# Estimation of Fatigue Crack AE Emissivity Based on the Palmer-Heald Model
## 2 Materials and Methods
Before the main tests, an experimental study of the stress-strain state of the metal at the tip of the crack was carried out on the test specimens made of 09G2S steel with a pre-grown fatigue crack. Studies were performed using the indentation method. For this, indents were applied on the side surface of the sample with a Vickers pyramid under a load of 0.015 kg and the microhardness values _HV0.015_ were determined. The indents were applied on an Instron Tukon 2500 Vickers hardness tester in rows with a pitch between the indentions of 50 \(\upmu\)m and the distance between the rows of 50 \(\upmu\)m (Figure 4). The values of the hardness _HV0.015_ of the metal at each point assessed the presence of plastically deformed metal. Thus, an increase in the _HV0.015_ hardness in the defined point relative to the hardness of the undeformed metal indicates its plastic deformation, and the higher the metal hardness value, the greater the degree of its plastic deformation [26]. Testing of specimens with fatigue cracks was carried out on an Instron 8801 machine. Acoustic signals were recorded during the tests using the A-Line 32D industrial system. The measuring path consisted of resonant transducers GT200 (LLC \"Global test\") with a resonance frequency of 165 kHz and preamplifiers PAEF-014. The peak noise of the preamplifier amounted to 26 dB in reference to 0 dB at 1 \(\upmu\)V. The peak acoustic noise level after installing the sample in the grips of the testing machine was 34 dB. In accordance with the recommendations [25], the threshold for discrimination of acoustic signals was set to 40 dB. A diagram of the loading cycle of the sample is presented in Figure 5.  
Figure 4: The methodology for the study of the deformed volume in the notch zone on samples of 09G2S steel. Two triangular cycles at the first stage of loading are necessary to equalize the internal mechanical stresses that occurred during the manufacture of samples and when placing them in equipment. The acoustic activity that occurs during such loading is usually not associated with the fracture processes. The main loading stage consists of four main stages: in the first, the load gradually increases from 0% to 50% \(\sigma_{max}\), in the second, from 50% to 75% \(\sigma_{max}\), and in the third, from 75% to 100% \(\sigma_{max}\). The fourth stage is carried out with a stress excess of \(\sigma_{max}\) for 25%. Between the areas of stress increase, a load is held for 90 s. For industrial AE testing, exposure periods are necessary to make a decision on the termination of loading in the event of an emergency. When conducting experiments in laboratory conditions, stress holding sections are introduced to ensure compliance with industrial testing conditions. In each experiment, the length of the fatigue crack was measured before and after the tests. During loading, parametric information was recorded--the value of the loading force and the position of the lower grip of the machine, the parameters of the AE impulses (amplitude, energy, duration and rise time), as well as the primary information--waveforms of AE impulses.