**3. Results and Discussion**

## *3.1. Threshold Strain and Maximum Crack Distance*

There are many quantitative indicators for evaluating the thermal crack sensitivities of materials. In this study, the threshold strain and maximum crack distance (MCD) are used as evaluation indexes of weld solidification cracks. Threshold strain refers to the strain at crack initiation during a Trans-varestraint test for a series of small to large strains. Saturation strain refers to the strain that exceeds the threshold value where the maximum crack length no longer shows a significant change; the MCD refers to the maximum crack length (MCL) measured for each value of the test strain above the saturation strain. Figure 2 shows the MCLs of the test materials for the transverse variable restraint welding solidification crack test under various strains. It can be seen from the graph that the threshold strain of the 441 ferritic stainless steel is between 0.5% and 1%, whereas the threshold strain of the 441Ce ferritic stainless steel is between 0% and 0.25%. The MCD values for 441 and 441Ce ferritic stainless steels are 239.5 ± 0.1 μm and 290.0 ± 0.1 μm, respectively. Thus, it can be concluded that the addition of Ce increases the weld solidification crack sensitivity of 441 ferritic stainless steel.

**Figure 2.** MCLs of the test materials under various strains.

## *3.2. Thermodynamic Calculation of Solidification Process*

Table 2 shows the solidification temperature range obtained from simulation calculation. It can be seen that the solidification temperature range of the 441Ce material with the rare earth element Ce reached 199 ◦C, which is approximately 14 ◦C higher than that of the 441 material, indicating that Ce expands the solidification temperature range. Thus, Ce addition increases the area and time of solid–liquid coexistence during solidification, greatly increases the risk of solidification cracking, and reduces the ability of stainless steel to resist solidification cracking.



## *3.3. Solidification Crack Distribution and Morphology*

Figure 3 depicts the crack distribution and morphology of the test specimen under Trans-varestraint test for the 5% strain condition. The direction of the columnar crystal of the weld is mostly perpendicular to the fusion line during solidification crystallization. This is because the liquid metal solidifies and crystallizes along the direction of the temperature gradient. When the columnar crystal grows, there is a liquid phase film between the front columnar crystals of the solidification interface. At this time, a transverse strain is applied to the welding metal, and the liquid phase film that has not solidified at the grain boundary is insufficient to fill the gap generated by the strain, thus forming cracks at the grain boundary. As can be seen from Figure 3, the cracks are primarily situated at the grain boundary position, verifying that the solidification cracks occur between the columnar crystals.

**Figure 3.** Crack distributions and morphologies under 5% strain for (**a**) 441 and (**b**) 441Ce type materials.

Figure 4 shows the typical shape of a crack formed in the Trans-varestraint test, which applies instantaneous strain to the specimen. Under the application of a sudden strain, owing to the temperature difference of the instantaneous cracking zone, the solidification crack morphology produced by the Trans-varestraint test has the characteristics of both high and low temperature zones [20]. The high temperature zone is close to the crystal front and shows the characteristics of liquid phase fracture; the liquid film traces at the time of fracture are visible between the crystals. Peng et al. [21] believe that the crystallization process of the columnar crystal at the moment of cracking in the high temperature region is complete or nearly complete, and the connection, contact, and void formation of adjacent columnar crystals are also complete; this means that at this moment, the adjacent columnar crystals have only the connections of the residual low-melting of the liquid phase film and the liquid bridge forms. The low temperature zone refers to the zone of solidification cracking that is away from the crystallization front. In this zone, it is observed that the columnar crystal plane with complete crystal morphology has annular or striped ridges, and the arrangement direction of each annular ridge and the main direction of the striped ridges are roughly parallel to the direction of the columnar crystals, similar to a waterfall; the low temperature zone is close to final solidification (i.e., in a liquid–solid zone with poor fluidity), which is pulled apart under a large tensile strain and forms the characteristic shapes of the annular and striped ridges.

**Figure 4.** Typical morphology of a crack. Test material: 441 steel, test strain: 5%.
