**1. Introduction**

Friction stir welding (FSW) is a solid-state welding process that was patented in the UK by "The Welding Institute" (TWI) in 1991. In this process, illustrated in **Figure 1**, a non-consumable rotating tool is used and the workpieces are joined in a solid state, without fusing the materi‐ als. This tool is classically made up of a cylindrical shoulder and a cylindrical or conical pin. To perform a weld, the rotation of the tool is initiated, and then the tool is forced into the parts to be welded. When the shoulder reaches the surface of the material, an important amount of friction heat is generated along the contact surface. The increase in temperature softens the

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material and helps the workpieces to become highly plastic. Although significant heat is generated, the material nevertheless stays in the solid state, at about 0.8–0.9 times the melting point. The combined effect of the increased temperature and the pressure exerted by the tool allows the workpiece material to be mechanically mixed. The plates are then joined together in a solid state as the tool advances along the weld seam.

**Figure 2.** The four main phases of friction stir welding.

aluminum alloys.

time to reach the temperature required for welding.

The dwell phase begins when the desired plunge depth has been achieved. The axial force **Figure 2** is maintained on the tool during this stabilization phase. The combined effect of the relative speed between the rotating tool and the material with the applied axial force generates heat due to friction at the tool-material interface. The tool is kept in place for a sufficiently long

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After the dwell phase, the tool starts to advance and accelerates to the prescribed translational velocity along the weld line. The acceleration may be fast if the dwell phase was sufficiently long and the temperature is high in the weld zone. However, too fast an acceleration can result in high mechanical stresses for both the tool and welding equipment, reducing their useful lifetime. Depending on the design of the tool and the specific process parameters, the FSW tool

In conventional arc-welding techniques, the material is physically melted to produce a weld. In FSW, numerous drawbacks associated with the presence of a liquid phase during welding are eliminated: solidification cracking is eradicated, and the distortions and the size of the heataffected zone (HAZ) are reduced. Spatter, fume, and ultraviolet (UV) emissions are also eliminated. Compared to arc-welded parts, the FSW assemblies frequently exhibit higher mechanical properties in tension, compression, bending, and an increased life in fatigue. In addition, no flux, protective gas, or filler material is needed during welding. Finally, the thickness of FSW welds may go from few tenths of millimeters up to more than 70 mm in

However, the FSW process has certain limitations as well. In order to bring the material into the plastic state, the required torque and forces can be very high. The axial force ap‐ plied on the tool can reach many kilonewtons (many tons of force). For this reason, the welding machine must be robust, typically leading to relatively expensive equipment. In order to have high-quality welds, it is also important to assure the appropriate clamping and support of the pieces to be welded. Further limitations of the FSW process are mostly related to geometrical factors. During welding, the tool shoulder must have constant and

may be tilted slightly (a few degrees) to improve the quality of the weld.

**Figure 1.** Friction stir-welding process.

FSW was initially developed and used to join aluminum alloys. However, since its invention, the application field of the process has been extended to weld various materials: copper, titanium, magnesium, steel, stainless steel, nickel, polymers, and lead.

To join two plates using the FSW process, a sequence of prescribed motions is performed. This sequence is normally divided into four different phases. Each phase plays a specific role in the welding process. These phases are illustrated in **Figure 2** and are identified as follows:


During the plunge phase, the rotation of the welding tool is initiated and the tool plunges into the workpieces. During this phase, the material is relatively cold; only the pin is in contact with the workpiece. The axial force (also called forging force) and the torque applied to the tool are high, and in most cases, reach their highest values. At the end of the plunge phase, the pin has fully penetrated the workpiece and the shoulder is in contact with the surface. The rotation speed of the tool during the plunge and advance phase is frequently the same.

