*4.1. Temperature Distribution and Weld Bead Geometry*

The temperature distributions in the welding process were calculated under different welding currents, including 60 A, 75 A, and 90 A. The specific temperature distribution results are shown in Figure 7. It should be noted that the welding voltage is 13.8 V, the welding speed is 5 mm/s, and the welding efficiency is 0.8. According to Equation (4), the welding input power can be derived.

**Figure 7.** The temperature fields under different welding currents at t = 16 s, with (**a**) the xy plane at I = 60 A, (**b**) the half xy plane at I = 60 A, (**c**) the yz plane at I = 60 A; (**d**) the xy plane at I = 75 A, (**e**) the half xy plane at I = 75, (**f**) the yz plane at I = 75 A, (**g**) the xy plane at I = 90 A, (**h**) the half xy plane at I = 90 A, and (**i**) the yz plane at I = 90 A.

From Figure 7, it can be seen that as the welding heat source moves, the molten pool advances stably and the shape of the molten pool remains substantially unchanged. When the welding current is gradually increased, the temperature in the central region of the moving heat source is increased. To further investigate the relationship between the welding current and the welding bead geometry,

the cross sections of the welding bead under different welding currents were observed, as shown in Figure 8. Then the bottom width of weld bead is represented by WD.

**Figure 8.** The cross sections of the welding bead under different welding currents.

From Figure 8, it can be found that as the welding current increases, the temperature of the central region of the moving heat source increases and the weld transverse cross section becomes wider, i.e., *WD*<sup>l</sup> > *WD*<sup>2</sup> > *WD*<sup>3</sup> . In addition, the temperature in the central region of the moving heat source is larger than the melting point of the titanium alloy (1650 ◦C).

In order to further analyze the effect of the welding current on the temperature distribution during the welding, the thermal cycle curves were obtained, as shown in Figure 9. From Figure 9, it can be found that due to the rapid heating rate of the welding, the curve rises extremely fast and the temperature rapidly reaches a peak; the closer the weld bead is, the faster the temperature rises and the higher the peak temperature. During the cooling phase, the temperature drops relatively slowly. In addition, the simulated temperature values under different distances and currents are listed in Table 4.

**Figure 9.** The simulated thermal cycle curves at different distances from the weld center: (**a**) 1 mm, (**b**) 2 mm, and (**c**) 3 mm.


**Table 4.** The simulated temperature maximum values under different distances and currents.

From Table 4, it can be found that the temperature value is lower than the melting point of the titanium alloy (1650 ◦C) under L = 3 mm and I = 60 A. However, the temperature is larger than the melting point of the titanium alloy under L = 3 mm and I = 90 A. Then, the welding heat input *P* can be calculated thus:

$$P = \frac{\eta L H}{V} \tag{19}$$

Here, *U* is the welding voltage, *I* is the welding current, *V* represents the welding speed, and *η* is the welding efficiency. According to Equation (19), the welding current is positively correlated with the welding heat input when *U* and *V* are determined. It should be noted that the welding efficiency is 0.8 and the welding voltage is 13.8 V in Equation (19). Then, the welding heat inputs under I = 60 A, I = 75 A, and I = 90 A are 132.48 J·mm−1, 165.60 J·mm−1, and 198.72 J·mm−1, respectively. When the welding heat input is too small, welding defects are easily caused; but when the welding heat input is too large, coarse columnar crystals are generated in the weld bead. This leads to the increase of the brittleness of the welded joints. Therefore, within the range of reasonable welding heat input, the weld grain size is more uniform. Based on the analysis mentioned above, the welding thermal cycle test is performed under the welding current I = 75 A.

The calibration between the simulated results and the experimental observations is presented as shown in Figure 10. The comparative analysis of both the simulated results and experimental observations was performed. Figure 10a shows that the experimental and simulated time–temperature curves match well, including the heating rate, peak temperature, and cooling rate. Here, the heating and cooling rates are calculated by dividing the difference between the initial and current temperature values by the fixed time step. The comparison between the simulated weld bead geometry and the measured macrograph of a polished and chemically etched weld bead transverse cross section is shown in Figure 10b.

**Figure 10.** The comparison between the simulated results under I = 75 A and the experimental observations: for (**a**) thermal cycle curves and (**b**) weld bead geometry.

According to the temperature contour above the melting point of 1650 ◦C, the fusion zone is determined in the FE model. From Figure 10b, it can be found that the simulated fusion boundary isotherm is in good accordance with the experimental fusion boundary and penetration depth. It is

preliminarily concluded that the weld bead transverse cross section is better when the welding current is 75 A.
