Patented in 1991, friction stir welding (FSW) has since been used widely to create strong joints in aluminum alloys. The aircraft industry has started to adapt this technology, and now the largest manufacturers, including Airbus, are studying how to cut manufacturing costs with it. First, though, they want mathematical modeling to help them fully understand the process before making massive investments in retooling their manufacturing lines.

Figure 1: In Friction Stir Welding, a shoulder sitson the metal surfaces and creates heat throughfriction, while a pin stirs the plasticized andheated materials to create the weld. (Photo:Eclipse Aviation)
FSW offers significant improvements over arc welding or riveted joints because the joints are stronger, lighter, and can be completed more quickly. In the FSW process (Figure 1), a cylindrical tool made up of a shoulder and a threaded pin is spun and inserted into the joint between two pieces of metal. The rotating shoulder and the pin generate heat, but not enough to melt the metal. Instead, the softened, plasticized material forms a solid phase made up of a finegrained material with no entrapped oxides or gas porosity.

Airbus is investigating plans to introduce this technology into its manufacturing plants. Riveting is a slow, laborintensive process, and replacing rivets with a continuous welded joint not only results in faster manufacturing at lower costs, but the distributed load results in a stronger joint. Yet, many aspects of the tooling and operating parameters can influence the amount of heat and the quality of the weld: the raw materials, tool diameter, tool geometry, rotational speed, weld travel speed, and down force. The process must be optimized for the materials used in commercial aircraft. Thus, Airbus asked several institutions to join it in a consortium to study FSW.

Figure 2: The multigeometric Multiphysics Model of Friction Stir Welding couples a 3D thermal analysisto 2D axisymmetric swirl flow.
At Cambridge University, the heat-generation model presented in this article was developed, while Nicholas Kamp, Joseph Robson, and Andrew Sullivan from Manchester University studied the microstructural aspects. First, a model of FSW was created that allows Airbus engineers to look "inside" a weld to examine temperature distributions and changes in microstructures. To enable Airbus engineers to access the model easily, a GUIdriven simulation tool was created so they could look at a weld's thermal properties, and ultimate strength and hardness.

Figure 3: A customized user interface runs a Mathematical Model of FSW to analyze various materialsand configurations.
A model built using the COMSOL Multiphysics® simulation software couples a 3D thermal analysis for calculating heat flow, to 2D axisymmetric swirl flow simulations for calculating both the flow and heat generation (Figure 2). The thermal analysis calculates the 3D temperature field from the heat flux imposed at the tool surface. It captures the effect of the tool movement, the thermal boundary conditions, and the thermal properties of the material being welded. The model then extrudes the temperature distribution near the tool surface from the 3D boundary to the domain in the 2D model. That next part of the model, in turn, analyzes the rotational flow of material through a 2D cross-section underneath the shoulder. As a final step, it calculates the overall heat flux from this section and couples it back to the 3D analysis.

Use of the 2D modeling domain saved computational memory and time, while results deviated only 1% to 2% from full 3D models of the flow. The analyses are solved simultaneously to guarantee faster and better solution convergence.

Figure 4: One result that users of the customized GUI can output is this 2D Contour Plot of the naturallyaged hardness measured on the Vickers Hardness Scale. The contour plot is produced by findingthe thermal profile at evenly spaced data points in the transverse direction (perpendicular to thewelding direction of the tool) and thickness of the weld.
To make this technology easily accessible, a custom user interface (Figure 3) was created using COMSOL Script™. Choosing a material from a pulldown menu selects the microstructural properties associated with that material from a database. The user also gives values for the tool's geometry and operating parameters. The model then creates a contour plot (Figure 4) by finding the thermal profile at various points in the transverse cross-section and then calculates the corresponding material microstructure.

Figure 5: The 3D Thermal Profile of the weld.
The final output plot is the 3D thermal profile (Figure 5). Here, an engineer can calculate various statistics such as the temperature of the welded material at the shoulder and tip of the pin, as well as the power input (or heat generation).

Looking at the model requirements, a flexible simulation tool was required in order to link the 2D axisymmetric physics to 3D physics— something that is extremely difficult to do. It was also easy to link in the microstructural-material aspects, which were developed in MATLAB®. Then, the underlying scripting language allowed the creation of the custom user interface that gave Airbus engineers easier access to the model's functionality.

Airbus is funding a follow-on project that will allow refinement of the model, both in terms of thermal and microstructural analysis.

This work was done by Dr. Paul Colegrove, Nicholas Kamp, Joseph Robson, and Andrew Sullivan using software from COMSOL, Inc. For more information, click here.