## 3 Fatigue Test Results
### Strain Evolution under Cyclic Loading  
The strain magnitudes of strain gauges in the fatigue test were not meaningful because the strain values were vulnerable to the environment and input current stability of strain gauges. However, the trend of the measured strains with the cyclic loading number reflected the damage evolution process. Studs No. 2 and No. 8 of specimen S-1 were broken when the specimen was finally in failure. Thus, the strain data from strain gauges near a good stud (Sr5) and a damaged stud (Sr8) were selected for analysis. The strains of the strain gauges Sr5 and Sr8 of specimen S-1 with the fatigue loading cycles are shown in Figure 8a. It can be seen that, in the fatigue test of specimen S-1, the strain change of strain gauge Sr8 could be divided into three stages with the loading cycles. Before 2.2 million fatigue loading cycles, the strain of Sr8 gradually increased to the peak value with the loading cycles. At about 2.2 million loading cycles, the strain of Sr8 changed abruptly, which should be due to the initiation of the fatigue crack damage in stud No. 8. From 2.2 million to 2.8 million loading cycles, the strain of Sr8 decreased slowly at a relatively uniform rate. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Specimen**} & \multirow{2}{*}{\
\begin{tabular}{c} **Stress Range** \\ **\(\Delta\tau\) (MPa)** \\ \end{tabular} } & \multicolumn{2}{c}{**Estimated Fatigue Lives**} & \multirow{2}{*}{
\begin{tabular}{c} **Actual Fatigue** \\ **Lives** \\ \end{tabular} } \\  & \(\Delta\tau\) (MPa) & & & & \\ \hline S-1 & 98.6 & 274,372 & 963,728 & 2,328,348 & 3,280,000 \\ S-2 & 118.4 & 81,598 & 222,923 & 538,579 & 890,000 \\ S-3 & 111.8 & 122,245 & 352,724 & 852,175 & 133,000 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Actual and estimated fatigue lives for push-out tests. The strain of Sr8 decreased rapidly when loading from 2.8 million to 3.0 million cycles. Stud No. 8 was damaged to a certain extent, and the stiffness decreased rapidly when it was loaded to 2.8 million cycles. The strain reached the minimum value when the specimen failed, which was only about 1/3 of the initial value. In contrast, the strain of measurement point Sr5 corresponding to the normal shear stud increased linearly and slowly with the loading cycles until the specimen failure. Finally, the strain of Sr5 was 1.6 times of the initial value. Due to the fatigue damage to some studs, the bearing capacities of shear forces decreased. With the redistribution of internal force, the shear stress borne by the good shear studs then gradually increased. For specimen S-2, strain gauges Sr7 near a good stud (stud No. 7) and Sr6 near a fractured stud (stud No. 6) were selected to analyze the strain data, as shown in Figure 8b. Before 490,000 fatigue loading cycles, the strains of the two strain gauges increased slowly with the fatigue loading cycles, and the two values were basically in the same order. However, after loading 490,000 cycles, the strains of the two strain gauges showed an obvious differentiation. The strain of strain gauge Sr6 decreased gradually with the loading cycles, while the strain of strain gauge Sr7 continued to increase linearly at the previous speed. Thus, the strain of Sr6 reached the peak value at 490,000 fatigue loading cycles. The strain of Sr7 attained the maximum at the final failure of the specimen. It indicated that stud No. 6 corresponding to strain gauge Sr6 may have had fatigue crack damage and led to the decrease in stud stiffness at 490,000 fatigue loading cycles. After 890,000 fatigue loading cycles, specimen S-2 failed. Compared with the peak value, the strain of Sr6 decreased slightly with a small range. This is due to the larger stress amplitude (118.4 MPa) of specimen S-2 that lead to the short fatigue life and crack propagation period. Figure 7: \(S\)–\(N\) curves in different specifications and fatigue test results of headed shear studs.