Study on the nonlinear interaction characteristics between rail cracks and ultrasonic based on finite element-spectral element coupling method

This study addresses nonlinear ultrasonic wave propagation induced by rail cracks. The domain decomposition theory of finite element-spectral element coupling underpins a computational method that combines the nonlinear effects in the crack region with far-field linear elastic behavior to investigate the nonlinear interactions between cracks and ultrasonic waves. The results show that the nonlinear parameter correlates positively with crack length and angle, reaching its maximum at 6 mm and 90 degrees, approximately 11 times higher than at 0 degrees. The crack angle influences the scattering energy coefficient with a "U-shaped" distribution, showing the highest values at 0 degrees and 90 degrees and lower values between 15 degrees and 60 degrees; at a fixed angle, the scattering energy coefficient increases significantly with crack length. Simulation and experimental errors remain within 5 %, fully validating the numerical results.