## 3 Results and Discussion  
### Fracture Toughness and Critical Stress Intensity Factor  
Figure 4 shows the plots of the applied tensile load vs. CMOD obtained from the fracture tests of the three tested SBS specimens. The linearity of the obtained load-CMOD curves remains up to failure, which indicates that this takes place in a small-scale yielding regime and entails that the measured toughness is size independent. The slopes of the linear parts of the three curves are consistent with the respective crack sizes, which are 9.45 mm in SBS_1, 10.22 mm in SBS_2, and 11.14 mm in SBS_3. The first graph (Figure 4a) corresponding to SBS_1 indicates that the crack front remains stationary until the critical load is reached and the specimen suddenly collapses. In the other two cases (Figure 4b,c), the collapse is preceded by a number of pop-ins under decreasingly lower loads, so that the first of them was identified as being the fracture load P\({}_{\text{m}}\) (Table 3). The pop-in occurrence can be explained by the decrease that experiences the stress intensity factor for this specimen configuration when the crack grows. Nevertheless, the pop-ins are likely to be activated by microstructural singularities that fail locally and cause the crack jumping. The probability of this crack behavior increases with the high presence of singularities. Figure 3: (**a**) Notched cylindrical specimen; (a, c—semi-axes of the ellipse assimilated to the fatigue crack front, b—half-width of the fatigue crack, and R—specimen radius); (**b**) image of the notched specimen; (**c**) image captured during the fatigue tests. According to ASTM E1304 [24], the yield stress \(\sigma_{\rm{ys}}\) = 988 MPa of the tested steel and the selected thickness, B = 12 mm, of the SBS specimen meet the condition to obtain a valid fracture toughness \(K_{\rm{lc}}\), because the measured toughness values were lower than the limit \(\sigma_{\rm{ys}}\) (0.8 B)\({}^{1/2}\) = 110 MPa m\({}^{1/2}\). The bar steel fracture toughness \(K_{\rm{lc}}\) was obtained by particularizing Equations (1) and (2) for the experimental values of the fracture load \(P_{\rm{m}}\) and the fatigue crack depth a, the latter measured by optical microscopy on the fracture surfaces of specimens and expressed as a fraction of the length of the specimen, \(\tilde{a}\) = a/W [25]:  
\[K_{\rm{lc}}=Y\left(\widetilde{\rm{a}}\right)\frac{P_{\rm{m}}}{B\sqrt{W}} \tag{1}\]  
\[Y\left(\widetilde{\rm{a}}\right)=\exp\left(12.2903-56.9\widetilde{\rm{a}}+13 6.83\widetilde{\rm{a}}^{2}-151.34\widetilde{\rm{a}}^{3}+66.097\widetilde{\rm{a }}^{4}\right) \tag{2}\]  
Table 3 gives the results of the three fracture tests. The deviation of the three measurements does not exceed 3% from the mean value of 75 MPa m\({}^{1/2}\), which consequently provides a reliable estimate for the fracture toughness \(K_{\rm{lc}}\) of the steel. This qualifies the analyzed bar steel as a medium-high toughness steel, which entails a limited risk of brittle behavior if the bars are used for structural engineering applications. Figure 5a shows the load-CMOD data obtained from the post-fatigue tensile fracture tests of seven notched cylindrical specimens. Accordingly, the large plastic deformation experienced by all of them before fracture is entirely incompatible with the small-scale regime necessary for the stress intensity factor K to control the crack tip stress field. Despite this, K was computed by particularizing Equations (3) and (4) for the maximum tensile load F, the specimen radius R, the optically measured maximum crack depth a (Figure 5b), and the crack width b (Figure 3a), given that the ratios \(\xi\) = a/b and \(\zeta\) = a/(2R) appear in the applied expression of K [26; 27]. Figure 4: Load-CMOD plots in the fracture toughness tests of specimens: (**a**) SBS_1; (**b**) SBS_2; (**c**) SBS_3.