, among others are tested. To better understand the material flow 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.

Abstract

Friction stir welding (FSW) process is a relatively recent welding process (patented in 1991). FSW is a solid-state joining process during which materials to be joined are not melted. During the FSW process, the behaviour of the material is at the interface between solid mechanics and fluid mechanics. In this paper, a 3D numerical model of the FSW process with a non-cylindrical tool based on a solid formulation is compared to another one based on a fluid formulation. Both models use advanced numerical techniques such as the arbitrary Lagrangian–Eulerian formulation, remeshing or the orthogonal sub-grid scale method. It is shown that these two formulations essentially deliver the same results.

Abstract

Friction stir welding process is a relatively recent welding process (patented in 1991). FSW is a solid-state joining process during which materials to be joined are not melted. During the FSW process, the behaviour of the material is at the interface between solid mechanics and fluid mechanics. In this paper, a 3D numerical model of the FSW process with a non-cylindrical tool based on a solid formulation is compared to another one based on a fluid formulation. Both models use advanced numerical techniques such as the Arbitrary Lagrangian Eulerian formulation, remeshing or the Orthogonal Sub-Grid Scale method. It is shown that these two formulations essentially deliver the same results.

Abstract

This work deals with the modeling of the material flow in Friction Stir Welding (FSW) processes using particle tracing method. For the computation of particle trajectories, three accurate and computationally efficient integration methods are implemented within a FE model for FSW process: the Backward Euler with Sub-stepping (BES), the 4-th order Runge–Kutta (RK4) and the Back and Forth Error Compensation and Correction (BFECC) methods. Firstly, their performance is compared by solving the Zalesak’s disk benchmark. Later, the developed methodology is applied to some FSW problems providing a quantitative 2D and 3D view of the material transport in the process area. The material flow pattern is compared to the experimental evidence.

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 conditions have been considered. The goal of this numerical example has been the comparison between different sub-grid scale stabilization methods for the velocity and temperature equations. In particular, using a GLS stabilization method for the pressure equation, a comparison between SUPG and OSGS convective stabilization methods has been performed. Additionally, using a SUPG stabilization method for the temperature equation, a comparison between GLS and OSGS pressure stabilization methods has been done. The second example deals with the 3D numerical simulation of a representative FSW process. Numerical results obtained have been compared with experimental results available in the literature. A good agreement on the temperature distribution has been obtained and predicted peak temperatures compare well, both in value and position, with the experimental results available.

Abstract

Friction stir welding (FSW) process is a solid‐state joining process during which materials to be joined are not melted. As a consequence, the heat‐affected zone is smaller and the quality of the weld is better with respect to more classical welding processes. Because of extremely high strains in the neighborhood of the tool, classical numerical simulation techniques have to be extended in order to track the correct material deformations. The Arbitrary Lagrangian–Eulerian (ALE) formulation is used to preserve a good mesh quality throughout the computation. With this formulation, the mesh displacement is independent from the material displacement. Moreover, some advanced numerical techniques such as remeshing or a special computation of transition interface is needed to take into account non‐cylindrical tools. During the FSW process, the behavior of the material in the neighborhood of the tool is at the interface between solid mechanics and fluid mechanics. Consequently, a numerical model of the FSW process based on a solid formulation is compared to another one based on a fluid formulation. It is shown that these two formulations essentially deliver the same results in terms of pressures and temperatures.

Abstract

This paper describes features of a fully coupled thermo-mechanical model for Friction Stir Welding (FSW) simulation. An apropos kinematic setting for different zones of the computational domain is introduced and an efficient coupling strategy is proposed. Heat generation via viscous dissipation as well as frictional heating is considered. The results of the simulation using the proposed model are compared with the experimental evidence. The effect of slip and stick condition on non-circular pin shapes is analyzed. Simulation of material stirring is also carried out via particle tracing, providing insight of the material flow pattern in the vicinity of the pin.

Abstract

This work describes the formulation adopted for the numerical simulation of the friction stir welding (FSW) process. FSW is a solid-state joining process (the metal is not melted during the process) devised for applications where the original metallurgical characteristics must be retained. This process is primarily used on aluminum alloys, and most often on large pieces which cannot be easily heat treated to recover temper characteristics. Heat is either induced by the friction between the tool shoulder and the work pieces or generated by the mechanical mixing (stirring and forging) process without reaching the melting point (solid-state process). To simulate this kind of welding process, a fully coupled thermo-mechanical solution is adopted. A sliding mesh, rotating together with the pin (ALE formulation), is used to avoid the extremely large distortions of the mesh around the tool in the so called stirring zone while the rest of the mesh of the sheet is fixed (Eulerian formulation). The orthogonal subgrid scale (OSS) technique is used to stabilize the mixed velocity–pressure formulation adopted to solve the Stokes problem. This stabilized formulation can deal with the incompressible behavior of the material allowing for equal linear interpolation for both the velocity and the pressure fields. The material behavior is characterized either by Norton–Hoff or Sheppard–Wright rigid thermo-visco-plastic constitutive models. Both the frictional heating due to the contact interaction between the surface of the tool and the sheet, and the heat induced by the visco-plastic dissipation of the stirring material have been taken into account. Heat convection and heat radiation models are used to dissipate the heat through the boundaries. Both the streamline-upwind/Petrov–Galerkin (SUPG) formulation and the OSS stabilization technique have been implemented to stabilize the convective term in the balance of energy equation. The numerical simulations presented are intended to show the accuracy of the proposed methodology and its capability to study real FSW processes where a non-circular pin is often used.

Abstract

This paper describes the formulation adopted for the numerical simulation of the shaped metal deposition process (SMD) and the experimental work carried out at ITP Industry to calibrate and validate the proposed model. The SMD process is a novel manufacturing technology, similar to the multi-pass welding used for building features such as lugs and flanges on fabricated components (see Fig. 1a and b). A fully coupled thermo-mechanical solution is adopted including phase-change phenomena defined in terms of both latent heat release and shrinkage effects. Temperature evolution as well as residual stresses and distortions, due to the successive welding layers deposited, are accurately simulated coupling the heat transfer and the mechanical analysis. The material behavior is characterized by a thermo-elasto-viscoplastic constitutive model coupled with a metallurgical model. Nickel super-alloy 718 is the target material of this work. Both heat convection and heat radiation models are introduced to dissipate heat through the boundaries of the component. An in-house coupled FE software is used to deal with the numerical simulation and an ad-hoc activation methodology is formulated to simulate the deposition of the different layers of filler material. Difficulties and simplifying hypotheses are discussed. Thermo-mechanical results are presented in terms of both temperature evolution and distortions, and compared with the experimental data obtained at the SMD laboratory of ITP.