Friction Stir Welding of an Aluminum Plate

Manufacturers use a modern welding method called friction stir welding to join aluminum plates. This application analyzes the heat transfer in this welding process. The model is based on a paper by M. Song and R. Kovacevic (Ref. 1).

In friction stir welding, a rotating tool moves along the weld joint and softens the aluminum through the generation of friction heat. The tool’s rotation stirs the soften aluminum such that the two plates are joined. Figure 1 shows the rotating tool and the aluminum plates being are joined.

Figure 1: Two aluminum plates being joined by friction stir welding.

The rotating tool is in contact with the aluminum plates along two surfaces: the tool’s shoulder, and the tool’s pin. The tool adds heat to the aluminum plates through both interfaces.

During the welding process, the tool moves along the weld joint. This movement would require a fairly complex model if you want to model the tool as a moving heat source. This example takes a different approach that uses a moving coordinate system that is fixed at the tool axis (Ref. 1 also takes this approach). After making the coordinate transformation, the heat transfer problem becomes a stationary convection-conduction problem that is straightforward to model.

The model includes some simplifications. For example, the coordinate transformation assumes that the aluminum plates are infinitely long. This means that the analysis neglects effects near the edges of the plates. Neither does the model account for the stirring process in the aluminum, which is very complex because it includes phase changes and material flow from the front to the back of the rotating tool.

Model Definition

The model geometry is symmetric around the weld. It is therefore sufficient to model only one aluminum plate. The plate dimensions are 120×102×12.7 mm, surrounded by two infinite domains in the x-direction. Figure 2 shows the resulting model geometry:

Figure 2: Model geometry for friction stir welding.

The following equation describes heat transfer in the plate. As a result of fixing the coordinate system in the welding tool, the equation includes a convective term in addition to the conductive term. The equation is

where k represents thermal conductivity, ρ is the density, Cp denotes specific heat capacity, and u is the velocity.

The model sets the velocity to 1.59·10−3 m/s in the negative x direction.

The model simulates the heat generated in the interface between the tool’s pin and the workpiece as a surface heat source (expression adapted from Ref. 2):

Here μ is the friction coefficient, rp denotes the pin radius, ω refers to the pin’s angular velocity (rad/s), and⎯Y(T) is the average shear stress of the material. As indicated, the average shear stress is a function of the temperature; for this tutorial, you approximate this function with an interpolation function determined from experimental data given in Ref. 1 (see Figure 3).

Figure 3: Yield stress (MPa) vs. temperature (K) for 6061-T6 aluminum.

Additionally, heat is generated at the interface between the tool’s shoulder and the workpiece; the following expression defines the local heat flux per unit area (W/m2) at the distance r from the center axis of the tool:

Here Fn represents the normal force, As is the shoulder’s surface area, and Tmelt is aluminum’s melting temperature. As before, μ is the friction coefficient and ω is the angular velocity of the tool (rad/s).

Above the melting temperature of aluminum, the friction between the tool and the aluminum plate is very low. Therefore, the model sets the heat generation from the shoulder and the pin to zero when the temperature is equal to or higher than the melting temperature.

Symmetry is assumed along the weld joint boundary.

The upper and lower surfaces of the aluminum plates lose heat due to natural convection and surface-to-ambient radiation. The corresponding heat flux expressions for these surfaces are

where hu and hd are heat transfer coefficients for natural convection, T0 is an associated reference temperature, ε is the surface emissivity, σ is the Stefan-Boltzmann constant, and Tamb is the ambient air temperature.

The modeling of an infinite domain on the left-hand side, where the aluminum leaves the computational domain, makes sure that the temperature is in equilibrium with the temperature at infinity through natural convection and surface-to-ambient radiation. You therefore set the boundary condition to insulation at that location.

You can compute values for the heat transfer coefficients using empirical expressions available in the heat-transfer literature, for example, Ref. 3. In this application, use the values hu = 12.25 W/(m2·K) and hd = 6.25 W/(m2·K)

Results and Discussion

Figure 4 shows the resulting temperature field. Consider this result as what you would see through a window fixed to the moving welding tool.

