**2. Thermal Modeling of Welding**

A visual thermal modeling of the welding process was performed to predict the thermal fields in the solidification area, by using the FE software ABAQUS and its user subroutines. The subroutines were implemented by the FORTRAN programmable language and linked to the ABAQUS software. The entire procedure of the coupling analysis is shown in Figure 1.

**Figure 1.** The flow chart of the coupled CA-FD model.

A TC4 alloy plate was used; its chemical compositions are listed in Table 1 and the material properties [19] used for thermal numerical simulation are shown in Figure 2.

**Table 1.** Chemical composition of the Ti-6Al-4V (TC4) titanium alloy plate.

**Figure 2.** The material properties used to simulate temperature distribution: (**a**) thermal conductivity, (**b**) specific heat capacity, (**c**) elasticity modulus and Poisson ratio, and (**d**) thermal expansion coefficient.

### *2.1. Meshing and Analysis Settings*

The TC4 plate (120 mm × 80 mm × 4 mm) was melted in the centerline by using a gas tungsten arc welding (GTAW) process without filler metal. The dimensions of the simulated welded thin plate were exactly identical to those used in the welding experiments. A total of 14,400 C3D8T elements were used in the simulation. In C3D8T, C represents a solid element, 3D indicates three-dimensional, and 8T denotes eight nodes. The FE model used is shown in Figure 3.

**Figure 3.** The FE model used in the numerical analysis.

It can be easily seen that the mesh in the central area of the weld bead is relatively fine and the other areas are sparse to obtain higher computation accuracy. In addition, the analysis type uses thermo-mechanical coupling analysis with two analysis steps: a heating analysis step and a cooling analysis step.
