## 3 Results and Discussion
### Senb  
Figure 4a shows the crack growth resistance curves for the standard SENB specimen (\(a\)/W = 0.5) with different strength mismatch levels. A strong effect of weld strength mismatch on the initial fracture toughness and dynamic fracture toughness can be clearly seen. The resistance curves significantly increase with the increase of strength mismatch levels (from \(M_{y}\) = 0.8 to \(M_{y}\) = 1.3). A similar result was also found in Ref. [39]. The related experimental data (Blue points) from [40] have been used to compare the Finite Element Method (FEM) results for the case of evenmatched (\(M_{y}\) = 1) a/W = 0.5 SENB specimens. It is observed that the comparison exhibits, good agreement in the range of \(\Delta\)a = 0.75, while it exerts a slight deviation above this value. It can be attributed to the discrepancy of material property. These results further validate the effectiveness of the FEM model. Figure 4b shows the normalized crack growth resistance (CTOD\({}^{My}\
eq 1.0\)/CTOD\({}^{My}=1.0\)), e.g., the resistance curves for \(M_{y}\
eq 1.0\) were normalized by the resistance curves for \(M_{y}\) = 1.0. The dash line without marker indicates the case for \(M_{y}\) = 1.0. It is obvious to see that the effect of the strength mismatch on resistance curve tends to be less relevant to the amount of crack extension.  
Figure 3: Schematic plots of pipe, (**a**) inner-cracked pipe; (**b**) schematic illustration of axisymmetric model.  
The opening stress distributions in front of the crack tip for all the mismatched specimens at \(\Delta a=0.1\) mm are charted in Figure 5 to better understand the effect of strength mismatch on the ductile tearing resistance curves for SENB specimens. It shows that the opening stress for different mismatched cases expressed a gradually lower peak value with the increases of \(M_{y}\) at the same crack growth, therefore yields the increasingly higher resistance curve, as shown above in Figure 4a. It can also be seen that, with the increase of distance from crack tip, the crack opening stress rapidly declines, and then transforms into compressive stress, which could be influenced by the remote field [40; 41].  
The equivalent plastic strain (\(\varepsilon_{p}\)) ahead of the current crack tip for all the mismatched SENB specimens at \(\Delta a=0.1\), \(0.5\) and \(1.5\) mm are also presented in Figure 6, respectively, for further understanding the effect of strength mismatch on resistance curves with crack growth. At crack initiation, \(\Delta a=0.1\) mm, a comparatively small influence of \(M_{y}\) on the equivalent plastic strain can be observed. But still, a higher \(\varepsilon_{p}\) for the mismatched SENB specimen can be expected for the case with a larger \(M_{y}\) (see Figure 6a). With further crack growth, e.g., \(\Delta a=0.5\) mm and \(1.5\) mm, a much more evident effect of mismatch ratio on the equivalent plastic strain can be seen for all of the mismatched SENB specimens. Moreover, the equivalent plastic strain significantly increases with the increase of strength mismatch ratios, which again well explains the increasing resistance curves with increasing mismatch ratios, as observed in Figure 4a.  
Figure 4: Effect of strength mismatch on crack growth resistance, (**a**) ductile resistance curves; (**b**) normalized crack growth resistance curves.  
Figure 5: The distribution of crack tip opening stress ahead of the crack tip at \(\Delta a=0.5\) mm for different mismatched SENB specimens.