# Residual Stress Relaxation of DRWDs in OSDs under Constant/Variable Amplitude Cyclic Loading
## 2 Welding Residual Stress Distribution
### Numerical Simulation  
A refined residual stress analysis model of DRWDs with the same geometric dimensions as the experimental specimen (as shown in Figure 6) is established. The Solid70 element, an eight-node hexahedral solid element, is used in FEM and its corresponding structural element is a Solid185 element. Figure 6a depicts the displacement boundary according to the actual installation conditions in the welding process of OSDs. Symmetry constraints are imposed on the symmetry area of the deck plate. Node translational displacement is constrained on the right and left sides of the deck plate in the y-direction and on one side of the cross section of the deck plate in the z-direction. Due to the drastic change in the temperature gradient, a dense mesh is adopted in the weld and the heat-affected zone, in which the length of the transition zone is 30 mm, and the rest of the mesh becomes sparser with the distance from the weld. In Figure 6b, the length of the smallest element is 0.5 mm and the length of the largest element is 8 mm.  
The temperature field calculation of welding process is part of the transient thermal analysis. In this section, heat production rates are imposed on the activated weld seam elements to simulate moving heat sources based on the element birth and death technology [23]. The initial temperature is set to room temperature, 20 \({}^{\circ}\)C. In this paper, temperature-dependent thermal and mechanical properties of Q345 qc steel are adopted, as illustrated in Table 1[24; 25]. The yield strength and elasticity modulus decrease with the increase of temperature, while the coefficient of thermal expansion increases with the increase of temperature. The welding rod is E50 type, and its thermophysical and mechanical properties are the same as the base materials.  
The yield strength and elasticity modulus decrease with the increase in temperature, while the coefficient of thermal expansion increases with the increase in temperature. In the welding process, the weld length and welding speed were 300 mm and 10 mm/s,  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Temperature**} & \multirow{2}{*}{\begin{tabular}{c} **Thermal** \\ **Conductivity** \\ **W/(m \({}^{\circ}\)C)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Specific** \\ **Heat** \\ **V/(kg m\({}^{\circ}\)C)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Poisson’s** \\ **Capacity** \\ **J/(kg \({}^{\circ}\)C)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Linear** \\ **Raio** \\ **10-5 \({}^{\circ}\)C** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Elasticity** \\ **Modulus** \\ **/GPa** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Yield** \\ **Stress** \\ **/MPa** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Tangent** \\ **Modulus** \\ **/GPa** \\ \end{tabular} } \\ \cline{1-1} \cline{6-10}  & & & & & & & /GPa \\ \hline
20 & 50 & 7820 & 460 & 0.28 & 1.10 & 205 & 370 & 2.050 \\
250 & 47 & 7700 & 480 & 0.29 & 1.22 & 187 & 280 & 1.870 \\
500 & 40 & 7610  
respectively. The welding time of each weld was 30 s. Figure 7 shows the temperature distribution in the whole process of model welding and cooling. It is seen that the cooling time between the two welds is 300 s; the welding time of the four welds is 1-30 s, 331-360 s, 661-690 s, and 991-1020 s. Once the welding starts, the weld temperature rises rapidly and the partial melting forms a molten pool. The temperature of the inner part of the black dotted line in Figure 7e is higher than the melting point. The shape of the weld is similar to that in Figure 1, which indicates that the heat applied by the model heat source is reasonable.