# Corrosion-Fatigue Evaluation of Uncoated Weathering Steel Bridges
## 5 Analysis on Corrosion-Fatigue of Structural Steel for Bridges
### Critical Fitting Depth of Steels  
As aforementioned, the pitting flaw can be treated as an equivalent crack. As suggested by [PERSON] [40; 56], the range of SIFs at the pitting flaw can be calculated as shown in Equations (17) and (18):  
\[\Delta K_{b}=\bigg{[}1.04+0.201(\frac{a}{h})^{2}-0.106(\frac{a}{h})^{4}\bigg{]} \frac{2}{\pi}\Delta\sigma\sqrt{\pi a}, \tag{17}\]  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Steel** & **Stress Ratio** & \(\Delta K_{th}\) (\(MPa\sqrt{m}\)) & \(A\) (\(MPa\sqrt{m}\)) \\ \hline HPS 70W & 0.0 & 5.5 & 120 \\  & 0.8 & 3.8 & 120 \\ \hline
14 MnNbq & 0.05 & 5.5 & 100 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Decreased fatigue limits and fracture toughness of the selected steel.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Material** & **Stage** & \(\Delta K_{th,0}\) (\(MPa\sqrt{m}\)) & \(\alpha\) \\ \hline HPS 70W & Propagation & 7.51 & 0.386 \\  & Initiation & 5.50 & 0.386 \\ \hline
14 MnNbq & Propagation & 7.03 & 1.060 \\  & Initiation & 5.80 & 1.060 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Stress intensity factor (SIF) threshold for fatigue crack propagation and initiation and their material parameter \(\alpha\).  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Steel** & **Stress Ratio** & \(\Delta K_{th}\) (\(MPa\sqrt{m}\)) \\ \hline HPS 70W & 0.10 & 7.22 \\ \hline  & 0.05 & 6.67 \\
14 MnNbq & 0.25 & 5.14 \\  & 0.50 & 3.32 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Fatigue limit for long cracks in the selected steel.  
\[\Delta K_{\rm s}=\left[1.04+0.201(\frac{a}{h})^{2}-0.106(\frac{a}{h})^{4}\right] \left[1.1+0.35(\frac{a}{h})^{2}\right]\frac{2}{\pi}\Delta\sigma\sqrt{\pi a}, \tag{18}\]  
where \(\Delta K_{b}\) and \(\Delta K_{\rm s}\) are the ranges of SIFs at the crack tip and the crack edge, respectively; \(a\) is the pitting depth; \(h\) is the plate thickness and \(\Delta\sigma\) is the remote stress range.  
As aforementioned, the critical size of pitting flaws is achieved when any of the SIFs reaches the fatigue limit. It can be found from Equations (17) and (18) that the critical size is determined by the remote stress range, stress ratio and the plate thickness. Thus, the critical size in the HPS 70W and 14 MnNbq was investigated under different combinations of parameters, as shown in Figures 7 and 8. The result indicates that critical pitting depth of these two types of steel decreased with the increase in stress range and stress ratio. For instance, when the stress range increased from 50 MPa to 200 MPa, the critical pitting depth reduced roughly by 93% in both types of steel. Meanwhile, as the stress ratio rose from 0.01 to 0.5, the critical depth reduced by 33% in the HPS 70W and 77% in the 14 MnNbq. Moreover, critical pitting depth was much more sensitive to stress range in low stress range state. It could also be found that the plate thickness had little impact on critical pitting depth, which was less than 3% change in the depth when the thickness increased from 20 mm to 50 mm. Besides, the result also suggests that the critical depth in the HPS 70W was not sensitive to the change in the stress ratio when compared with the 14 MnNbq. As a result, a considerable higher critical depth could be expected in the HPS 70W under a high stress ratio, which in turn indicates its better robustness in fatigue performance.  
Figure 7: Critical pitting depth of the steel 14 MnNbq with different plate thicknesses: (**a**) 20 mm; (**b**) 30 mm; (**c**) 40 mm and (**d**) 50 mm.