## 5 Experimental Verification
### Results and Discussion  
There is an overall number of three test pieces are examined. The 1# and the 2# test piece have the same initial crack positions, including edge cracks on the center of the weld and 20 mm from the center of the weld on the base metal. The initial crack on the base metal of the 3# test piece has the same position with that of the 1# and 2# test piece, while the initial crack on the weld is offset from the center line of the weld by 1.5 mm, as displayed in Figure 15a. The specimens after fatigue tests are shown in Figure 15b-d, all fatigue specimens are broken at the base metal, which testifies that the combination of fatigue design and post-weld treatment techniques recommended in this work is practicable. The 1# test piece failed at the base metal but did not break at the prefabricated crack. This indicates that there are initial micro cracks or crack-like defects in the base metal, and these small defects preferentially spread during the fatigue loading process. This confirms the premise of the FCG method, that is, there are initial micro-cracks or crack-like defects that are not easily found in most materials or structures. Both the 2# and the 3# test piece failed in the pre-cracking position of the base metal, which proves that the designed joint has a fatigue load bearing capacity not lower than that of the parent metal. Besides, the results of the 3# test piece show that the design method is independent of the crack position on the weld. The experimental outcomes are displayed in Table 3. f and \(\Delta\sigma\) denote the loading frequency and the stress amplitude calculated according to the gauge section of the specimen (30 mm \(\times\) 14 mm), respectively. The stress ratio is represented by R. T denotes the ambient temperature. Figure 14: MTS 809 fatigue test system. Figure 13: Macro shots of the designed welded joints. Table 4 displays the fatigue data's statistical analyzing results, executed following ISO 12107: 2012 [35]; \(p\) stands for the reliability of the estimation (say 99% probability); \((1-\alpha)\) denotes the reliability statement's confidence. As provided in ISO 12107: 2012 [35], the one-sided tolerance limit is represented by \(k_{(P,\,1-\alpha)}\). The statistical analyzing results show that, at a confidence degree of 95%, the lower limit of the fatigue life for a 0.1% possibility of failure is 400,976. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \(p\)/\% & \((1-\alpha)\) & \(k_{(p,\,1-\alpha)}\) & \(N_{(p,\,1-\alpha)}\) \\ \hline \multirow{2}{*}{10} & 95 & \(-\)6.158 & 918,241 \\  & 90 & \(-\)4.258 & 1,126,483 \\ \hline \multirow{2}{*}{5} & 95 & \(-\)7.655 & 781,658 \\  & 90 & \(-\)5.31 & 1,005,948 \\ \hline \multirow{2}{*}{1} & 95 & \(-\)10.55 & 572,483 \\  & 90 & \(-\)7.34 & 808,600 \\ \hline \multirow{2}{*}{0.1} & 95 & \(-\)13.86 & 400,976 \\  & 90 & \(-\)9.651 & 630,614 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Analysis results of the mathematical statistics. Figure 15: (a) Positions of initial cracks in test pieces; (b) 1# test piece after the fatigue test; (c) 2# test piece after the fatigue test; (d) 3# test piece after the fatigue test. \begin{table}
\begin{tabular}{c c c c c} \hline \hline _Sample No._ & \(\Delta\sigma\) (MPa) & \(f\) (Hz) & \(R\) & \(T\) (°C) & \(N\) (Stress Cycles) \\ \hline
1\# & 97.76 & 10 & 0.1 & 25 & 1,574,843 \\
2\# & 97.76 & 10 & 0.1 & 25 & 1,922,554 \\
3\# & 97.76 & 10 & 0.1 & 25 & 1,865,781 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Results of the fatigue experiments. Though the fatigue design approach that is provided in this work is effectual, there are certain limitations and prerequisites on its application. Firstly, the premise of applying the FCG method is that the object being analyzed must be a cracked body. So that this paper assumes that there are initial cracks of 0.1 mm deep both in the parent metal and the deposited metal. Secondly, during the sampling process and PWT, the residual stress of welds is sufficiently released.