A Mesh-Free Solid-Mechanics Approach for Simulating the Friction Stir-Welding Process http://dx.doi.org/10.5772/64159 29

**Figure 2.** The four main phases of friction stir welding.

material and helps the workpieces to become highly plastic. Although significant heat is generated, the material nevertheless stays in the solid state, at about 0.8–0.9 times the melting point. The combined effect of the increased temperature and the pressure exerted by the tool allows the workpiece material to be mechanically mixed. The plates are then joined together in

FSW was initially developed and used to join aluminum alloys. However, since its invention, the application field of the process has been extended to weld various materials: copper,

To join two plates using the FSW process, a sequence of prescribed motions is performed. This sequence is normally divided into four different phases. Each phase plays a specific role in the welding process. These phases are illustrated in **Figure 2** and are identified as follows:

During the plunge phase, the rotation of the welding tool is initiated and the tool plunges into the workpieces. During this phase, the material is relatively cold; only the pin is in contact with the workpiece. The axial force (also called forging force) and the torque applied to the tool are high, and in most cases, reach their highest values. At the end of the plunge phase, the pin has fully penetrated the workpiece and the shoulder is in contact with the surface. The rotation

speed of the tool during the plunge and advance phase is frequently the same.

titanium, magnesium, steel, stainless steel, nickel, polymers, and lead.

a solid state as the tool advances along the weld seam.

**Figure 1.** Friction stir-welding process.

**2)** Dwell or stabilization phase,

**3)** Welding or advancing phase,

**4)** Tool removal or retraction phase.

**1)** Plunge phase,

28 Joining Technologies

The dwell phase begins when the desired plunge depth has been achieved. The axial force **Figure 2** is maintained on the tool during this stabilization phase. The combined effect of the relative speed between the rotating tool and the material with the applied axial force generates heat due to friction at the tool-material interface. The tool is kept in place for a sufficiently long time to reach the temperature required for welding.

After the dwell phase, the tool starts to advance and accelerates to the prescribed translational velocity along the weld line. The acceleration may be fast if the dwell phase was sufficiently long and the temperature is high in the weld zone. However, too fast an acceleration can result in high mechanical stresses for both the tool and welding equipment, reducing their useful lifetime. Depending on the design of the tool and the specific process parameters, the FSW tool may be tilted slightly (a few degrees) to improve the quality of the weld.

In conventional arc-welding techniques, the material is physically melted to produce a weld. In FSW, numerous drawbacks associated with the presence of a liquid phase during welding are eliminated: solidification cracking is eradicated, and the distortions and the size of the heataffected zone (HAZ) are reduced. Spatter, fume, and ultraviolet (UV) emissions are also eliminated. Compared to arc-welded parts, the FSW assemblies frequently exhibit higher mechanical properties in tension, compression, bending, and an increased life in fatigue. In addition, no flux, protective gas, or filler material is needed during welding. Finally, the thickness of FSW welds may go from few tenths of millimeters up to more than 70 mm in aluminum alloys.

However, the FSW process has certain limitations as well. In order to bring the material into the plastic state, the required torque and forces can be very high. The axial force ap‐ plied on the tool can reach many kilonewtons (many tons of force). For this reason, the welding machine must be robust, typically leading to relatively expensive equipment. In order to have high-quality welds, it is also important to assure the appropriate clamping and support of the pieces to be welded. Further limitations of the FSW process are mostly related to geometrical factors. During welding, the tool shoulder must have constant and

uniform pressure on the workpieces. Certain traditional types of welds such as the fillet weld cannot be accomplished without modification of the standard tool geometry.

Numerical simulation of FSW is a popular field of research since the underlying physics is complex and requires the use of advanced multi-physics solvers. There are various numerical methods that can be used to simulate the friction stir-welding process. The finite difference method (FDM) and the finite element method (FEM) have certain applicability for studying the temperature distribution (heat transfer simulations). Lagrangian-based FEM typically will suffer excessive element distortion for processes that occur with large finite strains. The finite volume method (FVM) is also popular for studying the material flow and is strictly an Eulerian approach (cannot follow the evolution of each material point). Arbitrary Lagrangian Eulerian (ALE) is a meshed-based method that includes a material advection of the Lagrangian mesh within an Eulerian mesh. This allows for larger levels of plastic deformation to be studied. However, the method does have certain downfalls. Since the ALE scheme is highly dissipative, this makes simulating long processes (such as FSW) prone to precision error. The method also suffers from advection errors when the material movement is predominately out of the corner of an element (the classic ALE scheme advects material orthogonal to element faces). To date, mesh-free methods such as smoothed particle hydrodynamics (SPH) have shown the most potential to simulate the entire FSW process. Because SPH is meshfree, very large plastic deformation can be simulated without the problem of mesh distortion. Although the SPH method is computationally burdensome, the method can easily be adapted to run in parallel

A Mesh-Free Solid-Mechanics Approach for Simulating the Friction Stir-Welding Process

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31

on the graphics processing unit (GPU) to significantly improve the calculation time.

mations, stresses, and defects.

