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.

表面瑞利波和材料缺陷之间相互作用产生的高次谐波和次谐波已被广泛利用，用于表征波导表面上或附近的材料缺陷。然而，由于难以以明确和准确的方式对缺陷附近的瑞利波的应力和位移场进行分析建模，因此对缺陷引起的瑞利波非线性特征的基础物理学的理论解释仍然是一项艰巨的任务。在本研究中，基于弹性动力学互易定理，对表面或次表面微裂纹散射的瑞利波进行了分析研究，并研究了由微裂纹的拍打和摩擦行为触发的二次谐波。使用虚拟波方法，一个完整的分析，确定了传播瑞利波中微裂纹引起的二次谐波波场的显式解。进行概念验证数值模拟以验证解析解。分析结果和数值结果之间的定量一致性证明了该解在用于描绘表面/次表面裂纹扰动瑞利波场和校准裂纹引起的波非线性时的准确性。分析建模和解决方案推动了瑞利波的使用，以便对结构表面上或附近的胚胎材料缺陷进行早期认识和定量表征。分析结果和数值结果之间的定量一致性证明了该解在用于描绘表面/亚表面裂纹扰动瑞利波场和校准裂纹引起的波非线性时的准确性。分析建模和解决方案推动了瑞利波的使用，以便对结构表面上或附近的胚胎材料缺陷进行早期认识和定量表征。分析结果和数值结果之间的定量一致性证明了该解在用于描绘表面/次表面裂纹扰动瑞利波场和校准裂纹引起的波非线性时的准确性。分析建模和解决方案推动了瑞利波的使用，以便对结构表面上或附近的胚胎材料缺陷进行早期认识和定量表征。