Figure 4: Temperature field in the aluminum plate.

The temperature is highest where the aluminum is in contact with the rotating tool. Behind the tool, the process transports hot material away, while in front of the tool, new cold material enters.

References

1. M. Song and R. Kovacevic, “Thermal modeling of friction stir welding in a moving coordinate system and its validation,” Int’l J. of Machine Tools & Manufacture, vol. 43, pp. 605–615, 2003.

2. P. Colegrove et al., “3-dimensional Flow and Thermal Modelling of the Friction Stir Welding Process,” Proceedings of the 2nd International Symposium on Friction Stir Welding, Gothenburg, Sweden, 2000.

3. A. Bejan, Heat Transfer, John Wiley & Sons, 1993.

Heat_Transfer_Module/Thermal_Contact_and_Friction/friction_stir_welding

Modeling Instructions

From the menu, choose .

New

In the window, click .

Model Wizard

In the window, click .

In the tree, select .

Click .

In the tree, select .

Click .

Global Definitions

Parameters

On the toolbar, click .

In the window for , locate the section.

In the table, enter the following settings:


Name	Expression	Value	Description
T_melt	933[K]	933 K	Workpiece melting temperature
h_upside	12.25[W/(m^2*K)]	12.25 W/(m²·K)	Heat transfer coefficient, upside
h_downside	6.25[W/(m^2*K)]	6.25 W/(m²·K)	Heat transfer coefficient, downside
epsilon	0.3[1]	0.3	Surface emissivity
u_weld	1.59[mm/s]	0.00159 m/s	Welding speed
mu	0.4[1]	0.4	Friction coefficient
n	637[1/min]	10.617 1/s	Rotation speed (RPM)
omega	2pi[rad]n	66.706 rad/s	Angular velocity (rad/s)
F_n	25[kN]	25000 N	Normal force
r_pin	6[mm]	0.006 m	Pin radius
r_shoulder	25[mm]	0.025 m	Shoulder radius
A_s	pi*(r_shoulder^2-r_pin^2)	0.0018504 m²	Shoulder surface area

Interpolation 1 (int1)

On the toolbar, click and choose .

In the window for , locate the section.

In the text field, type Ybar.

In the table, enter the following settings:


t	f(t)
311	241
339	238
366	232
394	223
422	189
450	138
477	92
533	34
589	19
644	12

Click .

If you have entered the numbers correctly, the curve should look like that in Figure 3.

Step 1 (step1)

On the toolbar, click and choose .

In the window for , click to expand the section.

In the text field, type 5.

Geometry 1

In the window, under click .

In the window for , locate the section.

From the list, choose .

Block 1 (blk1)

On the toolbar, click .

In the window for , locate the section.

In the text field, type 320.

In the text field, type 102.

In the text field, type 12.7.

Locate the section. In the text field, type -160.

Click .

Block 2 (blk2)

On the toolbar, click .

In the window for , locate the section.

In the text field, type 420.

In the text field, type 102.

In the text field, type 12.7.

Locate the section. In the text field, type -210.

Click .

Cylinder 1 (cyl1)

On the toolbar, click .

In the window for , locate the section.

In the text field, type r_shoulder.

In the text field, type 12.7.

Click .

Cylinder 2 (cyl2)

On the toolbar, click .

In the window for , locate the section.

In the text field, type r_pin.

In the text field, type 12.7.

Click .

Block 3 (blk3)

On the toolbar, click .

In the window for , locate the section.

In the text field, type 2*r_shoulder.

In the text field, type r_shoulder.

In the text field, type 12.7.

Locate the section. In the text field, type -r_shoulder.

In the text field, type -r_shoulder.

Click .

Difference 1 (dif1)

On the toolbar, click and choose .

Select the objects and only.

In the window for , locate the section.

Find the subsection. Select the toggle button.

Select the object only.