Shi et al. [1] studied the effects of ultrasonic vibration to improve the weld quality using computational fluid dynamics (CFD). They validate their model by comparing predicted temperature and flow for experimental work. They note that the ultrasonic-assisted FSW process provides a larger flow region and allows for faster welding without the presence of defects. Since they use CFD, they are not able to follow the material history (Eulerian frame of reference). Furthermore, they cannot predict residual stresses or defects in the weld zone. Fraser et al. [2] have used FDM to predict the temperature distribution during the full FSW process. They use the results to find the optimal process parameters (based on an optimal temperature). Their method is efficient and was shown to correlate well with experimental work. The model is limited to temperature calculation and cannot be used to predict defor‐

Buffa et al. [3–5] used FEM to develop a hybrid model capable of determining the residual stresses in the resulting weld. They split the FSW process simulation into two phases. In the first phase, they model the plunge, dwell, and advance using a rigid viscoplastic model (fluidbased) that does not provide elastic stresses. Then, they switch to an elastic-plastic model to approximately calculate the resulting residual stresses during weld cooldown. They are able to obtain good correlation for the residual stresses. On the downside, their model does not

Guerdoux and Fourmont [6] used the ALE method to study the different phases of the entire process. They used an elastoviscoplastic rate and temperature-dependant material model with the Hansel-Spittel rheological model. On the downside, the Hansel-Spittel model requires coefficient fitting from tensile tests and the coefficients are not commonly available. Grujicic et al. [6–8] as well as Chiumenti et al. [7] used ALE to simulate the FSW process and considered

allow for tracking defects since the welding phase is based on a fluid model.

There are two main classes of FSW tools: single and double shoulder. The tool shown in **Figure 2** belongs to the first category, while the double-shoulder tools have a pin located between two shoulders. These double-shoulder tools create high pressure in the weld zone by forcing the parts into a space slightly narrower than their thickness. This method eliminates the need for a solid backing plate that bears the axial force in case of single-shoulder technol‐ ogy. Furthermore, in the case of double-shoulder tools, the problem of insufficient penetration is eliminated and the temperature distribution is symmetrical about the center of the weld zone.

After its invention, FSW has been rapidly introduced in various fields: in marine and rail industries, automotive, aeronautic, aerospace, and fixed structures. Various types of materials are now welded, and composite welds (e.g., Al-Cu or Al-steel) are performed. There are also many variations on the standard FSW process. For example, using a procedure essentially similar to FSW, a method that is comparable to traditional resistance spot welding called Friction Stir Spot Welding (FSSW) has been developed. These two techniques can produce similar punctual welds, for various parts with similar geometry and thickness. To produce a weld, a rotating tool is plunged into the material. The axial motion stops when the shoulder touches the surface of the workpiece, the rotating tool stays there for a short period of dwell, and then it is extracted. FSSW has the benefit of being easy to mechanize with a robot, leading to excellent repeatability and improved weld quality compared to resistance spot welding. Another variation on the standard FSW process is the use of a tool with a retractable pin; this type of tool can be used to mitigate the presence of the hole left behind when the tool is retracted in phase 4. This process can be used to join parts where the presence of a hole at the end of the weld line is unacceptable.

The physical principle of FSW has also been used to improve the microstructure of the workpieces. In this technique, called friction stir processing (FSP), an FSW tool is used to modify the microstructure of the material. The principal improvements made by FSP are as follows:


The local modifications performed by FSP to the microstructure can be very beneficial in a zone of high stress, where a good ductility is needed, or where the fatigue life should be increased.

