# Estimation of Fatigue Crack AE Emissivity Based on the Palmer-Heald Model
## 2 Materials and Methods  
An experimental study was conducted in the framework of which the loading of samples was carried out using the AE method. For research, three grades of steel were selected--09G2S, 45 and 65G (marked in accordance with Russian state standards). The chemical composition of the studied steels is presented in Table 1.  
Each of these steels is widely used in various industries [24]. These steels were investigated in the form of hot-rolled sheets with a thickness of 3...5 mm. Steel sheets were chosen so that each of these steels had a ferrite-pearlite structure, shown in Figure 1. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Steel**} & \multicolumn{8}{c}{**The Content of Chemical Elements (\% wt.)**} \\ \cline{2-10}  & **C** & **Mn** & **Si** & **Cr** & **Ni** & **Cu** & **As** & **S** & **P** \\ \hline
09G2S & \(\leq\)0.12 & 1.3–1.7 & 0.5–0.8 & \(\leq\)0.3 & \(\leq\)0.3 & \(\leq\)0.3 & \(\leq\)0.08 & \(\leq\)0.04 & \(\leq\)0.035 \\
45 & 0.42–0.5 & 0.5–0.8 & 0.17–0.37 & \(\leq\)0.25 & \(\leq\)0.25 & \(\leq\)0.25 & \(\leq\)0.08 & \(\leq\)0.04 & \(\leq\)0.035 \\
65G & 0.62–0.7 & 0.9–1.2 & 0.17–0.37 & \(\leq\)0.25 & \(\leq\)0.25 & \(\leq\)0.2 & - & \(\leq\)0.035 & \(\leq\)0.035 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The chemical composition of the studied steels. To assess the actual mechanical properties of the steels under study, static tensile tests of flat samples cut along and across the direction of rolling were carried out in accordance with ISO 6892. Stress-strain curves of the studied steels and their mechanical properties are presented in Figure 2 and Table 2.  
The studied steels were tested for static tension using a loading scheme adopted during industrial AE testing [25]. For this, samples were made from each of steels; the sample design is shown in Figure 3. \begin{table}
\begin{tabular}{c c c c} \hline
**Steel** & **Yield Strength \(\sigma_{y}\) MPa** & **Ultimate Tensile Stress \(\sigma_{u}\), MPa** & **Total Elongation \(A\), \%** \\ \hline
09G2S & 365 & 503 & 23 \\
45 & 333 & 622 & 15 \\
65G & 325 & 654 & 15 \\ \hline \end{tabular}
\end{table} 
Table 2: Mechanical properties of the studied steels (average values). Figure 1: Microstructure of the studied steels: (**a**) 09G2S; (**b**) 45; (**c**) 65G. Figure 3: The design of the test sample (**a**) and a photograph of one of the samples (**b**): 1—damping pads, 2—fixing bolts, 3—acoustic emission sensor. Figure 2: Stress–strain curves for the studied steels: 1—09G2S; 2—45; 3—65G. Flat samples with a working part width of 50 mm with an edge notch were made taking into account the recommendations of Russian State standard GOST 25.506-85, which describes the determination of crack resistance characteristics of structural materials. The notch width was chosen as equal to 4 mm, the opening angle \(\Theta\) = 45\({}^{\circ}\), and the notch depth \(h\) = 10 mm. Holes with a diameter of 12 mm are provided for fixing the damping pads, which reduce the level of acoustic interference of the loading machine. In total, 50 samples were made of 09G2S steel (of which 30 samples were made of sheets of a 3-mm thickness and 20 samples were made of sheets of a 5-mm thickness), 10 samples were made of 4 mm sheets of 45 steel, and 10 samples were made of 4 mm sheets of 65G steel. A fatigue crack was grown on each of the test samples. For this, the sample was subjected to cyclic tensile loading along the pulsation cycle (cycle asymmetry coefficient \(R_{c}\) = 0) with a frequency of 5 Hz and a maximum cycle load of \(\sigma_{max}\)\(\approx\) 0.6\(\cdot\)\(\sigma_{y}\). The \(\sigma_{max}\) values amounted to 210 MPa for samples of steel 09G2S and 190 MPa for steels 45 and 65G. The number of loading cycles was chosen so that the fatigue crack developing under cyclic loading in the lateral notch region would reach a certain length. Nominal crack lengths ranged from 3 to 15 mm. Thus, the total length of the notch and crack was approximately 15...28 mm, depending on the specimen.