Form Union (fin)

In the window, under click .

In the window for , click .

The model geometry is now complete.

Click the button on the toolbar to see the entire geometry.

Definitions

Variables 1

On the toolbar, click and choose .

In the window for , locate the section.

From the list, choose .

Select Boundary 14 only.

Locate the section. In the table, enter the following settings:


Name	Expression	Unit	Description
R	sqrt(x^2+y^2)	m	Distance in xy-plane from tool center axis
q_shoulder	(muF_n/A_s)(Romega)step1((T_melt-T)[1/K])	W/m²	Surface heat source, shoulder-workpiece interface

Variables 2

On the toolbar, click and choose .

In the window for , locate the section.

From the list, choose .

Select Boundaries 15 and 19 only.

Locate the section. In the table, enter the following settings:


Name	Expression	Unit	Description
q_pin	mu/sqrt(3(1+mu^2))(r_pinomega)Ybar(T[1/K])[MPa]*step1((T_melt-T)[1/K])	W/m²	Surface heat source, pin-workpiece interface

Heat Transfer in Solids (ht)

Set the ambient temperature to be used in boundary conditions and initial values of the Heat Transfer interface.

In the window, under click .

In the window for , locate the section.

In the Tamb text field, type 300[K].

Initial Values 1

In the window, under click .

In the window for , choose from the T list.

Solid 1

The domain selection for the default equation model is fixed to all domains to ensure that no domain lacks a defining equation. To modify the equation model for some specific domains, you simply add nodes that override the default equation.

In the window, under click .

Translational Motion 1

On the toolbar, click and choose .

In the window for , locate the section.

Specify the utrans vector as


-u_weld	x
0	y
0	z

Definitions

Infinite Element Domain 1 (ie1)

On the toolbar, click .

Select Domains 1 and 5 only.

Heat Transfer in Solids (ht)

Diffuse Surface 1

On the toolbar, click and choose .

Select Boundaries 3, 4, 8, 9, 13, 25, and 26 only.

Together, these boundaries form the top and bottom surfaces of the geometry.

In the window for , locate the section.

From the ε list, choose . In the associated text field, type epsilon.

Locate the section. From the Tamb list, choose .

Outflow 1

On the toolbar, click and choose .

Select Boundary 1 only.

Heat Flux 1

On the toolbar, click and choose .

Select Boundaries 3, 8, 13, and 25 only.

In the window for , locate the section.

Click the button.

In the h text field, type h_downside.

From the Text list, choose .

Heat Flux 2

On the toolbar, click and choose .

Select Boundaries 4, 9, and 26 only.

In the window for , locate the section.

Click the button.

In the h text field, type h_upside.

From the Text list, choose .

Heat Flux 3

On the toolbar, click and choose .

Select Boundary 14 only.

In the window for , locate the section.

In the q0 text field, type q_shoulder.

Boundary Heat Source 1

On the toolbar, click and choose .

Select Boundaries 15 and 19 only.

In the window for , locate the section.

In the Qb text field, type q_pin.

Temperature 1

On the toolbar, click and choose .

Select Boundary 28 only.

In the window for , locate the section.

From the T0 list, choose .

Materials

Now specify the materials. By default, the first material you add applies to all domains. To specify a different material in some domains you simply add another material for those domains.

Add Material

On the toolbar, click to open the window.

Go to the window.

In the tree, select .

Click in the window toolbar.

Materials

Aluminum (mat1)

On the toolbar, click to close the window.

Add a material for the pin and specify the required properties.

Material 2 (mat2)

On the toolbar, click .

In the window for , type Pin in the text field.

Select Domain 4 only.

Locate the section. In the table, enter the following settings:


Property	Name	Value	Unit	Property group
Thermal conductivity	k	42[W/(m*K)]	W/(m·K)	Basic
Density	rho	7800[kg/m^3]	kg/m³	Basic
Heat capacity at constant pressure	Cp	500[J/(kg*K)]	J/(kg·K)	Basic