## 3 Results and Discussion
### Crack Opening Displacement and Crack Closure  
The \(\Delta\)P-COD example curves of the welded series and the BM plotted in Figure 7, where the non-linear part of the curves were marked by the tangent points, illustrate a different behavior in relation to the crack closure phenomenon: the S1 and S5 series  
Figure 6: Fatigue crack growth rate at Paris regime for series (**a**) S1, (**b**) S3, (**c**) S2 and (**d**) S5. did not present crack closure, in the S2 series it was so minimal that in practice it can be considered null, while in the S3 series and in the BM this phenomenon was presented, but, in a different way. In the crack size range of 1-12 mm, for the BM, the load range at which the point of tangency occurred was approximately constant, meanwhile, for the S3 series, the load range increased and subsequently decreased. Should the crack tip plasticity be assumed as the main cause of the crack closure, the behavior observed could be explained considering the hardness and ductility of the microstructures. The BM has low hardness and good ductility while the welded series had propagation paths in the HAZ and the FZ where the hardness was high and therefore the ductility was low. On other hand, it has been explained in [32] that due to the presence of residual tensile stresses, there is no crack closure. The particular behavior of the S3 series could be caused by the crack path that also crossed the FGHAZ (which is softer) since the weld bead size was smaller than in the other series, and there could be residual compressive stresses presents in this series that contribute to the crack closure as reported in [32]. According to the above results, and considering the average of the load ranges values \(\Delta\)P where the tangent points were observed for the crack sizes from 1 to 12 mm, the crack opening stress range \(\Delta\)S\({}_{\text{op}}\) and the \(\Delta\)K\({}_{\text{eff}}\)/\(\Delta\)K ratio were calculated for the BM and the S3 series. The results are respectively: 24.43 MPa, 0.82 and 15.94 MPa, 0.89; meanwhile for the series S1, S2 and S5, the values of \(\Delta\)S\({}_{\text{op}}\) were assumed equal to zero and therefore the \(\Delta\)K\({}_{\text{eff}}\)/\(\Delta\)K ratio equal to one. The crack growth rates in the function of the stress intensity factor range (SIFR), of the specimens from which the excess weld was removed and of the BM, are shown in Figure 8a. As can be seen, the S1, S2 and S3 series had practically the same crack growth rate, the S5 series had a slightly higher rate than the previous ones, while the BM had the highest crack growth rate due to having a lower hardness as was described previously. With the \(\Delta\)K\({}_{\text{eff}}\)/\(\Delta\)K ratio already obtained, for the BM and welded series the effective SIFR, \(\Delta\)K\({}_{\text{eff}}\), was determined and the da/dN-\(\Delta\)K\({}_{\text{eff}}\) curves were redrawn (Figure 8b). Table 4 shows the parameters A and n of the Paris law for the welded series and the BM. Figure 7: \(\Delta\)P-COD example curves of each welded series and BM. Figure 8: Fatigue crack growth rate at Paris regime. (**a**) da/dN-\(\Delta\)K and (**b**) da/dN-\(\Delta\)K\({}_{\text{eff}}\). The results found for the welded series suggest that weld ripples, porosity, residual stress and the microstructure were factors that influenced the crack growth rate. In relation to weld ripples, even though the effect was very small, their size and shape can modify a more or less straight path to a zigzag one and therefore the propagation line [33]. Since the BM microstructure was constituted of ferrite-bainite, while the welded series basically constituted of mixtures of bainite-martensite [29], there is a clear effect of a decrease in the crack growth rate that can be attributed to the microstructure due to the higher proportion of bainite and the presence of martensite. This agrees with the works [34; 35] where a retarding effect was reported in the growth of cracks due to the presence of hard phases such as martensite and bainite.