## 5 Conclusions  
The main objective of this study was to confirm the potential for application of a new ultrasonic method for the non-destructive measurement of residual stress in rails. For this purpose, the measurement of residual stress of rails was carried out using LCR waves. According to the results of the studies conducted, the following conclusions can be drawn:  
1. A probe consisting of one transmitter and two receivers was fabricated using PZT piezoelectric elements with a center frequency of 2.25 MHz and a wedge made of PMMA material.
2. The acoustoelastic coefficient was calculated through a plurality of tensile tests. By analyzing the correlation between stress and travel time, it was found that the regression lines whose slope values are the acoustoelastic coefficient are very close to straight lines. This indicates that the calculated acoustoelastic coefficient values have high reliability, and stress can be measured using these values.
3. Residual stresses on used rails were measured using the calculated acoustoelastic coefficients, and their distributions were analyzed. Using rail specimens under different conditions, it was verified whether the characteristics of the residual stress inherent in the rails could be grasped through the measured values. Through this process, it has been proven that ultrasonic testing using LCR waves is a non-destructive measurement technique that can be applied for accurate residual stress measurement of used rails.  
Because LCR waves travel to different penetration depths depending on the frequency, if LCR wave probes with different frequencies are manufactured and residual stress values are measured for the same location of the subject made of a material for which the acoustoelastic coefficient has already been calculated through a tensile testing, even the stress gradient of the subject can be obtained. In addition, because this approach uses equipment that is not large (or which could be miniaturized), it has also been confirmed that it could be applied to measure stress in real time under actual field conditions by constructing a portable system. Therefore, it is possible to overcome the limitations of the existing X-ray diffraction method or Barkhausen noise method used to measure the residual stress of rails. It can also be seen that more specific information can be obtained more simply and quickly from the field directly, which has the additional potential to be a suitable technique.  
Conceptualization, K.-B.K.; Data curation, G.K.; Formal analysis, G.K.; Funding acquisition, J.-H.P. and M.Y.C.; Investigation, Y.-I.H.; Methodology, Y.-I.K. and K.-B.K.; Project administration, M.Y.C. and K.-B.K.; Resources, J.-H.P.; Software, Y.-I.H. and G.K.; Supervision, K.-B.K.; Validation, Y.-I.K.; Visualization, Y.-I.H.; Writing--original draft, Y.-I.H.; Writing--review & editing, K.-B.K. All authors have read and agreed to the published version of the manuscript.  
This research was partially supported by a \"development of safety measurement technology for infrastructure industry\" grant funded by the Korea Research Institute of Standards and Science (KRISS-2021-GP2021-0008) and \"development of IoT-based rail break and buckling detection system for climate change\" grant (21 CTAP-C152115-03) among the railroad technology research projects supported by the Korea Agency for Infrastructure Technology Advancement (KAIA).  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Not applicable.  
**Conflicts of Interest:** The authors declare no conflict of interest.