The Plane Thermoelastic Problem of a Central Opening Crack in the 1D Hexagonal Quasicrystal Non-Periodic Plane

ZHAO Xuefen; LU Shaonan; MA Yuanyuan; ZHANG Baowen

doi:10.21656/1000-0887.440302

Volume 45 Issue 3

Mar. 2024

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Article Navigation > Applied Mathematics and Mechanics > 2024 > 45(3): 303-317

ZHAO Xuefen, LU Shaonan, MA Yuanyuan, ZHANG Baowen. The Plane Thermoelastic Problem of a Central Opening Crack in the 1D Hexagonal Quasicrystal Non-Periodic Plane[J]. Applied Mathematics and Mechanics, 2024, 45(3): 303-317. doi: 10.21656/1000-0887.440302

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The Plane Thermoelastic Problem of a Central Opening Crack in the 1D Hexagonal Quasicrystal Non-Periodic Plane

doi: 10.21656/1000-0887.440302

1.
School of Information Engineering, Ningxia University, Yinchuan 750021, P.R.China
2.
Xinhua College of Ningxia University, Yinchuan 750021, P.R.China
3.
School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, P.R.China

Received Date: 2023-10-10
Rev Recd Date: 2023-11-14
Publish Date: 2024-03-01

Abstract

Abstract

Considering the thermal conductivity of the medium inside the crack, the plane thermoelastic problem of the 1D hexagonal quasicrystal with a central open crack in an aperiodic plane, was studied. With the Fourier integral transformation technology, the closed form solutions of thermal stresses, thermal stress intensity factors and strain energy density factors were obtained. Numerical examples were used to analyze the effects of the thermal conductivity, the external load, and the phonon field-phason field coupling coefficient on the thermal stress intensity factor and the strain energy density factor at the crack tip. The results indicate that, the heat flux density gradually increases but the thermal stress intensity factor gradually decreases with the thermal conductivity. The phonon field-phason field coupling coefficient has a significant impact on the crack propagation. When the phonon field load is relatively small or the heat flux density is relatively high, the crack is not easy to propagate. The heat flux density exhibits a concentration effect at the crack tip. The work provides a theoretical basis for the application of thermodynamic properties of quasicrystals, and the optimization of design and preparation of quasicrystal components.
- 1D hexagonal quasicrystal,
- central opening crack,
- Fourier integral transformation,
- thermal stress intensity factor,
- strain energy density factor

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References(26)

References

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