## 4 Experimental Data and Discussion
This is illustrated by the Paris laws obtained from the dataset of Table 1, using the present enlarged set of definitions of \(K_{eq}\). The corresponding Paris law representation, in terms of different \(K_{eq}\) definitions, is provided in Figure 6.  
One example of the consequences of the presented analysis is the expected FCG rate for a given \(\Delta K_{eq}\) value, considering different definitions for \(K_{eq}\). For the dataset used, and as shown in Figure 4, the ranking of growth rates is not constant along the values of \(\Delta K_{eq}\). Indeed, above \(\sim\)700 MPamm\({}^{-1/2}\), the ranking of the FCG rates would be different. With data for \(K_{eq}\) = 400 MPamm\({}^{-1/2}\) and for \(K_{eq}\) = 800 MPamm\({}^{-1/2}\), one such example is provided in Table 2. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & _da/dN_ **[mm/cycle]** & \
\begin{tabular}{c} \(K_{I, max}\) \\ **[MPamm\({}^{-1/2}\)]** \\ \end{tabular} &
\begin{tabular}{c} \(K_{I, max}\) \\ **[MPamm\({}^{-1/2}\)]** \\ \end{tabular} \\ \hline \multirow{4}{*}{spec. \#1} & 0.00015 & 172.3 & 512.9 \\ \cline{2-4}  & 5.9 \(\times\)\(10^{-5}\) & 738.6 & 9.6 \\ \cline{2-4}  & 0.001 & 834.6 & 51 \\ \cline{2-4}  & 0.01 & 1.08 \(\times\)\(10^{3}\) & 83.7 \\ \hline \multirow{4}{*}{spec. \#3} & 9.70 \(\times\)\(10^{-5}\) & 344.7 & 258.9 \\ \cline{2-4}  & 0.0014 & 574.9 & 100.5 \\ \cline{1-1} \cline{2-4}  & 0.00041 & 840 & 50.6 \\ \cline{1-1} \cline{2-4}  & 0.006 & 919.4 & 183.5 \\ \cline{1-1} \cline{2-4}  & 0.019 & 1169.8 & 132.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Tests at \(R\) = 0.1, maximum values of \(K_{l}\) and \(K_{ll}\) per cycle, and FCG rate [5]. Figure 5: 4-point bend test, showing machined V notch, subsequent mode I precrack, and FCG path starting at the precrack; details in [5]. As mentioned in the introduction section, one aim of the application of Fracture Mechanics to fatigue is to model fatigue crack propagation in real structural components, starting from existing or assumed cracks that progress under a cyclic load up to a larger size or final rupture. Clearly, those applications are successful in mode I, where no doubts exist concerning the transformation of the stress state of the cracked component or structure into a value of \(K_{l}\). However, as seen above, for mixed-mode situations, a variety of \(K_{\alpha l}\) definitions are currently in use, and they may lead to rather different FCG predictions. Recent work by [PERSON] et al. illustrates the point in several structures and specimen geometries. The work of these authors evaluates the FCG predictability performance of different \(K_{\alpha l}\) criteria, using CTS specimens with various precrack inclination values [54]. The experimental \(a\) vs. \(N\) curve was compared with the predictions. In the region just after the precrack, the differences found were more important, and they diminished as the crack grew. This is consistent with the fact that in CTS specimens, after the initial shift from the precrack direction, most of the FCG takes place under the approximate mode I condition. Interestingly, in [55], the same authors examined plates with an inclined central precrack and found a similar trend of larger errors near the initial precrack. It is worth recalling that the inclined central crack in a plate tends to grow into a mode I situation. Furthermore, using a single definition of \(K_{eq}\), the same value of \(K_{eq}\) may be achieved via an infinity of different combinations of \(K_{I}\) and \(K_{II}\), and it is clear that different combinations imply different FCG rates. The still unanswered question is therefore: what could be a definition of \(K_{eq}\) that aims at a wide and universal applicability? A perspective to counteract the shortcomings presented would be to address the modelling methodology in a data-driven fashion. Unsupervised learning may help to reveal hidden patterns that will potentially support our understanding of the material's behavior.