## 4 Discussion and Results
### Evaluation of Beam Profiles on the Defect Types  
Figure 10 shows the size of the amplitude according to the distance between the transmitting and receiving transducers for the defect depth of the \"Circum\" defect type. To compare the amplitudes of the ultrasonic defect signals according to the defect depth, we performed a standardization process for 100 \(\upmu\)m, 300 \(\upmu\)m, and 700 \(\upmu\)m based on the amplitude when there was no defect. The Rayleigh wave scan section (\(-5\)\(\rightarrow\)3 mm), as shown in Figure 6b, was where the ultrasonic signals were received. This section was expected to be a null field, as shown in Figure 1 because there was no correlation according to the size of the defect. Moreover, the amplitude of the ultrasonic signals received beyond 3 mm becomes larger as the size of the defect decreases. We can also see an increase in the ultrasonic waves leaking into the water as the distance between the two transducers increases. Figure 11 shows the size of the amplitude according to the distance between the transmitting and receiving transducers for the defect depth of the \"Axial\" defect type. The same standardization process as that shown in Figure 10 was performed. In terms of the \"Axial\" defect type, the amplitude of the ultrasonic defect signals also decreases as the distance between the two transducers increases. In particular, the amplitude of the ultrasonic signal decreases slowly around 2-3 mm and then decreases rapidly after 5 mm. This is because the defect length is in the same direction as the  
Figure 11: Experiment result of amplitude profiles of Axial defect type. Figure 10: Experiment result of amplitude profiles of Circum defect type. propagation of the ultrasonic waves, and the ultrasonic wave propagation characteristics change according to the defect type. Figure 12 shows the size of the amplitude according to the distance between the transmitting and receiving transducers for the defect depth of the \"Shear\" defect type. In the case of the \"Shear\" defect type, ultrasonic signals of 300 \(\upmu\)m and 700 \(\upmu\)m appear at similar locations. This is because the ultrasonic waves and the defect intersect at an angle of 45\({}^{\circ}\). Thus, the ultrasonic waves scatter in various forms, such as diffraction, reflection, and transmission, when the defect and ultrasonic waves come into contact. Based on Figures 10-12, we chose the 700 \(\upmu\)m crack with the highest resolution of Rayleigh waves and compared the normalized peak-to-peak amplitudes of the non-crack and three crack types. Figure 13 shows the correlation of the defect types when the defect depth is 700 \(\upmu\)m. When the defect depth is 700 \(\upmu\)m, the ultrasonic waves transmit to a certain extent in the \"Axial\" and \"Shear\" defect types. However, most of the ultrasonic waves cannot transmit in the \"Circum\" defect type. It is also difficult to distinguish the defect types from the amplitude of the ultrasonic waves received from about 8 mm. We can see a difference depending on the crack type in the vicinity of 5 mm on the X axis. The peak-to-peak amplitude is very low because the \"Circum\"-type crack can block a large number of Rayleigh waves. As expected, the \"Axial\"-type crack shows a higher peak-to-peak amplitude than the \"Circum\" crack does. Figure 12: Experiment result of amplitude profiles of Shear defect type. Figure 13: Experiment result of amplitude profiles with the same crack size (700 \(\upmu\)m). Figure 14 shows the peak-to-peak amplitudes of the Rayleigh waves according to the crack type and depth of the piston rod. The figure shows a correlation of the defect types according to crack depth when the distance of the receiving transducer is 6.5 mm from the crack location. In all of the defect types, the amplitude of the received signals tends to decrease as the crack depth increases. The amplitude of the ultrasonic signal is the smallest in the \"Circum\"-type defect, where the crack is perpendicular to the propagation of the Rayleigh waves.