Scattering of Rayleigh wave by inclined surface open cracks: Numerical simulations based on reciprocity theorem and verification using finite element method

Abstract

Surface cracks typically exhibit a range of characteristics, including varying depths and inclined angles. Investigating the interaction between ultrasonic surface waves and these cracks is crucial for the non-destructive evaluation of their properties. In this work, the amplitudes of Rayleigh waves scattered in the far field by inclined surface open cracks with depths exceeding the wavelength are investigated in a two-dimensional plane. An integral equation, derived from the reciprocity theorem, is formulated for the scattered Rayleigh waves, which is equivalent to the radiated fields from forces and tractions generated by the incident waves at the surface of the crack. Within this integral equation framework, the crack opening displacements caused by the incident Rayleigh waves are determined by solving singular integral equations based on Chebyshev's theorem. An oblique coordinate system is introduced to obtain solutions for the scattered Rayleigh waves generated by inclined cracks. Numerical solutions for the scattered Rayleigh waves are provided, employing reflection and transmission coefficients to investigate the influence of crack length, inclined angle, and depth on wave scattering. It is found that the transmission coefficients of Rayleigh waves exhibit high sensitivity to crack depth, whereas the reflection coefficients depend on both the crack depth and its inclined angle. The finite element method has been used to validate the simulation results obtained from the proposed theory. This theory can further enhance the quantitative assessment of surface cracks.