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Interface crack behaviors disturbed by Love waves in a 1D hexagonal quasicrystal coating–substrate structure

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Abstract

The scattering of Love waves by an interface crack between a one-dimensional (1D) hexagonal quasicrystal (QC) coating and a half-space elastic substrate is investigated by using the superposition principle and integral transform technique. Introducing the dislocation density function, the wave scattering problem is transformed into the Cauchy singular integral equations, and the dynamic stress intensity factors (SIFs) of the left and right crack tips are solved. By degrading the quasicrystalline coating to the elastic dielectric layer, the correctness of the present numerical results is verified compared to the classical one. Then, the effects of the material combinations, incidence direction, crack sizes, and coupling coefficient on the dynamic SIFs are analyzed. The results show that the appropriate material combinations and incidence direction can hinder crack expansion. Moreover, the smaller the absolute value of the coupling coefficient and the crack sizes, the smaller the peak and volatility of the dynamic SIFs. The conclusions of this paper provide a theoretical basis for the dynamic failure analysis and nondestructive tests of QCs.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (12262033, 12062021 and 12062022), Ningxia Hui Autonomous Region Science and Technology Innovation Leading Talent Training Project (KJT2020001), and the Natural Science Foundation of Ningxia (2022AAC03013; 2022AAC03068). Yueting Zhou would like to acknowledge the supports by the National Natural Foundation of China (11972257 and 12272269).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Ningxia University, Yinchuan, 750021, China

    Yuanyuan Ma, Juan Yang, Xuefen Zhao & Shenghu Ding

  2. **nhua College, Ningxia University, Yinchuan, 750021, China

    Xuefen Zhao

  3. Institute of Ethnic Preparatory Education, Ningxia University, Yinchuan, 750002, China

    Juan Yang

  4. School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai, 200092, China

    Yueting Zhou

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  1. Yuanyuan Ma
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Contributions

YM, YZ, and XZ wrote the main manuscript text, and JY and SD prepared Figs. 1, 2, 3, 4, 5, 6, 7. All authors reviewed the manuscript.

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Correspondence to Xuefen Zhao or Shenghu Ding.

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Ma, Y., Zhou, Y., Yang, J. et al. Interface crack behaviors disturbed by Love waves in a 1D hexagonal quasicrystal coating–substrate structure. Z. Angew. Math. Phys. 74, 61 (2023). https://doi.org/10.1007/s00033-023-01947-5

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  • DOI: https://doi.org/10.1007/s00033-023-01947-5

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