*2.1. Geometry and Material Model*

A 2024-T3 aluminum alloy plate with a length of 120 mm, a width of 35 mm, and a thickness of 6 mm was used for the geometry model. The shoulder diameter of the stirring tool is 16 mm with concentric ring grooves. The diameter of the top and root of the pin is 6 mm and 3 mm, respectively. The length of the pin is L, which changes from 5.8 to 6.0 mm. The conical angle θ changes from 14.5◦ to 14◦ with the pin length changing from 5.8 to 6.0 mm. Figure 1 shows the diagram of the workpiece and the stirring tool with the corresponding size.

**Figure 1.** Schematic diagram of tool size and welding sample.

The chemical composition of 2024-T3 aluminum alloy is shown in Table 1. The thermal conductivity, specific heat capacity, thermal expansion coefficient, elastic modulus, Poisson's ratio, and other physical parameters of aluminum alloy 2024 are shown in Figure 2.

**Table 1.** Chemical composition of aluminum alloy 2024.


**Figure 2.** Thermophysical properties of aluminum alloy 2024 with temperature change. (**a**) Density and thermal expansion coefficient; (**b**) Young's modulus and Poisson's ratio; (**c**) thermal conduction coefficient and specific heat capacity [35].
