## 3 Results and Discussion  
Figures 5 and 6 highlight the effects of the specimen's thickness and surface peening on the crack propagation curves, respectively. Figure 5a-d shows the influence of the thickness on the _da/IN-AK_ curves. It is well known [31] that the thickness influence on the fatigue crack propagation is related both to the microstructure and stress state. In the present study, specimens were machined from the same thickness bars, so there is no microstructure change between 4 and 8 mm thickness specimens. Therefore, the effect of thickness is only caused by changes in stress distribution along cross section and consequent variation on crack closure level [31]. The analysis of Figure 5 shows a reduced thickness effect on _da/dN_ for both surface treatments (MP and SP specimens), including in the near-threshold region. The higher thickness specimens have higher _da/dN_ for the same \(\Delta K\) values in all conditions analyzed in Figure 5. It is also possible to notice that, for \(R\) = 0.05, the increase in _da/dN_ is higher with increasing \(\Delta K\). Specim's thickness effect is more noticeable for lower \(R\)-values and _MP_ samples. As expected, independently of the surface treatment, the thicker specimens have higher crack growth rates over all the \(\Delta K\) range analyzed. Figure 4: Calibration curves based on the compliance, \(C\), for 4 and 8 mm thick specimens. Figure 5: Thickness effect on the _da/lN_-\(\Delta K\) curves for specimens: (**a**) MP, \(R\) = 0.05; (**b**) SP, \(R\) = 0.05; (**c**) MP, \(R\) = 0.4; and (**d**) SP, \(R\) = 0.4. Figure 6: Shot peening effect on _da/lN_-\(\Delta K\) curves for specimens: (**a**) \(B\) = 4 mm, \(R\) = 0.05; (**b**) \(B\) = 8 mm, \(R\) = 0.05; (**c**) \(B\) = 4 mm, \(R\) = 0.4; and (**d**) \(B\) = 8 mm, \(R\) = 0.4. The main purpose of current work was the analysis of the surface peening effect on the crack propagation. Figure 6a-d shows the influence of the shot peening on the _da/dN-\(\Delta K\)_ curves for both thicknesses and stress ratios. Taking into account that shot peening has a very localized effect near the surface, which results in the introduction of compressive residual stresses, the propagation of cracks will be affected only in these areas. To analyze the retardation of crack propagation around the surface, the fractured specimens were observed by optical microscopy. Figure 7a,b presents exemplary photos showing the marks of crack growth shape for machined and shot peening specimens, with 8 mm thickness, respectively. These marks were produced during variable amplitude loading with periodic overload blocks tests. Although the specimen's thickness is small to ensure tri-axial plain strain conditions in the center of the sample, the crack path presents a significant tunnel effect, as shown in Figure 7a,b, and also according to [PERSON] et al. [9]. The visual observation of the images does not show a clear evidence of the shot peening effect on the crack path. For a detailed analysis, a tunnel effect parameter was defined by the Equation (4):  
\[tunnel\ effect=\frac{a_{2}-\left(\frac{a_{1}+a_{3}}{2}\right)}{a_{0}} \tag{4}\]  
where \(a_{1}\) and \(a_{3}\) are the crack lengths at the specimen's surfaces, \(a_{2}\) is the current crack length at the center and \(a_{0}\) is the initial crack length. The tunnel effect is a well-studied manifestation in fatigue crack propagation. Specimens stress state affect fatigue crack propagation, thus propagation rate is distinct at the crack flanks front relatively to specimens' central points. The effect of stress state is usually explained by crack closure mechanisms. Typically, a plane stress state occurs at the surface that promotes crack tip plastic deformation and accordingly plasticity induces crack closure [32]. In turn, inside the specimen, there is a tri-axial stress state which prevents plastic deformation. As fracture surface roughness may be different, promoting roughness induces crack closure, especially for low values of \(\Delta K\)[33].