## 3 Results and Discussion
### R/A-AF Association Analysis  
R/A-AF association analysis shows an effective way to illustrate the failure modes of materials. R/A (measured in ms/v) is defined as the ratio of rise time and amplitude, while AF (measured in kHz) is defined as the ratio of the ringing counts and duration. The two parameters can be calculated using the following equations:  
\[\text{AF}=\text{Ringing counts/Duration}, \tag{3}\]  
\[\text{R/A}=\text{Rise time/Peak Amplitude}, \tag{4}\]  
[PERSON] et al. [30] demonstrated that shear and tensile damage have different R/A and AF values. Generally, a large amount of energy is released immediately when a tensile crack occurs, which leads to a high associated AF value. On the contrary, a shear crack occurs leading to a long rise time and duration, which results in a high associated R/A value. The types of cracks including tensile or shear formed in the concrete under different load stages can be qualitatively classified by analyzing the R/A-AF association diagram. Figure 9 illustrates the R/A-AF association diagrams at 20% of the ultimate load and at the failure load. For RC structures, the bond damage in concrete is primarily caused by shear stress exerted from the ribs on the surface of the steel bar. As can be seen from all the R/A-AF association diagrams in Figure 9, shear damage dominates during the entire loading process for all the RC beams, which can be explained by the fact the ribs on the surface of the steel bar shear the surrounding concrete. For corroded RC beams, as the steel corrosion increases, the proportion of large AF values tend to increase. This phenomenon means the contribution of the tensile damage mode increases, and the action of steel corrosion leads the shear cracks to transform into tensile cracks. The reason can be explained that when the steel bar shears the surrounding concrete, the bevel of the steel bar's rib tenses the concrete. Before the loading process, the steel corrosion- and expansion-induced tensile stress causes a large number of tensile cracks in the concrete, and the higher the steel corrosion ratio is, the more tensile cracks form in the concrete. Once the loading process begins, the original tensile cracks will continue to expand and cause greater tensile damage. Figure 8: Ultimate flexural load. In addition, from the R/A-AF association diagrams of the five RC beams at the initial load stage (i.e., 20% of the ultimate load), the effect of steel corrosion on the types of cracks can be analyzed in  
Figure 9: R/A-AF association diagram: (**a**) Unorroded RC beam; (**b**) 10% corroded RC beam; (**c**) 20% corroded RC beam; (**d**) 30% corroded RC beam; (**e**) 40% corroded RC beam. detail. In the initial load stage of the 10% corroded beam, the proportions of tensile cracks and shear cracks are approximately the same, which indicates that the shear action and tensile action provided by the steel bar are the same. The balance between the shear and tensile action could result in a large bearing capacity of the RC beam. Furthermore, when comparing with the uncorroded beam in the initial stage, it is evident that the tensile action of the 20% corroded beam tends to increase while the shear action tends to decrease. The reasons for this can be explained as, in the uncorroded RC beam, the concrete in the compression zone is sheared by the steel bar's rib; as the steel corrosion ratio increases, the reduced area of the compression zone causes the steel bars to put pressure on almost all the concrete, which increases the proportion of tensile cracks. Meanwhile, the corroded rib on the surface of steel bars reduces its ability to shear the surrounding concrete, resulting in the declined shear action. Moreover, in the 30% and 40% corroded RC beams, the development of tensile and shear cracks, which is reflected in the increase in the large R/A and AF values indicates that severe damage occurs in the initial load stage.