## 4 Experimental Results and Discussion
### Notched Cement Mortar Beams under Three-Point Bending
#### 4.2.2 Specimen Reinforced with Short Metallic Fibers (RM)  
The main difference of the specific test, compared to all tests described until now, is that there is not a uniquely defined fracture instant or, equivalently, there is not an instant at which the load is zeroed. Indeed, the presence of the reinforcing fibers prohibits the rapid propagation of the macroscopically visible crack front. This is clearly seen in Figure 8a, in which the temporal evolution of the load applied is plotted, in juxtaposition to the respective evolution of the amplitude of the acoustic hits recorded (again it is recalled that the specimen is loaded under displacement-control conditions): At the instant t = 1519 s, the load attains its maximum value, equal to L\({}_{\text{max}}\approx\) 14.05 kN. Then the load remains practically constant until the instant t = 1524 s, and it starts decreasing relatively smoothly (while the crack front has not yet started propagating) until the instant t\({}_{\text{f}}\) = 1531 s, indicating the \"ductility\" gained by the specimen, due to the presence of the metallic reinforcing fibers. This gain in ductility of the otherwise \"brittle\" concrete is a common feature and, besides the increase in strength, is the main reason for adding the reinforcing fibers [27; 28; 29; 30; 31; 32]. After this instant t\({}_{\text{f}}\), the load decreases abruptly to a level equal to about 9 kN, at which it remains almost constant for a relatively long time-interval, during which the macorrack is propagating steadily. The instant t\({}_{\text{f}}\) is considered here as a \"conventional fracture instant\" (although the specimen is not fragmented into two pieces) since after the instant  
Figure 7: The evolution of the F-function versus the Natural Time X in juxtaposition to the respective evolution of the Load applied for the R0 test. \(t_{f}\) the crack front is moving very slowly from the crown of the notch towards the load transferring roller. The number of acoustic hits recorded until the instant \(t_{f}\) was equal to N = 2598 (more than two times the hits recorded in the test with the unreinforced specimen, R0). Although comparing the number of AE hits recorded in two different tests is perhaps not a good practice, it provides some interesting conclusions (of qualitative nature) in case of identical specimens. In this case, the conclusion is definitely justified taking into account the additional damage mechanism activated, namely the debonding between the concrete matrix and the reinforcing fibers. The evolution of the above two quantities (load and amplitude of the acoustic hits) in natural time, \(\chi\), is plotted in Figure 8b. Each acoustic hit is now located at a \"distance\" equal to \(\Delta\chi\approx 3.85\times 10^{-4}\) from its right and left neighbors. The instant at which the load is maximized corresponds to a natural time equal to \(\chi\) = 0.60. Almost 60% of the acoustic hits were recorded until this instant, i.e., until maximization of the load applied. Concerning now the evolution of the F-function, in terms of the Natural Time X, it is plotted in Figure 9, in juxtaposition to that of the load applied L(X). For this to be achieved, the F-function was calculated using a sliding window of n = 50 successive interevent times. The short, thick, blue linear segment, corresponding to the last value of the F-function, denotes, again, the last \"window\", i.e., the last n = 50 values of the Natural Time (\(\chi\)). Figure 8: The temporal evolution of the load applied, in juxtaposition to that of the amplitude of the acoustic hits, in (**a**) the conventional- and (**b**) the Natural-Time domains for the RM test. It is seen from Figure 9 that, for this specimen, there are two X-intervals at which the F-function is governed by the power law of Equation (5). The first one is the 0.17 \(<\) X \(<\) 0.24 interval (yellow-colored rectangle in Figure 9). For this first interval, the fitting procedure (dark green line) provides a numerical value for the exponent m equal to m = 7.5.