## 3 Experimental Work
### Cyclic Properties of a Welded Joint  
The crack initiation of welded A-type frame started from the weld toe, as shown in Figure 2, so it was necessary to figure out the cyclic characteristics of the weld metal. Fully reversed cyclic loading was applied on the flat butt joint under strain control, and the strain amplitude changed from 0.1% to 0.45%. The gage length of the extensometer was 10 mm. The fatigue failure criterion was 50% drop of load. The strain was measured by an Epsilon uniaxial extensometer to obtain cyclic mechanical responses. For the low strain amplitude testing, the 70 MPa cyclic loading under load control was first performed on the specimen for 0.1 million cycles to make the weld metal stable and avoid a possible buckling phenomenon. For the high strain amplitude testing, the low loading frequency with no more than 1 Hz was required to keep the material stable. The experimental results between all strain amplitudes and number of reversals (2\(N\)) are shown in Figure 6. \begin{table}
\begin{tabular}{c c c} \hline  & **Base Metal** & **Weldment** \\ \hline Young’s modulus \(E\) (GPa) & 200.4 & 210.1 \\ Yield Strength \(\sigma_{5}\) (MPa) & 451 & 456 \\ UTS \(\sigma_{b}\) (MPa) & 621.5 & 615.9 \\ Elongation \(\varepsilon_{f}\) (\%) & 27 & 18 \\ True fracture stress \(\sigma_{t}\) (MPa) & 57 & 24 \\ True fracture strain \(e_{t}\) (\%) & 0.336 & 0.279 \\ \hline \end{tabular}
\end{table} 
Table 2: Mechanical properties under monotonic tensile test. Figure 4: (a) Installation diagram of monotonic tensile test; (b) Stress and strain curve of base metal under monotonic tensile test. Figure 5: Stress and strain curve of weldment under monotonic tensile test. In order to acquire cyclic properties, the Manson-Coffin equation was utilized to describe the fatigue characteristics:  
\[\varepsilon_{a}=\frac{\Delta\varepsilon^{c}}{2}+\frac{\Delta\varepsilon^{p}}{2}= \frac{\sigma_{f}^{\prime}}{E}(2N_{f})^{b}+\varepsilon_{f}^{\prime}(2N_{f})^{c} \tag{1}\]  
where \(\varepsilon_{a}\) is total strain amplitude, and \(\Delta\varepsilon^{c}/2\) and \(\Delta\varepsilon^{p}/2\) are elastic and plastic strain amplitude, respectively. The fatigue strength coefficient and the fatigue ductility coefficient are represented by \(\sigma_{f}^{\prime}\) and \(\varepsilon_{f}^{\prime}\), respectively. The fatigue strength exponent and the fatigue ductility exponent are represented by \(b\) and \(c\), respectively. The cyclic stress versus strain relationship for the weld metal could be described by the Ramberg-Osgood equation as:  
\[\varepsilon_{a}=\frac{\Delta\sigma/2}{E}+(\frac{\Delta\sigma/2}{K^{\prime}})^{ 1/n^{\prime}} \tag{2}\]  
where \(\Delta\sigma/2\) is the stabilized stress amplitude, and \(K^{\prime}\) is the cyclic strength coefficient, and \(n^{\prime}\) is the cyclic strain hardening exponent, respectively. The Ramberg-Osgood coefficients were calculated by fitting a curve with power equation to experimental plastic strain amplitude and stress, as shown in Figure 7. Those parameters are listed in Table 3.  
Figure 6: Relationship between strain amplitude and cycles under cyclic loading. Figure 7: Fitting curve for Ramberg-Osgood coefficients. \begin{table}
\begin{tabular}{c c c c c} \hline \(\sigma_{f}^{{}^{\prime}}\) (MPa) & \(b\) & \(\varepsilon_{f}^{{}^{\prime}}\) & \(c\) & \(\text{K}^{{}^{\prime}}\) & \(\text{\boldmath$n$}^{{}^{\prime}}\) \\ \hline
1163.4 & \(-\)0.1243 & 0.159 & \(-\)0.2615 & 860.99 & 0.1792 \\ \hline \end{tabular}
\end{table} 
Table 3: Fatigue parameters of the welded joint. To clarify the material parameters mentioned above, the total strain amplitude was decomposed to elastic and plastic parts, as shown in Figure 6. Then, the cyclic parameters were calculated by fitting linear curves under logarithmic coordinate to be elastic and plastic strain amplitude versus number of reversals. Those parameters are listed in Table 3. According to the results, the plastic strain amplitude was much higher than the elastic strain amplitude for each strain level.