The Antiplane Problem of a Lip-Shaped Orifice With 4 Edge Cracks in 1D Hexagonal Piezoelectric Quasicrystal

WANG Chengyan; LIU Guanting

doi:10.21656/1000-0887.440346

Volume 45 Issue 7

Jul. 2024

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WANG Chengyan, LIU Guanting. The Antiplane Problem of a Lip-Shaped Orifice With 4 Edge Cracks in 1D Hexagonal Piezoelectric Quasicrystal[J]. Applied Mathematics and Mechanics, 2024, 45(7): 886-897. doi: 10.21656/1000-0887.440346

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The Antiplane Problem of a Lip-Shaped Orifice With 4 Edge Cracks in 1D Hexagonal Piezoelectric Quasicrystal

doi: 10.21656/1000-0887.440346

WANG Chengyan^1
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LIU Guanting^{1, 2
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1.
College of Mathematics Science, Inner Mongolia Normal University, Hohhot 010022, P.R.China
2.
Inner Mongolia Center of Applied Mathematics, Hohhot 010022, P.R.China

Received Date: 2023-12-05
Rev Recd Date: 2024-01-09
Publish Date: 2024-07-01

Abstract

Abstract

Through construction of the conformal mapping and with Stroh's formula, the antiplane problem of 4 secondary cracks at the lip-shaped orifice of 1D hexagonal piezoelectric quasicrystal, was studied. The effects of geometrical parameters and external loads on stress intensity factors and energy release rates were analyzed with numerical examples. The results show that, the crack length growth on either corner side of the orifice or the orifice length increase can promote the crack propagation. The crack length growth on the upper and lower sides has no obvious effect on the crack propagation on the left and right sides. The higher the orifice height is, the more significant the inhibition effect on the crack growth on both corner sides will be; the increase of the external mechanical load and electric load can promote the crack propagation. Some special defects can be derived from the degradation of the relevant parameters of the defects, such as the secondary 2 cracks in the orifice, the lip-shaped crack, and the Griffith crack, etc.
- conformal mapping,
- orifice edge crack,
- Stroh's formula,
- stress intensity factor

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References

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