## 2 FSW Experiments Considering Productivity
### Inherent Strain Method  
The thermal elasto-plastic analysis method can simulate the actual welding process, so the welding deformation and residual stress results of this method are known to be most similar to actual test results. Thermal elasto-plastic analysis calculates the distribution of temperature over time by analyzing the heat transfer according to the actual welding process. After applying the calculated temperature distribution into the structural analysis model as the thermal load, the structural boundary conditions by the welding jig are assigned to perform the analysis. Therefore, the numerical results are most similar to the experimental results, but the process takes a long period of time. This analysis method is the most suitable for test pieces, but is not suitable for actual-size structures because it requires a huge computational analysis time. Therefore, the inherent strain method was proposed to overcome those drawbacks. The total strain (\(\epsilon\)) is usually expressed as the sum of elastic strain (\(\epsilon_{\text{e}}\)), plastic strain (\(\epsilon_{\text{p}}\)), thermal strain (\(\epsilon_{\text{th}}\)), and phase transformation strain (\(\epsilon_{\text{pt}}\)), as shown in Equation (1). Permanent deformation occurs when an external force is applied to a structure, so long as the structure does not return to its original state after removing that force. Such permanent deformation is caused by permanent strain, and corresponds to plastic strain, thermal strain, and phase transformation strain. That is, subtracting the elastic strain from the total strain results in the permanent strain, as shown in Equation (2), which is defined as the inherent strain (\(\epsilon^{*}\)). In general, permanent deformation caused by welding includes thermal strain caused by the heat input during welding, the plastic strain caused by fixing the structure with the jig, and phase transformation strain caused by melting and solidifying the weld. However, phase transformation strain does not occur in FSW, which is a solid-state welding process. That is, the inherent strain in FSW is expressed as the sum of plastic strain and thermal strain. \[\epsilon=\epsilon_{\text{e}}+\epsilon_{\text{p}}+\epsilon_{\text{th}}+\epsilon _{\text{pt}} \tag{1}\]  
\[\epsilon^{*}=\epsilon\text{ -}\epsilon_{\text{e}}=\epsilon_{\text{p}}+ \epsilon_{\text{th}}+\epsilon_{\text{pt}} \tag{2}\]  
The inherent strain method calculates the final inherent strain remaining in a structure after welding according to the welding process conditions. Then, it calculates the final strain and residual stress of the structure by performing an elastic analysis, inputting the inherent strain value into a finite element (FE) model. In the case of FSW, unlike manual welding, automatic welding is performed under certain process conditions until the tool enters and exits. Thus, the temperature distribution is assumed as  
Figure 6: Test results of FSW experiment. quasi-stationarity during the FSW process, and the welding deformation and residual stress values are repeatedly distributed according to the direction of the welding line. These results can be confirmed in the research of [PERSON] et al. [15]. This means that the inherent strain value is also repeatedly distributed along the direction of the welding line. In that respect, it is easy to apply the inherent strain method to FSW. Therefore, if the inherent strain value can be calculated in a reasonable manner according to the welding process condition, we can significantly reduce the analysis time compared to the thermal elasto-plastic analysis method and obtain numerical results similar to experimental results. The inherent strain method was proposed according to the following background. Many welding processes are carried out in the shipbuilding industry; and the piece assembly, sub-block assembly, and block assembly are performed to assemble the initial hull structure.