## 2 Materials and Methods  
The main chemical composition of the axle material is C, Si, Mn, and Fe (Table 1). The specimens were obtained from a new railway vehicle commercial axle. The longitudinal direction of the specimen coincided with that of the axle. The surface was polished by lapping. Tensile tests were performed according to ASTM A370. The measured yield and tensile strengths of three cylindrical specimens of \(\Phi\)8.75 were within the ranges of 392-440 and 656-698 MPa, respectively (Figure 1). Figure 2 presents a microstructural image. The material is composed of ferrite (black part) and pearlite (gray part). The pearlite has a variety of shapes. The distance between Fe\({}_{3}\)C layers in a pearlite grain is different for each grain. Figure 3a shows the fatigue test specimen and the sampling location of the specimen from the axle. The minimum and maximum diameters of the specimen were 4 and 16 mm, respectively. The specimen was designed according to reference [7]. The stress and strain in the specimen were obtained from the elastic wave theory [7]. Natural vibration frequencies were obtained using ABAQUS software. The convergence of the solution was checked as the number of elements increased. The material properties listed in Table 2 were used for the simulation. The Young's modulus and Poisson's ratio of the specimen were measured according to ASTM 1876-01. Properties of the horn were taken from the literature. Figure 3 shows the natural modes of the specimen, the horn, and the assembly. The lateral displacement of the specimen in the middle of the hourglass section was zero, and the natural frequency was 19,784 Hz. This frequency is close to the excitation frequency of the input generator, 20 kHz. Figure 4 shows the newly developed piezoelectric UFT (ultrasonic fatigue test) equipment, which operates at a frequency of 20 kHz. The stress ratio (R = minimum load/maximum load) was R = \(-\)1. The UFT system consisted of a power generator, a converter (piezo actuator), and a horn attached mechanically to the converter by a screw. A personal computer controlled the generator  
Figure 3: Modal analysis of the specimen and horn using the finite element method. Figure 2: Microstructures of the axle material. and converter to impose a vibratory amplitude at the end of the horn. The power generator converts a 60 Hz voltage signal into a 20 kHz sinusoidal ultrasonic electrical signal. The converter converts the 20 kHz ultrasonic excitation signal into a mechanical signal. The boost and horn, with a natural frequency of 20 kHz, amplify the vibration. Displacement at the horn end was measured using a photonic sensor to calculate the stress value of the specimen. The stress value at the middle of the specimen was linearly proportional to the displacement of the specimen end and the dynamic modulus of elasticity of the specimen [6,7]. At 20 kHz, high-cycle fatigue testing generates excessive heat in the specimen, so countermeasures against heat generation are necessary. To ensure that the specimen was not heated, the test was performed by applying a load to the specimen for 0.3 s and stopping it for 3 s. As a result, the increase of specimen temperature due to the deformation caused by the load was negligible. Several specimens were subjected to preliminary tests to confirm the variation of specimen temperature using an infrared camera. The low-temperature test condition was achieved by injecting liquid nitrogen into the chamber through a nozzle. The temperature of the chamber was controlled by opening and closing the nozzle. The resolution of temperature control was about \(\pm 2~{}^{\circ}\)C. As shown in Figure 4, the horn and the specimen were located in the chamber, in which a low temperature below \(-160~{}^{\circ}\)C could be realized. The developed equipment is expected to be useful for low-temperature fatigue testing. Figure 5 shows a drawing and photograph of the Charpy impact test specimen. The specimens were produced according to ASTM A370 from a commercial railway vehicle axle.