## 3 Results and Discussion
### Damage Tolerance of the Bar Steel  
Two Failures Assessment Diagrams (FADs) given in Figure 8a,b are used to analyze the results of the previous fracture tests of the fatigue-cracked cylindrical specimens. In Figure 8a, the experimental fracture data, namely the failure loads \(\mathrm{P_{max}}\), are plotted vs. the cracked areas \(\mathrm{A_{f}}\) using as respective units the bearing load capacity \(\mathrm{P_{0}}\) and the cross section \(\mathrm{A_{0}}\) of specimens in undamaged condition. In addition, the diagram contains the theoretical failure predictions for plastic collapse \(\mathrm{P_{Y}}\) and brittle fracture \(\mathrm{P_{F}}\). The plastic collapse occurs with the resistant ligament subjected to either pure tensile load (Line 1) or combined tension and bending load (Line 2) and depends on the compliance of the specimen to deflect transversely and align the ligament centroid with the load line. In both cases, the measured tensile strength of the bar steel is assumed to be the ideal yield strength that determines the plastic collapse. Consequently, Line 1 is given by:  
\[\frac{\mathrm{P_{Y}}}{\mathrm{P_{0}}}=1-\frac{\mathrm{A_{f}}}{\mathrm{A_{0}}} \tag{7}\]  
Figure 8: Failure assessment diagrams, with experimental data, involving: (a) damage level; (b) toughness and yielding capacity effects. Figure 7: (a) Relative crack depth \(\mathrm{a/R}\) as a function of specimen radius vs. relative fatigue cracked area \(\mathrm{A_{f}/A_{0}}\) as a function of uncracked area; (b) The Paris-Erdogan law obtained from the experimental data of FC1–FC5 tests. while, according to [29], if the aspect ratio of the crack front given by the quotient a/c belongs to the interval [0, 1], with 0 defining the straight crack front and 1 the circular crack front, Line 2 can be approximated by:  
\[\frac{\mathrm{P_{Y}}}{\mathrm{P_{0}}}=\left(1-\frac{\mathrm{A_{f}}}{\mathrm{A_{ 0}}}\right)^{2.1} \tag{8}\]  
Then, assuming that the stress intensity factor K in the linear elastic regime controls the brittle fracture resulting from the stress and strain concentration at the crack tip, K can be used for design purposes, as loading action vs. fracture toughness \(\mathrm{K_{c}}\) as a material resistance indicator. The load \(\mathrm{P_{F}}\) that would cause the brittle fracture of the bar steel can be predicted from Equations (3) and (4), by particularizing the stress intensity factor K for the value of 75 MPa m\({}^{1/2}\) measured as fracture toughness \(\mathrm{K_{c}}\) in the tests performed with pre-cracked chevron notched specimens. This prediction would generally result in an area, if plotted in the diagram shown in Figure 8a, rather than in a single curve, because two independent variables determine the crack geometry. However, given that the crack aspect ratios measured on the fracture surfaces of cylindrical specimens hardly deviate from the mean value of 1.26, a single curve, corresponding to this mean value, has been plotted as Line 3 in Figure 8a. The positions occupied by the experimental failure data in the diagram given in Figure 8a, when compared with Line 1, Line 2, and Line 3, indicate that no failure preceding plastic collapse and caused by toughness occurs, even though they fit around Line 3. This is due to the resistant ligament of the specimens that progressively displaces towards the load line. The transversal compliance provided by the crack produces high enough stresses to surpass the tensile-bending collapse load, theoretically predicted by Equation (8), but capable of approaching the pure tensile collapse, given by Equation (7). However, toughness-controlled failure (Line 3) prevents this from being reached, so that pure tensile plastic collapse does not occur. The failure assessment diagram adopted by Eurocode 3 for the design of steel structures against brittle failure [1] has also been used to assess the damage tolerance of the bar steel resulting from the tested cylindrical specimens.