## 3 Fatigue Test Results
### Fatigue Life Estimation  
In the current different fatigue design specifications, fatigue strength curves were adopted to estimate the fatigue lives of headed shear studs according to the shear stress range as:  
\[\log(N)+m\log(\Delta\tau)=C \tag{1}\]  
where \(N\) is the number of loading cycles at a constant stress range \(\Delta\tau\), \(m\) is the slope of the \(S\)-\(N\) curve in log-log coordinates and \(\Delta\tau\) is the constant shear stress range of studs. \(C\) is a constant. Based on several typical civil specifications, i.e., the AASHTO [41], the Eurocode 4 [38] and the BS5400 [42], the fatigue lives of headed shear studs were estimated. The actual fatigue lives from the fatigue tests were compared with the estimated theoretical fatigue lives, as shown in Table 3.  
Figure 6: Fatigue failure details of headed shear studs: (**a**) global failure of specimen S-1; (**b**) stud No. 2 of specimen S-1; (**c**) stud No. 8 of specimen S-1; (**d**) global failure of specimen S-2; (**e**) stud No. 4 of specimen S-2; (**f**) stud No. 6 of specimen S-2; (**g**) global failure of specimen S-3; (**h**) stud No. 4 of specimen S-1; (**i**) stud No. 6 of specimen S-1.  
Specimen S-1 failed after 3.28 million times of cyclic loading, and the specific failure mode is shown in Figure 6a-c. The global failure pattern of specimen S-2 was the fracture of stud No. 4 and No. 6 after loading 890,000 cycles (Figure 6d-f). For specimen S-3, it failed prematurely with the fracture of studs No. 4 and No. 6 after about 133,000 fatigue loading cycles. Then, the fracture details of studs No. 4 and No. 6 of specimen S-3 were analyzed in Figure 6h,i to find the reason behind it. For broken studs No. 2 and No. 8 of specimen S-1, No. 4 and No. 6 of specimen S-2 and No. 6 of specimen S-3 in fatigue testing, the crack initiation positions of these studs were all at the edge of the welding toe. However, for stud No. 4 of specimen S-3, the initial failure position was in the center of the stud section. This indicates that stud No. 4 of specimen S-3 had initial welding defects, which was also reflected by its fractured surface after the fatigue test in Figure 6h. With the initial welding defects, the stress concentration happened at the initial welding defects of stud No. 4 under fatigue loading, which caused the initial weld defects more prone to fatigue cracking than the welding toe. Compared with the estimated fatigue lives from Eurocode 4 and the BS5400, specimen S-3, thus, finally occurred fatigue failure prematurely after about 133,000 loading cycles. Due to the initial welding defects in stud No. 4 of specimen S-3; the fatigue life data of specimen S-3 were not included in the fatigue life analysis.  
It can be seen from Table 3 that the actual fatigue lives obtained from the push-out tests were larger than the estimated fatigue lives based on different codes. The actual fatigue lives of specimens S-1 and S-2 were 11.9 and 10.9 times of the estimated fatigue lives from AASHTO, respectively. Compared with the Eurocode 4, the actual fatigue lives of the two specimens were 3.4 and 4.0 times of the corresponding estimated fatigue lives. According to Table 3, the actual fatigue lives of specimens S-1 and S-2 were 1.4 and 1.6 times of the estimated fatigue lives of the BS5400, separately. Figure 7 shows the stud fatigue lives from the push-out tests with the \(S\)-\(N\) curves recommended in the AASHTO LRFD, the Eurocode 4 and the BS5400. In all the three codes, the safe fatigue life estimation of headed shear studs can be guaranteed. The safety redundancies of the three specifications were different. Compared with the \(S\)-\(N\) curves of the BS5400 and the Eurocode 4, the AASHTO fatigue life evaluations had much more safety redundancies. It can be found that the push-out test results were closer to the \(S\)-\(N\) curve of the BS5400 than the other two curves.