# Residual Stress Relaxation of DRWDs in OSDs under Constant/Variable Amplitude Cyclic Loading
## 4 Residual Stress Relaxation of DRWDs by External Cyclic Loading
### Welding Residual Stress Release of DRWDs under Variable Amplitude Cyclic Loading
As depicted in Table 3, the second to fifth cyclic loading stresses were all 65 MPa, but the first cyclic loading stresses increased from 31.5 MPa to 130 MPa in C6-C9. Figure 21b shows the stable transverse residual stress after relaxation at the weld toe in C6-C9. It is seen that stress release only occurs during the first cyclic loading, except for C6. This is because the first cyclic stress (\((\sigma_{app})_{1}\)) in C7-C9 has reached the maximum stress amplitude. In C6, stress relaxation occurs under the first loading cycle. During the second loading cycle, the stress continues to relax, because the second cyclic stress is greater than the first cyclic stress (\((\sigma_{app})_{2}>(\sigma_{app})_{1}\)). At this point, the slope of the stress decline line is greater than that of the first stress relaxation, indicating that the stress relaxation decreases nonlinearly with the increase in loading stress. In C9-C12, three stress amplitudes were set to 65 MPa, 100 MPa, and 130 MPa, respectively. The first cyclic loading stress of C9-C11 reached the maximum. As shown in Figure 21c, the total stress release in the four cases is almost equal after five cycles. In C9-C11, the stress release only occurred during the first cyclic loading, while stress was released in the first two cyclic loadings of C12. Figure 20: The stress time-history curves of C1 and C12: (**a**) C1; (**b**) C12. Table 4 shows the transverse residual stress and release stress under variable-amplitude loading cycles from 0 to 5. For variable amplitude loading cases, if \(\left(\sigma_{app}\right)_{1}\ \geq\ \left(\sigma_{app}\right)_{2}\ \geq\ \left(\sigma_{app}\right)_{3}\ \geq\ \left(\sigma_{app} \right)_{4}\ \geq\ \left(\sigma_{app}\right)_{5}\), the residual stress is released only during the first stress cycle. Therefore, the residual stress release behavior is controlled by the maximum amplitude stress. Once the residual stress is released, the stress will not continue to be released if the DRWDs have the same or smaller amplitude loading. As illustrated in Table 5, the simulation and calculation values of \(\sigma_{x}\) under variable-amplitude cyclic loading cases are compared. To simplify the calculation, it is assumed \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Cases**} & \multicolumn{6}{c}{**The Transverse Residual Stress (TRS) and Release Stress (RS)**} \\ \cline{2-10}  & \multicolumn{2}{c}{\(n\) = 1} & \multicolumn{2}{c}{\(n\) = 2} & \multicolumn{2}{c}{\(n\) = 3} & \multicolumn{2}{c}{\(n\) = 4} & \multicolumn{2}{c}{\(n\) = 5} \\ \cline{2-10}  & **TRS** & **RS** & **TRS** & **RS** & **TRS** & **RS** & **TRS** & **RS** & **RS** \\ \hline C1 & 131.99 & 14.78 & 131.89 & 0.15 & 131.89 & 0.00 & 131.89 & 0.00 & 131.89 & 0.00 \\ C2 & 143.59 & 3.03 & 131.99 & 11.75 & 131.90 & 0.10 & 131.90 & 0.00 & 131.90 & 0.00 \\ C3 & 143.59 & 3.03 & 143.43 & 0.09 & 131.99 & 11.66 & 131.89 & 0.02 & 131.89 & 0.00 \\ C4 & 143.59 & 3.03 & 143.43 & 0.09 & 143.43 & 0.00 & 131.87 & 11.54 & 131.82 & 0.12 \\ C5 & 143.59 & 3.03 & 143.43 & 0.09 & 143.43 & 0.00 & 143.43 & 0.00 & 132.09 & 11.79 \\ C6 & 144.00 & 2.69 & 141.60 & 2.41 & 141.50 & 0.09 & 141.50 & 0.00 & 141.50 & 0.00 \\ C7 & 141.60 & 5.02 & 141.34 & 0.21 & 141.34 & 0.00 & 141.34 & 0.00 & 141.34 & 0.00 \\ C8 & 137.59 & 9.12 & 137.49 & 0.12 & 137.49 & 0.00 & 137.49 & 0.00 & 137.49 & 0.00 \\ C9 & 131.99 & 14.78 & 131.88 & 0.17 & 131.88 & 0.00 & 131.88 & 0.00 & 131.88 & 0.00 \\ C10 & 131.99 & 14.78 & 131.84 & 0.19 & 131.84 & 0.00 & 131.84 & 0.00 & 131.84 & 0.00 \\ C11 & 131.99 & 14.78 & 131.86 & 0.15 & 131.86 & 0.00 & 131.86 & 0.00 & 131.86 & 0.00 \\ C12 & 141.60 & 5.02 & 131.99 & 9.76 & 131.85 & 0.20 & 131.85 & 0.00 & 131.85 & 0.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The transverse residual stress and release stress under variable-amplitude cyclic loading cases (unit: MPa). Figure 21: The transverse welding residual stress of C1-C12: (**a**) C1-C5; (**b**) C6-C9; (**c**) C9-C12.