## 3 Results and Discussion
This stress state effect on fatigue crack propagation slows down crack growth at the surface and hence promotes the tunnel effect. Several different parameters are used to understand to what extend tunnel affects the specimens' behavior. The simplest and most common parameter is \(d/B\) (Figure 7c). Other used parameters are used and presented in the literature [34; 35]. Note that the stable shape of the crack front has a uniform distribution of effective stress intensity factor range. The tunnel effect parameter is plotted in Figure 7d against the fatigue crack length (\(a_{2}\)-\(a_{0}\)). As expected, shot peening increases the retardation of the surface crack propagation observed by a higher tunnel effect parameter for crack length lesser than 10 mm. As mentioned above, tunnel effect can be caused by residual stresses profiles. For MP specimens, average residual stress in load direction obtained from four measurements at the surface was about +290 MPa, while for SP samples compressive residual stresses occur around the surface. Figure 8 shows the profile of residual stresses and X-ray diffraction peak breadth against the depth from surface. According to the diffraction peak breadth profiles, the thickness layer affected by all surface treatments is circa 200 \(\upmu\)m. The average value of the compressive residual stresses occurring trough a layer below the free surface with a 150 \(\upmu\)m depth is about 200 MPa. Regarding the MP specimens, the residual stress measurements, for the same depth of the SP specimens presented an average value of 180 MPa. The reduced thickness of this layer, justifies the reduced influence on the overall propagation of fatigue cracks observed, in accordance to [PERSON] et al. [36]. Figure 8: Residual stresses profile and X-ray diffraction peak breadth against the depth from surface for SP specimens. _”\(\circ\)”_ corresponds to the residual stress in rolling direction (MPa) and “\(\square\)” to the diffraction peak breadth (\(\circ\)). Figure 7: Impression marks of the crack path and tunnel effect: (**a**) MP specimens; (**b**) SP specimens; (**c**) schematic indication for tunnel effect parameters; and (**d**) tunnel effect value distribution for MP and SP specimens. Results obtained for both stress ratios \(R=0.05\) and \(R=0.4\) are compared in Figure 9, for both surface treatments and thicknesses. As expected, a meaningful influence of the stress ratio was noticed in both Paris law regime and near-threshold condition. As reported in the literature, this effect is mainly consequence of the significant reduction on crack closure level for higher stress ratio \(R=0.4\)[31]. This is why above 15 MPa\(\surd\)m the \(R\) does not present any significate effect. Fatigue crack propagation resulting in the stable regime were modeled by Paris law equation. Table 3 summarizes the values of the coefficients and intervals of validity of Paris' law and the correlation coefficients for all test conditions. To analyze the transient effects after overloads, variable amplitude loading with \(R=0.04\) were carried out, in which periodic overload blocks of 300 cycles were applied with intervals of \(N_{int}\) of 7500 and 15,000 cycles, as shown in Figure 3. The results obtained were compared with the reference \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**B [mm]** & **Specimen** & **R** & **C** & **m** & **Validity [MPa m\({}^{1/2}\)]** & **Correlation Factor** \\ \hline
4 & MP & 0.05 & \(1.41\times 10^{-8}\) & 3.94 & 7–13 & 0.995 \\
4 & MP & 0.4 & \(2.42\times 10^{-6}\) & 2.04 & 12–24 & 0.996 \\
4 & SP & 0.05 & \(2.95\times 10^{-7}\) & 2.94 & 8–14 & 0.970 \\
4 & SP & 0.4 & \(2.70\times 10^{-7}\) & 3.05 & 5–10 & 0.982 \\
8 & MP & 0.05 & \(2.72\times 10^{-8}\) & 3.89 & 7–12 & 0.996 \\
8 & MP & 0.4 & \(1.96\times 10^{-6}\) & 2.16 & 13–22 & 0.998 \\
8 & SP & 0.05 & \(2.53\times 10^{-7}\) & 2.97 & 9–16 & 0.991 \\
8 & SP & 0.4 & \(2.63\times 10^{-7}\) & 3.25 & 5–17 & 0.973 \\ \hline \hline \end{tabular}
\end{table}