*4.2. Calculations and Measurements of the CET*

For further evaluating the validity and rationality of the obtained welding process parameters from the welding temperature field analysis, these parameters act as the heat input parameters of the CA-FD coupling model. Then, the microstructure evolution is calculated by the CA-FD coupling model. The welding voltage is 13.8 V and the welding current is 75 A in this calculation, and the calculation areas are divided into rectangular macroscopic grids. In addition, these macroscopic grids consist of uniform microscopic grids, the grid size is 5 μm, and the time step is 0.5 ms. Of importance, the iteration number is set as 130, 372, and 454, respectively. The grains' growth tends to be dramatically changed with the influence of heat dissipation direction. The growth morphology of the dendrites in the weld pool varies with time during the solidification, as shown in Figure 11.

**Figure 11.** The morphology of grains in the weld pool at different times: (**a**) t = 0.065 s, (**b**) t = 0.186 s, and (**c**) t = 0.227 s.

From Figure 11a, it can be seen that the columnar crystals are formed at the edge of the weld pool at the beginning of solidification. With the progress of solidification, these columnar crystals continuously grow and some fine equiaxed crystals form at their tips, as shown in Figure 11b. The solidification layer continues to move inward and the solid-phase cooling capability is gradually weakened. It should be pointed that when the constitutional supercooling is high enough, the nonuniform nucleation is activated and the equiaxed crystals' nucleation starts in the center of the molten pool. From Figure 11c, it is shown that the growth of the columnar crystals is greatly affected by the growth of the central equiaxed grains. This leads to the arrest of the longitudinal growth for the partial columnar crystals, whereas their radial growth and secondary dendrite arms are intensified. The transformation from the columnar crystals to the equiaxed crystals is eventually achieved. When the grain growth direction is perpendicular to the heat dissipation direction of the molten pool wall, columnar crystals are formed. If the heat dissipation is along all directions around the melt, equiaxed crystals are formed. It can be concluded that the morphology of the dendrites exhibits randomness and asymmetry under the effect of the altering temperature field in the molten pool.

The solute concentration is the key factor of the liquid–solid state during the dendritic nucleation and growth. When the solute field is changed, the direction and morphology of the grain growth will be changed. Hence, the corresponding liquid solute concentration and solid solute concentration, as shown in Figure 12, are discussed. From Figure 12a,c,e, it can be seen that the release of solutes in the solid phase makes the liquid phase solute concentration located at the front of solid–liquid interface increase. Simultaneously, the solute diffusion rate in the liquid phase of the dendritic tip is much smaller than the dendrites' growth speed at the solid–liquid interface. In addition, when the competitive growth of columnar and equiaxed crystals occurs, the solute fields formed by the growth of equiaxed grains and columnar crystals will affect each other.

**Figure 12.** The solute distribution for solid and liquid phases in the weld pool at different times: (**a**) liquid phase at t = 0.065 s, (**b**) solid phase at t = 0.065 s, (**c**) liquid phase at t = 0.186 s, (**d**) solid phase at t = 0.186 s, (**e**) liquid phase at t = 0.227 s, and (**f**) solid phase at t = 0.227 s.

In light of Figure 12b,d,f, it can be seen that the growth of dendrites is always followed by the segregation phenomenon when observing the distribution of solute concentration in the solid phase during the CET process. At the beginning of the CET, the region of highest solute concentration is the columnar crystal tip. When the CET transformation is conducted at the final stage, the equiaxed crystals grow well and the solid solute concentration reaches 15%. At this point, it is prone to forming regional segregation after solidification. Therefore, the evolution of columnar–equiaxed crystals is not only influenced by the growth of columnar crystals being hindered by the equiaxed grains, but also the interaction between the solid and liquid solute concentrations.

The cross section of the TC4 alloy welded joint is selected for the purpose of testing the validity of the simulated microstructure evolution results. It was vertical to the direction of the weld moving heat source and was ground and polished. The welding samples were etched by 10 mL HF + 20 mL HNO3 + 50 mL H2O. Microstructure observation was conducted using an inverted GX671 metallographic microscope produced by OLYMPUS (Tokyo, Japan). Owing to the whole welding pool having good symmetry, the microscopic morphology of only half of the weld pool is shown in Figure 13a.

**Figure 13.** The micrograph of the TC4 alloy in the weld pool: (**a**) the test result and (**b**) the simulated result.

From Figure 13a, it can be seen that the equiaxed crystals mainly concentrate in the central region of the weld pool and the CET appears in the region near the fusion line. It can be concluded that the simulated results are in good agreement with the metallographic tests.
