# Residual Stress Relaxation of DRWDs in OSDs under Constant/Variable Amplitude Cyclic Loading
## 5 Conclusions  
Based on the above investigations, the main conclusions are as follows:  
* The stress relaxation condition of weld residual stress under the mechanical stress, which is induced by the external cyclic loading, depends on the sum of initial residual stress (\((\sigma_{res})_{iii}\)) and Mises structure stress (\((\sigma_{app})_{Mises}\)) and exceeds the yield strength of the material (\(f_{y}\)), rather than observing the stress variation of a certain uniaxial (longitudinal or transverse stress).
* Most of the welding residual stress release (about 95%) occurred in the first loading cycle under the constant amplitude cyclic loading. As the number of external loading cycles increased, the overall distribution trend of welding residual stress remained almost unchanged, and the stress decreased until it was stable after five cycles.
* The welding residual stress relaxation coefficient A decreases with the increase in stress amplitude (TSA), and decreases approximately linearly with the stress ratio (R); that is to say, the releasing amount of welding residual stress increases with the increase in stress amplitude (TSA) and increases approximately linearly with the increase in the stress ratio (R).
* The release behavior of residual stress is controlled by the maximum amplitude stress in the variable amplitude cyclic loading. Thus, the stress will not continue to be released if the DRWDs have the same or smaller amplitude loading after the residual stress is released.  
All authors discussed and agreed on the idea and scientific contribution. [PERSON] did the mathematical modeling, performed the simulations, and contributed to the writing. [PERSON], [PERSON], [PERSON] and [PERSON] contributed to the revisions and discussion of the results. All authors have read and agreed to the published version of the manuscript.  
The research was supported by the Fund for Distinguished Young Scientists of Jiangsu Province (grant no. BK20190013), the Program of National Natural Science Foundation of China  
\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)**} \\ \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}  & **Ca** & **Si** & **Ca** & **Si** & **Ca** & **Si** & **Ca** & **Si** & **Ca** & **Si** \\ \hline C1 & 131.99 & 132.54 & 131.89 & 132.39 & 131.89 & 132.39 & 131.89 & 132.39 & 131.89 & 132.39 \\ C2 & 143.59 & 144.29 & 131.99 & 132.54 & 131.90 & 132.44 & 131.90 & 132.44 & 131.90 & 132.44 \\ C3 & 143.59 & 144.29 & 143.43 & 144.19 & 131.99 & 132.54 & 131.89 & 132.52 & 131.89 & 132.52 \\ C4 & 143.59 & 144.29 & 143.43 & 144.19 & 143.43 & 144.19 & 131.87 & 132.65 & 131.82 & 132.53 \\ C5 & 143.59 & 144.29 & 143.43 & 144.19 & 143.43 & 144.19 & 133.43 & 144.19 & 132.09 & 132.40 \\ C6 & 144.00 & 144.63 & 141.60 & 142.22 & 141.50 & 142.13 & 141.50 & 142.13 & 141.50 & 142.13 \\ C7 & 141.60 & 142.30 & 141.34 & 142.09 & 141.34 & 142.09 & 141.34 & 142.09 & 141.34 & 142.09 \\ C8 & 137.59 & 138.20 & 137.49 & 138.08 & 137.49 & 138.08 & 137.49 & 138.08 & 137.49 & 138.08 \\ C9 & 131.99 & 132.54 & 131.88 & 132.36 & 131.88 & 132.36 & 131.88 & 132.36 & 131.88 & 132.36 \\ C10 & 131.99 & 132.54 & 131.84 & 132.35 & 131.84 & 132.35 & 131.84 & 132.35 & 131.84 & 132.35 \\ C11 & 131.99 & 132.54 & 131.86 & 132.38 & 131.86 & 132.38(grant nos. 51978154 and 51608258), and the Scientific Research Foundation of the Graduate School of Southeast University (grant no. YBJJ1819).  
The data presented in this study are available on request from the corresponding author. The data are not publicly available due to privacy.  
The authors declare no conflict of interest.