## 3 Results and Discussion
The results of the experiment show that as a function of time, the number of AE pulses in the hardened samples has an atypical form, with a period of attenuation in the middle of the stage of elastic deformations. As can be seen in Figure 3, activity sharply stops, which is explained by the fact that large elements from the \"tail\" zone of the \(\Psi(\omega)\) distribution \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Strengthening Technology/Average Parameter Value** & **Untreated Samples** & **Ultrasonic Treatment** & **Beveling** & **Heat Treatment** & **Correlation Coefficient for the Number of Cycles to Failure** \\ \hline X\({}_{\text{AE}}\), s\({}^{-1}\) & 0.066 & 0.054 & 0.036 & 0.024 & \(-\)0.992 \\ Y\({}_{\text{AE}}\), MPa\({}^{-1}\) & 0.0049 & 0.0042 & 0.0028 & 0.0012 & \(-\)0.999 \\ W\({}_{\text{AE}}\) & 0.548 & 0.349 & 0.260 & 0.152 & \(-\)0.934 \\ MARSE, mV\({}^{2}\)-ms & 121,011 & 139,038 & 234,456 & 243,607 & 0.993 \\ Number of pulses (N) & 75 & 120 & 188 & 243 & 0.982 \\ Amplitude, mV & 58.2 & 59.5 & 57.7 & 58.6 & 0.055 \\ Activity, 1/N & 7.8 & 9.9 & 15.7 & 18.6 & 0.995 \\ Increase in service life, \% & 0 & 22 & 25 & 48 & - \\ Number of cycles to failure from [35] & 2951 & 4246 & - & 10,399 & - \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Correlation coefficients for the average values of the concentration and kinetic indicators and the average values of the key acoustic emission indicators. Figure 4: Comparing the results of failure simulation modeling (Equation (4)) (red line) and the number of AE pulses (dots) to find the limits of the uniform fracturing period using one of the samples as an example. Based on this, we find the values of the quality criterion X\({}_{\text{AE}}\) as the ratio of the logarithm of the number of pulses at the beginning and end of the uniform fracturing period to the duration of this period (ln\(N_{2}\)-Ln\(N_{1}\)/\(t_{2}\)-\(t_{1}\) = 4.673–4.043/95–88 = 0.09 s\({}^{-1}\)). (Equation (3)) stopped emitting, and there is a complete absence of signals (Figure 5). From the point of view of the model used, this is interpreted by smoothing or even separating the \"tail\" from the \"bell\" of the \(\Psi(\omega)\) distribution, with a further shift of the \"bell\" to the region of small values of \(\omega\). The general distribution, which had both \"bell\" and \"tail\" shapes, smoothed out, i.e., strengthening caused medium-strength elements to move into the \"bell\" zone, and the values of \(\Psi(\omega)\) in the \"tail\" region decreased. A decrease in \(\Psi(\omega)\) to zero corresponds to the separation of the \"tail\" from the \"bell\". The presence of a plateau in the time function of the number of AE pulses was substantiated by the gap between the \"bell\" and the \"tail\" of the \(\Psi(\omega)\) distribution. Such a gap can be the result of strengthening operations removing internal stresses from heterogeneous elements that have values of \(\omega\) in the \"tail\" part of the \(\Psi(\omega)\) distribution. Since these elements do not determine the service life of the material, such removal does not lead to strengthening, which explains the distrust in methods for assessing the quality of strengthening technologies based on internal stress testing, which is carried out by reflection or scattering methods on large elements of the \"tail\" that are more conducive to both reflection and scattering. By comparing the experimental curve and the simulation curve (Equation (2)), we can conclude that the \"tail\" is separated from the \"bell\" of the distribution. The first AE signals demonstrate kinetically heterogeneous fracturing with high \(\omega\) values of the \(\Psi(\omega)\) distribution function. Then, there is a period of attenuation, after which the \"bell\" begins to manifest itself, i.e., the elements begin to \"sound\" at the stage of uniform fracturing, where the values of the times to fracture measured by AE signals have high values, with a minimum value of the strength parameter of the \(\Psi(\omega)\) distribution function.