# Residual Stress Relaxation of DRWDs in OSDs under Constant/Variable Amplitude Cyclic Loading
## 2 Welding Residual Stress Distribution
### Welding Residual Stress Analysis  
Using the measured strain of each measuring point, the residual stress test value is obtained by the Kirsch formula [26]. Figures 8 and 9 depict the comparison of welding residual stress test data and finite element simulation results. The simulation results and experimental data of the welding residual stress are compared in Figures 8 and 9. To facilitate readers' understanding of this paper, the welding residual stress is perpendicular to the welding direction, which is also known as transverse residual stress, and denoted as \(\sigma_{x}\). The welding residual stress is parallel to  
Figure 8 shows a comparison of residual stress test data and FE simulation results on Paths P1 (on the top surface of the deck plate) and P2 (on the bottom surface of the deck plate). Excluding the drill centricity and strain anomaly points, there are 29 and eight effective measuring points on Paths P1 and P2, respectively. Because of the limitation of the operating space, the strain gauges around the weld seam and interior of the U-rib cannot be arranged; therefore, the measuring points on Path P2 are only arranged on the bottom surface of the deck plate outside the U-rib at both ends. First, in Figure 8, it is shown that the distribution tendencies of welding residual stress on Paths P1 and P2 are roughly the same. In general, the closer to the weld, the greater the stress value is measured. The maximum simulation values of \(\sigma_{x}\) on Paths P1 and P2 are approximately \(0.31f_{y}-0.44f_{y}\) and \(0.43f_{y}-0.55f_{y}\), respectively; whereas the maximum simulation values of \(\sigma_{z}\) on Paths P1 and P2 are approximately \(0.36f_{y}-0.42f_{y}\) and \(1.08f_{y}\), respectively. However, the \(\sigma_{z}\) on Paths P1 and P2 are compressive stresses at distances far from the weld and the average compressive stress is close to \(-0.05f_{y}\). Due to the deformation of specimens caused by the welding process, the \(\sigma_{x}\) is compressive stress in Path P1, but tensile stress in Path P2. Secondly, there are two peak points of \(\sigma_{x}\) within the heat-affected zone around each weld seam in Path P2, which correspond to the locations of the left weld root and right weld toe, and the maximum simulation value is approximately 150 MPa. The distribution of \(\sigma_{z}\) in Path P2 is shown as the tensile stress in the central area and compressive stress on both sides. The maximum value (370 MPa) occurs at the weld center and has exceeded the material yield limit, which is about 2.5 times the maximum \(\sigma_{x}\). Third, the welding sequence of this test is 1 st weld to 2 nd weld to 3 rd weld to 4 th weld. The maximum simulation \(\sigma_{x}\) appears at the first welding seam (1 st weld) on Path P1, while the peak values of the other welding seam are less than those of the first, and the compressive stress away from the weld zone also decreases with the welding sequence. However, the maximum simulation \(\sigma_{x}\) occurs at the last welding seam (4 th weld) on Path P2 and the compressive stress increases with the welding sequence. The reason for this phenomenon is that the first welding seam has the preheating effect of the second welding seam, resulting in a reduction of \(\sigma_{x}\) on the top surface of the deck plate at the second welding seam, while \(\sigma_{x}\) on the bottom surface of the deck plate increases. However, the longitudinal compressive stress is almost constant. Fourth, the simulation results of Paths P1 and P2 generally fit well with the experimental data. At the weld zone, the experimental values of \(\sigma_{x}\) and \(\sigma_{z}\) are the tensile stress, and the maximum deviation between the maximum experimental and simulation values of \(\sigma_{x}\) and \(\sigma_{z}\) on Path P1 are within 10 MPa and 13.5 MPa, respectively. The experimental values are generally compressive stress at the zone far from weld, and only a small number of points have low tensile stress.