## 3 Experiments  
The rail to be tested was a type called KR60, one commonly used for freight transportation in Korea. The material properties and cross-section of the rail are shown in Table 1 and Figure 3.  
To minimize the effect of stress disturbance caused by cutting the rail, the test specimens were cooled while being subjected to wire cutting. The specimens were extracted from the lower part of the head in used rails, where the degree of deformation against the longitudinal residual stresses was the lowest. Both ends of each specimen were coated by glass fiber reinforced plastic (GFRP) to prevent the specimens from slipping during the tensile tests. The dimensions of the welded plate were 270 \(\times\) 40 \(\times\) 6 mm, while those of the GFRP coating were 30 \(\times\) 40 mm. Figure 4 shows specimens for use in tensile testing. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Yield Strength [MPa]**} & **Elongation Percentage** & **Hardness [HBW]** & **Modulus of Elasticity** & **Linear Expansion** \\  & **[\%]** & **[MB]** & **[MPa]** & **Coefficient [mm/\({}^{7}\)C]** \\ \hline \(>\)800 & \(>\)10 & \(>\)235 & 210,000 & \(1.14\times 10^{-5}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Mechanical properties of KR60 rail [42]. Figure 2: Wheel-rail contact geometry [40]. The center frequency of the LCR wave transducers adopted was 2.25 MHz. This was suitable because the penetration depth calculated according to Equation (7) [43] was less than the thickness of the fabricated specimens. \[D=V_{CR}\times f^{-0.96} \tag{7}\]  
where, \(D\) is the penetration depth of the LCR wave, \(V_{CR}\) is the velocity of the LCR wave in the component, and \(f\) is the frequency of the ultrasonic transmitter and receiver. PZT elements (0.75 inch diameter) were used to fabricate the LCR wave transducers, and the wedge designed and manufactured for the LCR wave to pass through was a polymethyl methacrylate (PMMA) material. Because the longitudinal wave velocity of the KR60 rail used as test pieces was about 5860 m/s, and the longitudinal wave velocity of PMMA was 2760 m/s, the wedge angle for LCR wave generation was 28.1\({}^{\circ}\), as determined by applying [PERSON]'s law. One ultrasonic transmitter and two receivers were arranged according to the calculated angle. To eliminate the effect of environmental temperature on travel time, a three-transducer array with two receivers and one transmitter was arranged  
Figure 4: Photograph of specimens manufactured for the tensile tests. Figure 3: Cross-section of a KR60 rail [42]. in a row, and the intervals between them were each 29.3 mm. Therefore, the transmission time of the LCR wave received by each receiver was about 11.3 and 16.2 us, respectively. Figure 5 shows the designed and manufactured LCR wave probe. The experimental setup shown in Figure 6 includes a pulser-receiver (APR-8035, AcouLab, Bucheon-si, Korea), an oscilloscope (WaveRunner 640 Zi, Teledyne LeCroy, Chestnut Ridge, NY, USA), and a servo-hydraulic test system (Landmark 370.10, MTS, Eden Prairie, MN, USA). The fabricated probe set was connected to the pulser-receiver of this setup with the test piece attached. Using a computer connected to the pulser-receiver, ultrasonic waves were excited through the transmitter. Then, ultrasonic waves propagated along the wedge of the probe set and along the specimen were received by each receiver and visualized on an oscilloscope. To measure the changes in stress, ultrasonic signal acquisition experiments were performed through tensile tests to calculate the acoustoelastic coefficient of longitudinal waves propagating in the same direction as the applied stress field. Each ultrasonic signal was acquired by applying a load of 0 to 89.68 kN in steps of 2.80 kN. Figure 5: Photograph of a manufactured LCR wave probe. Figure 6: Photograph of the experimental setup for measuring tensile stress using LCR waves. For the residual stress measurement using the LCR wave, three rail samples cut at different sites were used.