An approximate formula for the Rayleigh wave velocity in the machined surface with residual stress

The present paper is concerned with the Rayleigh wave propagation in the machined surface with a thin damaged layer with residual stress. We assume that the layer and the half-space are bonded perfectly to each other. Biot’s theory of small deformations influenced by initial stress forms the basis f...

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Bibliographic Details
Published in:Journal of vibration and control 2024-09, Vol.30 (17-18), p.4146-4156
Main Authors: Liu, Zaiwei, Lin, Bin, Liang, Xiaohu, Ma, Xiaokang, Wan, Yangfan
Format: Article
Language:English
Subjects:
Boundary conditions
Deformation effects
Fine grinding
Half spaces
Initial stresses
Nondestructive testing
Propagation velocity
Rayleigh waves
Residual stress
Stress propagation
Wave propagation
Wave velocity
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Summary:The present paper is concerned with the Rayleigh wave propagation in the machined surface with a thin damaged layer with residual stress. We assume that the layer and the half-space are bonded perfectly to each other. Biot’s theory of small deformations influenced by initial stress forms the basis for this study. With the help of the effective boundary condition method, a third-order approximate secular equation of Rayleigh waves is established for the case that the layer and half-space are both orthotropic. In addition, an explicit third-order approximate formula for the Rayleigh wave velocity is derived from the secular equation. By considering a sample of silicon wafer by fine grinding with fine abrasive grains, the accuracy of the approximate formula has been verified. This study is meant to serve as the mathematical foundation for non-destructive testing of residual stress in the practical applications.
ISSN:1077-5463
1741-2986
DOI:10.1177/10775463231207139