**4. Discussion of the Results**

Figure 3 presents force-deflection and force-time correlation obtained during bending–tension tests of a quasi-brittle cement composite with dispersed reinforcement. Presentation of these two charts in one figure enables a better recognition of the destruction processes. The force-deflection curve enables the identification of the proportionality, strengthening, deflection control, and crack propagation areas. The sudden decreases in the ability to carry stress that are recorded on the force-deflection curve indicate the appearance of macro-cracks/fractures including fiber breaking.

The force–time curve allows one to indicate the effects occurring at the same time as the recorded AE effects and the AE totals, which should be referred to the force-deflection curve. In order to precisely assess the composite destruction process, it is necessary to correlate both force-deflection and force–time curves with the measured AE effects. The recorded acoustic effects in the proportionality area is presented in 4, Figures 7b and 8a. The obtained data indicate the recording of signals and AE micro events in the proportionality area AE. The measured AE effects have been linked mainly to the sound background signal occurring during the tests and to the occurring events. In the figures, AE events can be observed that have been linked to the individual microcracks occurring within the area of the Hooke's law and micro-regrouping in the structure (micro-relaxation), which do not affect the stress-deflection linear correlation. The occurrence of microcracks before the occurrence of fcr, has been confirmed in other publications [20,26,36].

A micro-event precedes the occurrence of critical point fcr. As shown by Figures 4–8, in the initial period of the operation of Hooke's law, in addition to the background noise, single micro-events/signals appear. The spectra that correspond to sound backgrounds are characterized by the smallest relative amplitude (Figures 6 and 7). Slightly larger intensities of the sound component correspond to micro-events, which do not affect the stress-deflection linear relationship. If the correlating spectra do not occur in groups and there is no increase in sound intensity components, then they may be considered as insignificant (Figure 7a).

The ability to identify them makes it possible to avoid the catastrophic destruction process in traditional cement composites and in quasi-brittle composites to avoid exceeding fcr. As is shown by the presented data, the sound spectrum corresponding to fcr is characterized by the largest intensity of the sound spectrum component, which ends the concentration of events (Figures 6b and 8a).

Recognition of the destruction process by means of the 3D spectrum has already been presented earlier [36] with respect to various cement composites and has also been confirmed in this paper.

What has been observed in this study is a clear division of relative sound amplitudes at the level of circa 7 kHz. Medium- and low-frequency sounds are characterized by a lower intensity of sound spectrum component compared to high-frequency sounds.

The analysis of the low-frequency spectra was not clear (it results from the measurement range of the head recording the sound), which is why it was disregarded in the presentation of the 3D image (Figures 7 and 8). The analysis of sound spectra was conducted in the range of 1–40 kHz.

After exceeding fcr, the multicracking effect was observed in the tested composite, resulting in the appearance of the intensities of sound components stronger than the background spectra and single events in the proportionality area, but significantly smaller than the spectrum of fcr (Figure 7c). The appearance of a macrocrack at point ftb and the deflection control process AD resulted in spectra with the sound intensity similar to fcr with larger amplitudes in the range of 8–20 kHz (Figures 6–8).

Figure 5 shows a 2D spectrogram that presents the possibility of the identification of destruction processes. It is a method of data imaging used previously by researchers. The obtained image does not show the velocity of increase in the relative amplitudes and contains too large ranges of amplitudes, which may contain various signals, especially those with small amplitudes, which makes it difficult to recognize them (especially with respect to single events and the phenomenon of their concentration). The spectrogram enables the recognition of AE effects with large differences in amplitudes. The use of frequency ranges makes it difficult to identify which area is responsible for the reinforcement breaking, and which is responsible for the pull-out of the reinforcement from the matrix. The 3D sound spectrum contains such information. The spectra responsible for fiber breaking and the occurrence of microcracks are characterized by a course of sharp, high amplitudes in the entire range of the spectrum 1–40 kHz (Figure 8b), whereas the pull-out of fibers and their partial destruction caused an increase in the relative amplitudes, mainly in the area of high frequencies Figure 8c.

The conducted tests indicate that it is possible to accurately identify the destruction processes in cement composites. It should be emphasised, however, that their correct recognition requires an appropriate correlation of the spectra with the individual micro and macro destruction effects.
