## 4 Results
### Effect of Grooving Corrosion  
For the grooving corroded tubular joint, the results of the surface stress extrapolation method are compared with those of the through-thickness linearization method for the axial loading condition. The SCFs as a function of d are shown in Figure 11. The trends of SCFs are different. The SCFs obtained by the surface stress extrapolation method decrease with d, and the decrease is not continuous, while the SCFs obtained by the through-thickness linearization method continuously increase with d. The difference in the SCF between the two methods becomes significant when d varies from 0 to 2.5 mm.  
It has been observed that surface stress typically increases approaching the weld toe, and the stress at the first reference point (0.4 T) is higher than at the second reference point (1.0 T). However, in the case of grooving corrosion degradation, the increasing surface stress is subjected to a decrease and subsequent increase when approaching the weld toe [25]. As a result, the stress at the first reference point is lower than that at the second reference point for some cases. The use of the surface extrapolation method to determine hot-spot stresses can yield lower SCFs. When employing a surface stress extrapolation, it is assumed that the nonlinear component has effectively disappeared on the plate surface at a distance greater than 0.4 T from the weld toe, and stress and strain increase almost linearly near the weld toe [26]. However, the complex stress distribution and the inconsistency with the assumption for grooving corrosion conditions pose challenges to the use of the surface extrapolation method. The use of the through-thickness linearization method is more reasonable for grooving corrosion degradation conditions.  
Figure 11: Thickness linearization method and surface stress extrapolation method.  
By using the through-thickness linearization method, the SCFs are obtained for various corrosion depths, as shown in Figure 12. The SCFs of critical locations are all increased with corrosion depth. Under axial loading and OPB, the maximum SCF always appears at the saddle, and the minimum SCF always appears at the crown. However, under IPB, the SCF distribution along the intersection changes with corrosion depth. The maximum SCF appears between the saddle and crown when there is no corrosion degradation at the tubular joint or under uniform corrosion degradation conditions. However, for grooving corrosion conditions, as the corrosion depth d increases, the position of the maximum hot-spot stress gradually shifts to the saddle.  
The results of the grooving corrosion cases are compared with those of the uniform corrosion cases, as shown in Figure 13. In contrast to the linear increase in the SCF with d for uniform corrosion cases, the SCF increases nonlinearly with d for grooving corrosion cases. Compared with uniform corrosion degradation, grooving corrosion results in higher SCFs. Therefore, grooving corrosion is more detrimental than uniform corrosion for the tubular joint, and the remaining fatigue life is significantly reduced.  
Figure 12: SCFs of the weld toe on the chord for grooving corrosion under (**a**) axial loading; (**b**) in-plane bending; and (**c**) out-of-plane bending.