# Acoustic Emission and Modal Frequency Variation in Concrete Specimens under Four-Point Bending
## 4 Results  
Figure 5 shows the load-displacement curves obtained from the three tests. The load and displacement values reported in the figure are the force measured by the loading cell, and the displacement of the hydraulic jack, respectively. In particular, the load values do not include the weight of the concrete specimen, of the steel I beam and cylinders, or of transducers and cables (almost negligible), for a total of about 0.3 kN. Tests 1 and 2 were of the kind (b) described above, whereas test 3 was of the kind (a). As expected, the curve related to test 3 is more regular than those related to tests 1 and 2 that, conversely, reflect the discontinuous character of the loading process. In fact, not only was the test stopped several times, but the beam was also perturbed by external impulses at the end of each incremental step to excite the free vibrations. This explains the numerous jumps in the load-displacement curve of the first two tests. Moreover, the softening branch was globally quite stable for test 1, while an unstable crack propagation was registered for tests 2 and 3, where global snap-backs were observed (Figure 5). In Figure 6a, the load vs. displacement and cumulated AE energy vs. displacement diagrams of test 1 are superimposed. The figure shows that no sensible AE was detected until about the 90% of the peak load (however, first events were registered near the 60% of the peak load, see the zoom in the box of Figure 6a). A large jump in the AE energy appears in correspondence of the maximum load point after which the AE energy progressively increases up to the end of the test. Figure 5: Experimental load vs. displacement curves for the three four-point bending tests conducted. Figure 6: Test 1: (**a**) load and cumulated AE energy vs. displacement diagrams; (**b**) RA values of detected Acoustic Emission (AE) events (S\({}_{\text{AE1}}\) = wideband sensor, S\({}_{\text{AE2}}\) = resonant sensor). The failure occurred due to crack propagation in the notched section, provoked principally by tensile stresses. Considering the static scheme, plus the small ratio self-weight/maximum external force applied and the stress diffusion according to Saint Venant's principle, the central part of the intermediate span was mainly subjected to bending stresses (see Figure 7a). A sub-vertical main crack developed near the notch: the initial inclined path was followed by an almost vertical propagation (Figure 7b). The fracture mode of test 1 was analyzed by means of the relationship between RA and AF values estimated for each sensor, as shown in Figure 6b. Considering that a decrease in the AFs by approaching the final stage of the test is obtained, and that the RA values are all lower than 2.5 ms/V, a dominant presence of tensile cracks (Mode I) characterizes the damage evolution up to the final collapse [7; 13; 16; 17; 18]. However, a certain amount of Mode II cracks also appeared due to local mixed mode crack propagations around inhomogeneities. These findings were in agreement with literature studies, e.g., see [36; 37]. Direct visual observation (when possible) and identification of the cracking mode by AE wave's RT analysis, as far as not supported by other survey methods such as digital image correlation [38] or X-ray diffraction analysis [39], was important; in fact, this allowed for the characterizing the cracking mode based on information obtained from a small number of sensors. Figure 8a,b shows the load vs. displacement and cumulated AE energy vs. displacement curves of test 2, 3, respectively. As previously pointed out, the load-displacement graph of tests 2 and 3 denote a more brittle behavior than that of test 1 (see the large load jumps in the post-peak phase in Figure 8a,b). In order to describe this catastrophic behavior and the relevant acoustic emission better, the effect of the self-weights mentioned above is shown in Figure 8a,b (see negative load values), so that the entire load-displacement path can be visualized.