## 5 Discussion and Concluding Remarks
### Comparative Consideration of the Tests with Notched Beams (Tests R0 and RM)  
For both notched specimens (unreinforced and reinforced with metallic fibers), the overall evolution of the F(X)-function exhibits some common characteristics. The first  
Figure 11: Magnified view of the intervals where the law of Equation (5) is valid (thick lines), in terms of the Natural Time (**a**) and the conventional time (**b**) for the protocol with intact specimens. Figure 10: Comparative consideration of the evolution of the F-functions in the Natural-Time Domain for the specimens of the protocol with intact specimens. The dark blue and the dark red lines correspond to the parts of the F-function which obey the power law of Equation (5). one is that severe increase of the values of the F(X)-function (and therefore of the rate of micro-cracking) is observed while the load applied approaches closely its maximum value (but before this value is attained) (Figure 12a). This interval is denoted from here on as Region I. In addition, the values of the F(X)-function increase rapidly, obeying a power law, also a little before the instant of macroscopic fracture (either actual or \"conventional\"), while the load applied has already attained its maximum value and has started decreasing very smoothly. This interval is denoted from here on as Region II. In this interval, one observes the most intense generation of acoustic hits, or equivalently the most intense micro-cracking procedure. Both Regions (I and II) of intense micro-cracking are plotted with thick red line in Figure 12, in which the evolution of the load applied (Figure 12a) and that of the F-function (Figure 12b) is plotted in the Natural Time domain, for both the unreinforced and the reinforced beams. Concerning Region I, the F(X) function exhibits significantly higher values in the case of the reinforced specimen (Figure 12b). This is attributed to the increased number of micro-cracks developed due to the fact that there are damage mechanisms activated both in the bulk of the material and also along the mortar-fibers interfaces (which do not exist in the unreinforced specimen). On the contrary, things are completely different for Region II. The values of the F(X)-functions are now quite significantly higher for the unreinforced beam (test R0). This is obviously due to the fact that the intense acoustic activity in the plain beam has a much shorter duration compared to the respective duration in the reinforced beam. This is explained by the presence of the metallic reinforcing fibers, which offer an increased \"ductility\" to the beam. This is even more evident if one is \"transferred\" from the Natural Time Domain X to that of the conventional time \(\tau\) and considers comparatively (for the reinforced and the unreinforced specimens) the respective evolution of the F(\(\tau\))-functions and that of the Load applied (L(\(\tau\)) functions). The results for the very last loading stages (i.e., just before fracture) are plotted in Figure 13.  
Figure 12: Comparative consideration of the evolution of the load (**a**) and of the F-function (**b**) in the Natural Time domain for the protocol with notched specimens. The thick red lines correspond to the portions of the load plot for which the respective F-function is described by the power law of Equation (5). It is observed from this figure that, for the R0 beam, the interval at which the F(\(\tau\))-function exhibits rapid increase has a duration equal to about only 1 s. On the other hand, for the RM beam, the respective duration is equal to about 5 s. Moreover, from the same Figure 13a,b, it is observed that at the interval during which the load oscillates (remaining practically constant) around the maximum value attained, the values of the F-function for the RM beam are equal to about 50 hits/s, while for the R0 beam, the respective values increase from the level of 10 hits/s to the level of 30 hits/s.