# Investigation of Acoustic Emission of Cracks in Rails under Loading Close to Operational
## 3 Results and Discussion
The distribution of AE hits amplitudes for all specimens predominantly (in more than 90% of cases) corresponds to an exponential law, which is confirmed using the \(\chi^{2}\) goodness of fit criterion, with a \(p\)-value exceeding 0.05. In the opinion of most researchers [31], an exponential distribution is characteristic of the stage of diffuse fracture of the material preceding the formation of a macroscopic defect, which also confirms the hypothesis of structural noise [20]. When testing a specimen with a pre-grown crack, hits with an amplitude of up to 80 dB were recorded (Figure 8). Another difference from the data obtained when loading a defect-free specimen is that AE hits are recorded both with increasing and decreasing load. Figure 6: Rail microstructure (**a**) and non-metallic inclusions (highlighted in red) in the longitudinal section (**b**); photograph (**c**) and EDX-spectrum (**d**) of a nonmetallic sulfide inclusion revealed in a fracture of a rail fragment by EDX-analysis. In addition to signals of small amplitude and duration, similar in waveform and spectrum to the signals shown in Figure 5, while testing specimens with a defect, signals with a specific waveform are also recorded. For example, signals that have a longer decay time and, therefore, a longer duration of the order of several milliseconds (Figure 9a,b), as well as narrow-band signals with amplitude modulation, the source of which may be the friction of the crack edges (Figure 9c,d). AE waveforms are presented without gain coefficient compensation. The appearance of a crack leads to a change in the law of the probability distribution of AE hits amplitudes; for a specimen with a crack, the distribution of amplitudes in each loading cycle corresponds to the half-normal law. Figure 10 shows typical distributions of amplitudes at various values of the load, and red graphs correspond to the theoretical distribution law. In the presence of a defect, the amplitude distribution tends to be normal in comparison with a defect-free specimen. This phenomenon could be explained due to the presence of several independent AE sources, such as the structural noise of an object, crack growth, and friction of its edges. Compliance with the half-normal law is determined reliably using the \(\chi^{2}\) test in 78% of cases with a \(p\)-value of more than 0.05. Figure 8: Dependence of AE hits amplitudes on time (blue) and dependence of loading force on time (red) for defective specimen. Figure 7: Distribution of AE hits amplitudes for a defect-free specimen at various load values 15 kN (a) 30 kN (b) 45 kN (c). When testing specimens with different sizes and locations of cracks, significant variability of the data was observed. The proportion of high-amplitude AE hits was different for different specimens, and the AE hits rate was manifested to a different extent. AE data parameters recorded during experiments for defect specimens (with different defect locations) and for defect-free specimens are shown in Table 3. Since the main task of data analysis is the separation of defective and defect-free specimens, the AE hits rate, expressed in the number of AE hits per loading cycle, and the quantile of the amplitude distribution of the order of 0.9, characterizing the distribution tail, were considered as descriptors. Figure 10: Distribution of AE hits amplitudes for a specimen with defect at various load values 15 kN (a); 30 kN (b); 45 kN (c). Figure 9: Typical waveform (a,c) and spectrums (b,d) of AE signals obtained during the loading specimens containing crack. Parameters represented in Table 3 show that the AE hit rate and amplitudes of AE hits increased when the load was increasing. At a load of 15 kN, the activity and energy of AE hits are low for both defective and defect-free specimens. Still, with a load rise, an increase in the AE hit rate is manifested to a greater extent for defective specimens than for defect-free specimens.