## 4 Discussion
### Mechanism of Fatigue-Crack Generation  
Next, we mainly analyze the main mechanism of the cracking of fatigue cracks at the pores. Cracking is mainly affected by stress concentration and the strength of stress distribution depends on stress-intensity factor K. The larger stress-intensity factor K is, the more concentrated stress is, and the easier the sample is to crack. In Figure 10, we can see that incomplete penetration corresponds to the existing precrack, as shown in Figure 13a, so we can establish a model of the precrack to calculate the stress-intensity factor of the precrack tip. Stress-intensity factor K of the precracked tip is derived from Westergaard [22]:  
\[\mathrm{K}=\beta\sigma\sqrt{\pi\mathrm{L}} \tag{6}\]  
where \(\beta\) is a dimensionless factor related to the geometry of the sample, \(\sigma\) is the applied stress, and L is the length of the precrack. However, from Figure 10, we can observe that there were pores in the incomplete penetration, and when the pores are connected to the incomplete penetration, it can be regarded as increasing the length of the preset crack, as shown in Figure 13b. So, we can modify Equation (6):  
\[\mathrm{K}=\beta\sigma\sqrt{\pi(\mathrm{L}+2\mathrm{r})} \tag{7}\]  
where r is the pore radius. When the pores are connected to the incomplete penetration, it is equivalent to increasing the length of the precrack. From Equation (7), we can conclude that, when pores  
Figure 12: Pore-forming mechanism at lack of penetration. (**a**) Bubbles floating up in the bath; and, (**b**) bubbles forming pores near the weld line.  
are connected to the incomplete penetration, K increases significantly, resulting in greater stress concentration. Cracking is more likely to occur here:  
When fatigue cracks occur around the pores, a large number of microcracks appear around the pores. This shows that fatigue cracks appear in many parts around the pores, and as fatigue-test cracks continue to expand, some of the microcracks stop growing, and other parts of microcracks intersect to form a main crack, eventually leading to fatigue fracture.  
In addition, pores were located near the fusion line, so the pore edges were surrounded by elongated columnar crystals. As shown in Figure 14a, protrusions and depressions were formed at the intersections of the grain boundaries of the columnar crystals, and the pores, and gaps formed at the depressions. [PERSON] pointed out in their article that the gap could increase the stress concentration factor and the increased degree is related to the size of the gap [23]. If there are many equiaxed crystals inside the pore, the distance between them and the gap might be very small. In this way, stress-concentration factor at the gap is generally greater, so the crack always initiates at the gap.  
Similarly, in this experiment, the elongated columnar crystals around the pores create larger gaps, which results in greater stress concentration, so cracks sprout under very small stresses. Fatigue cracks expand after the initiation of the gap at the pore edges, forming numerous microcracks. As shown in Figure 14b, if these microcracks are perpendicular to the applied load, they expand in an accelerating manner. During the expansion process, microcracks continuously to form the main crack, while some of the microcracks stopped expanding. This continuous expansion of the main crack eventually leads to fatigue fracture.  
Figure 14: Fatigue-crack initiation mechanism at pore: (**a**) fatigue-crack initiation at the intersection of columnar grain boundary and pore; and, (**b**) crack propagation after initiation.  
Figure 13: Cracking mechanism in the case of no penetration; (**a**) no pores; (**b**) pores.