Surface/sub-surface crack-scattered nonlinear rayleigh waves: A full analytical solution based on elastodynamic reciprocity theorem

High-order harmonics and sub-harmonics that are engendered upon interaction between surface Rayleigh waves and material flaws have been exploited intensively, for characterizing material defects on or near to waveguide surfaces. Nevertheless, theoretical interpretation on underlying physics of defect-induced nonlinear features of Rayleigh waves remains a daunting task, owing to the difficulty in analytically modeling the stress and displacement fields of a Rayleigh wave in the vicinity of defect, in an explicit and accurate manner. In this study, the Rayleigh wave scattered by a surface or a sub-surface micro-crack is scrutinized analytically, and the second harmonic triggered by the clapping and rubbing behaviors of the micro-crack is investigated, based on the elastodynamic reciprocity theorem. With a virtual wave approach, a full analytical, explicit solution to the micro-crack-induced second harmonic wavefield in the propagating Rayleigh wave is ascertained. Proof-of-concept numerical simulation is performed to verify the analytical solution. Quantitative agreement between analytical and numerical results has demonstrated the accuracy of the solution when used to depict a surface/sub-surface crack-perturbed Rayleigh wavefield and to calibrate the crack-induced wave nonlinearity. The analytical modeling and solution advance the use of Rayleigh waves for early awareness and quantitative characterization of embryonic material defects that are on or near to structural surfaces.