Numerical simulation of FSW is a popular field of research since the underlying physics is complex and requires the use of advanced multi-physics solvers. There are various numerical methods that can be used to simulate the friction stir-welding process. The finite difference method (FDM) and the finite element method (FEM) have certain applicability for studying the temperature distribution (heat transfer simulations). Lagrangian-based FEM typically will suffer excessive element distortion for processes that occur with large finite strains. The finite volume method (FVM) is also popular for studying the material flow and is strictly an Eulerian approach (cannot follow the evolution of each material point). Arbitrary Lagrangian Eulerian (ALE) is a meshed-based method that includes a material advection of the Lagrangian mesh within an Eulerian mesh. This allows for larger levels of plastic deformation to be studied. However, the method does have certain downfalls. Since the ALE scheme is highly dissipative, this makes simulating long processes (such as FSW) prone to precision error. The method also suffers from advection errors when the material movement is predominately out of the corner of an element (the classic ALE scheme advects material orthogonal to element faces). To date, mesh-free methods such as smoothed particle hydrodynamics (SPH) have shown the most potential to simulate the entire FSW process. Because SPH is meshfree, very large plastic deformation can be simulated without the problem of mesh distortion. Although the SPH method is computationally burdensome, the method can easily be adapted to run in parallel on the graphics processing unit (GPU) to significantly improve the calculation time.

uniform pressure on the workpieces. Certain traditional types of welds such as the fillet

There are two main classes of FSW tools: single and double shoulder. The tool shown in **Figure 2** belongs to the first category, while the double-shoulder tools have a pin located between two shoulders. These double-shoulder tools create high pressure in the weld zone by forcing the parts into a space slightly narrower than their thickness. This method eliminates the need for a solid backing plate that bears the axial force in case of single-shoulder technol‐ ogy. Furthermore, in the case of double-shoulder tools, the problem of insufficient penetration is eliminated and the temperature distribution is symmetrical about the center of the weld

After its invention, FSW has been rapidly introduced in various fields: in marine and rail industries, automotive, aeronautic, aerospace, and fixed structures. Various types of materials are now welded, and composite welds (e.g., Al-Cu or Al-steel) are performed. There are also many variations on the standard FSW process. For example, using a procedure essentially similar to FSW, a method that is comparable to traditional resistance spot welding called Friction Stir Spot Welding (FSSW) has been developed. These two techniques can produce similar punctual welds, for various parts with similar geometry and thickness. To produce a weld, a rotating tool is plunged into the material. The axial motion stops when the shoulder touches the surface of the workpiece, the rotating tool stays there for a short period of dwell, and then it is extracted. FSSW has the benefit of being easy to mechanize with a robot, leading to excellent repeatability and improved weld quality compared to resistance spot welding. Another variation on the standard FSW process is the use of a tool with a retractable pin; this type of tool can be used to mitigate the presence of the hole left behind when the tool is retracted in phase 4. This process can be used to join parts where the presence of a hole at the end of the

The physical principle of FSW has also been used to improve the microstructure of the workpieces. In this technique, called friction stir processing (FSP), an FSW tool is used to modify the microstructure of the material. The principal improvements made by FSP are as

**•** Creation of very fine microstructures to obtain super plasticity (nanograins can be pro‐

**•** Homogenization of the microstructure to reduce segregation, eliminate porosity, and

**•** Introduction of particles to develop composite surface (metal matrix composite (MMC)) and modify the elasticity, wear resistance, thermal and electrical conductivity, or internal

The local modifications performed by FSP to the microstructure can be very beneficial in a zone of high stress, where a good ductility is needed, or where the fatigue life should be

increase mechanical properties, ductility, and corrosion resistance;

weld cannot be accomplished without modification of the standard tool geometry.

zone.

30 Joining Technologies

weld line is unacceptable.

damping of the material.

follows:

duced);

increased.

Shi et al. [1] studied the effects of ultrasonic vibration to improve the weld quality using computational fluid dynamics (CFD). They validate their model by comparing predicted temperature and flow for experimental work. They note that the ultrasonic-assisted FSW process provides a larger flow region and allows for faster welding without the presence of defects. Since they use CFD, they are not able to follow the material history (Eulerian frame of reference). Furthermore, they cannot predict residual stresses or defects in the weld zone. Fraser et al. [2] have used FDM to predict the temperature distribution during the full FSW process. They use the results to find the optimal process parameters (based on an optimal temperature). Their method is efficient and was shown to correlate well with experimental work. The model is limited to temperature calculation and cannot be used to predict defor‐ mations, stresses, and defects.

