Anti-plane problem of nano-cracks emanating from a regular hexagonal nano-hole in one-dimensional hexagonal piezoelectric quasicrystals

doi:10.1088/1674-1056/ab9ddf

中国物理B ›› 2020, Vol. 29 ›› Issue (10): 104601-.doi: 10.1088/1674-1056/ab9ddf

Dongsheng Yang(杨东升)¹, Guanting Liu(刘官厅)¹^,†()

收稿日期:1900-01-01 修回日期:1900-01-01 接受日期:1900-01-01 出版日期:2020-10-05 发布日期:2020-10-05
通讯作者: Guanting Liu(刘官厅)

Anti-plane problem of nano-cracks emanating from a regular hexagonal nano-hole in one-dimensional hexagonal piezoelectric quasicrystals

Dongsheng Yang(杨东升) and Guanting Liu(刘官厅)†

¹ College of Mathematics Science, Inner Mongolia Normal University, Hohhot 010022, China

Received:1900-01-01 Revised:1900-01-01 Accepted:1900-01-01 Online:2020-10-05 Published:2020-10-05
Contact: ^†Corresponding author. E-mail: guantingliu@imnu.edu.cn
About author:
†Corresponding author. E-mail: guantingliu@imnu.edu.cn
* Project supported by the National Key R&D Program of China (Grant No. 2017YFC1405605), the Innovation Youth Fund of the Ocean Telemetry Technology Innovation Center of the Ministry of Natural Resources, China (Grant No. 21k20190088), the Natural Science Foundation of Inner Mongolia, China (Grant No. 2018MS01005), and the Graduate Students’ Scientific Research Innovation Program of Inner Mongolia Normal University (Grant No. CXJJS19098).

摘要/Abstract

Abstract:

By constructing a new conformal mapping function, we study the surface effects on six edge nano-cracks emanating from a regular hexagonal nano-hole in one-dimensional (1D) hexagonal piezoelectric quasicrystals under anti-plane shear. Based on the Gurtin–Murdoch surface/interface model and complex potential theory, the exact solutions of phonon field, phason field and electric field are obtained. The analytical solutions of the stress intensity factor of the phonon field, the stress intensity factor of the phason field, the electric displacement intensity factor and the energy release rate are given. The interaction effects of the nano-cracks and nano-hole on the stress intensity factor of the phonon field, the stress intensity factor of the phason field and the electric displacement intensity factor are discussed in numerical examples. It can be seen that the surface effect leads to the coupling of phonon field, phason field and electric field. With the decrease of cavity size, the influence of surface effect is more obvious.

Key words: one-dimensional quasicrystals, piezoelectricity, surface effect; energy release rate

中图分类号: (General theory of continuum mechanics of solids)

46.05.+b

46.25.-y (Static elasticity) 46.50.+a (Fracture mechanics, fatigue and cracks)

Dongsheng Yang(杨东升), Guanting Liu(刘官厅). [J]. 中国物理B, 2020, 29(10): 104601-.

Dongsheng Yang(杨东升) and Guanting Liu(刘官厅)†. Anti-plane problem of nano-cracks emanating from a regular hexagonal nano-hole in one-dimensional hexagonal piezoelectric quasicrystals[J]. Chin. Phys. B, 2020, 29(10): 104601-.

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参考文献 26

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Anti-plane problem of nano-cracks emanating from a regular hexagonal nano-hole in one-dimensional hexagonal piezoelectric quasicrystals

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