## 4 Stress Intensity Factor of Weld Crack
### Stress Intensity Factor Analysis
#### 4.2.3 Stress Intensity Factor after Reinforcement  
In order to study the influence of the number of reinforcement layers on the effect, CFRP with a longitudinal length of 200 mm and a width of 100 mm was selected to reinforce the surface cracks at the weld toe. The schematic diagram of CFRP reinforcement is shown in Figure 16. Since the crack is mainly affected by K\({}_{\rm I}\), the reinforcement effect of CFRP on the crack is analyzed through the change of K\({}_{\rm I}\). Figure 17 shows the relationship between the stress intensity factor K\({}_{\rm I}\) and the number of CFRP layers.  
In Figure 17, it can be seen that the K\({}_{\rm I}\) of the crack at the weld toe decreases with the increase of the number of CFRP layers, while the K\({}_{\rm I}\) of the crack at the weld root does not change significantly with the increase of the number of CFRP layers. This is because CFRP is attached to the surface of the crack at the weld toe. When the crack surface is subjected to tensile stress, CFRP can limit the growth of the weld toe crack, while the crack at the weld root is not in contact with CFRP and is far away, thereby unable to play a reinforcing role. Therefore, the following text will only conduct reinforcement research on cracks at the weld toe.  
Figure 18 shows the decreasing amplitude of stress intensity factor K\({}_{\rm I}\) of cracks between adjacent layers of CFRP. The decreasing amplitude is large before the fifth layer and decreases after the fifth layer. From the first layer to the fifth layer, the decrease in K\({}_{\rm I}\) was 24 MPa\(\cdot\)mm\({}^{1/2}\), 14 MPa\(\cdot\)mm\({}^{1/2}\), and 7 MPa\(\cdot\)mm\({}^{1/2}\), respectively. When CFRP increased to the seventh and ninth layers, the decrease in K\({}_{\rm I}\) was 7 MPa\(\cdot\)mm\({}^{1/2}\) and 6 MPa\(\cdot\)mm\({}^{1/2}\), respectively. When the number of CFRP layers exceeds five, the reinforcement effect on cracks decreases.  
Figure 16: The schematic diagram of CFRP reinforcement.  
Figure 17: The relationship between K\({}_{\rm I}\) and the number of CFRP layers. (**a**) Weld toe; (**b**) weld root.  
Through analysis, it is found that selecting five layers for CFRP reinforcement is more reasonable, but the reinforcement effect of CFRP is also affected by size. Therefore, variables of different lengths and widths are set to analyze the reinforcement effect of different sizes. Figure 19 shows the relationship between the crack \(K_{I}\) at the weld toe and different CFRP lengths while keeping the CFRP width unchanged at 100 mm. When the length exceeds 100 mm, the improvement in the reinforcement effect becomes weaker by increasing the CFRP length. Figure 20 shows the relationship between the crack \(K_{I}\) at the weld toe and different CFRP widths while keeping the CFRP length unchanged at 200 mm. Compared with the CFRP length, different widths have a smaller impact on the reinforcement effect. When the width exceeds 50 mm, increasing the CFRP width weakens the improvement of the reinforcement effect. To sum up, five layers of CFRP with a length of 100 mm and a width of 50 mm are selected for reinforcement. Figure 21 shows the Stress intensity factor \(K_{I}\) of the weld toe crack after reinforcement. \(K_{I}\) in the figure is much larger than \(K_{II}\) and \(K_{III}\). Compared with the unreinforced ones, \(K_{I}\) at the crack tip after reinforcement decreases by 35 MPa\(\cdot\)mm\({}^{1/2}\), and \(K_{I}\) at the deepest crack decreases by 33 MPa\(\cdot\)mm\({}^{1/2}\).  
Figure 19: Relationship between weld toe crack \(K_{I}\) and CFRP length. (**a**) Crack tip A and B; (**b**) crack tip C.  
Figure 18: The relationship between the decreasing amplitude of weld toe crack \(K_{I}\) and the number of CFRP layers.