Buffa et al. [3–5] used FEM to develop a hybrid model capable of determining the residual stresses in the resulting weld. They split the FSW process simulation into two phases. In the first phase, they model the plunge, dwell, and advance using a rigid viscoplastic model (fluidbased) that does not provide elastic stresses. Then, they switch to an elastic-plastic model to approximately calculate the resulting residual stresses during weld cooldown. They are able to obtain good correlation for the residual stresses. On the downside, their model does not allow for tracking defects since the welding phase is based on a fluid model.

Guerdoux and Fourmont [6] used the ALE method to study the different phases of the entire process. They used an elastoviscoplastic rate and temperature-dependant material model with the Hansel-Spittel rheological model. On the downside, the Hansel-Spittel model requires coefficient fitting from tensile tests and the coefficients are not commonly available. Grujicic et al. [6–8] as well as Chiumenti et al. [7] used ALE to simulate the FSW process and considered the effect of pin shape, contact friction, material and temperature flow. Their models are highly sophisticated, but are not able to predict residual stresses and defects. They noted that the calculation time is many weeks with their approach.

What makes the SPH method meshfree is that the set of field equation (conservation equations for a solid body in this case) is solved by interpolation using a kernel, *W*(*r*, *h*), from a set of *j* neighbor particles that are within the influence domain of a particle of interest, *i*. **Figure 3** gives a graphical representation of this concept. In this method, continuous field equations are "weakened" into a set of discrete ordinary differential equations. A continuous function is

is called the kernel, also commonly referred to as the smoothing function. It is a function of the spatial distance between the point at which the function is to be calculated (calculation point, *x*¯), the interpolation location (*x*¯ ′), and the smoothing length, *h*. The kernel is the key to the SPH method. The continuous SPH interpolation equation can then be written for a set of

( ) ( ) ( )

 a ,

<sup>=</sup> å (2)

th particle. *mj*

*<sup>α</sup>* |. The interpolation kernel, *W*(*r*,*h*), will be written as

and *ρ<sup>j</sup>* are the mass and

) of the *j* particles

1

= r

*<sup>α</sup>* − *xj*

*Wij* throughout the rest of the paper. The sum is taken over the total number (*Ni*

*m f x f x W rh*

*Ni j i j j j*

a

*xi* is the spatial location vector for particle *i* and *xj* for the *j*

th particle and *r* = | *xi*

( ) ( ) ( ) , ,, *f x f x W x x h dx* =ò - , (1)

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approximated by an interpolant through the use of a convolution integral:

**Figure 3.** Smoothed particle interpolation.

discrete material points:

density of a *j*

Bohjwani [8] used the SPH method to study the FSW process with the Johnson-Cook constit‐ utive model in LS-DYNA. At the time, it was not possible to perform a coupled thermome‐ chanical SPH simulation. As such, thermal softening is not taken into consideration. Timesli et al. [9] used the SPH method in two dimensions (2D) to simulate the FSW process. They have used the fluid formulation that directly calculated the deviatoric stress from the strain rate and a non-Newtonian viscosity (function of temperature). They showed that their model correlates well to an equivalent CFD model; however, they did not validate the model experimentally. Recently, Pan et al. [10] used the SPH method to solve the fully coupled thermomechanical problem for the FSW process in three dimensions (3D). Their approach gives detailed grain size, hardness, and microstructure evolution using the SPH method. However, they use a fluidbased formulation that does not allow the determination of elastic strains and stresses. Fraser et al. [11–13] have used the SPH method to simulate various FSW processes using a fully coupled thermos-mechanical SPH-FEM model. The tool is modeled with rigid FEMs and the workpieces with SPH. The model is able to predict temperatures, stresses, and defects all within a Lagrangian framework. This approach permits following the material point history throughout the entire welding process. Since the tool is modeled with FEMs, friction contact can be included.

In this chapter, we describe our approach toward simulating the entire FSW process using SPH on the GPU. In Section 2, we explain what SPH is and how the method can be used to solve large plastic deformation problems with an elastic-plastic formulation, including a description of our parallelization strategy on the GPU. Section 3 introduces the simulation model of a complex aluminum alloy joint. The simulation model will be used to show the power of the SPH method. A validation case is presented to show that the model is able to predict tool torque, force, and the temperature distribution, as well as the size and shape of the flash. Finally, Section 4 wraps up the chapter with concluding remarks and an outlook toward the future of FSW simulation.
