电半渗透下正<i>n</i>边形纳米孔带<i>s</i>条纳米裂纹的表面效应

刘欣宇; 武志林; 刘官厅

doi:10.21656/1000-0887.450328

电半渗透下正n边形纳米孔带s条纳米裂纹的表面效应

doi: 10.21656/1000-0887.450328

刘欣宇^1,,
武志林¹,
刘官厅^{1, 2, ,}

1.
内蒙古师范大学数学科学学院, 呼和浩特 010022
2.
内蒙古自治区应用数学中心, 呼和浩特 010022

基金项目:

国家自然科学基金 12162027

内蒙古自然科学基金重点项目 2024ZD21

内蒙古自治区高等学校科学技术研究自然科学重点项目 NJZZ22574

内蒙古自治区一流学科科研专项项目 YLXKZX-NSD-001

内蒙古自然科学基金 2023LHMS01017

内蒙古师范大学基本科研业务费 2023JBZD005

内蒙古自治区研究生科研创新项目 KC2024027B

详细信息

作者简介:
刘欣宇(2000—)，女，硕士生(E-mail: 15148245045@163.com)

通讯作者:
刘官厅(1966—)，男，博士(通讯作者. E-mail: guantingliu@imnu.edu.cn)

中图分类号: O346.1
计量
- 文章访问数: 68
- HTML全文浏览量: 16
- PDF下载量: 11
- 被引次数: 0
出版历程
- 收稿日期: 2024-12-12
- 修回日期: 2025-04-02
- 刊出日期: 2026-03-01

Surface Effect on s Nano-Cracks Emanating From Electrically Semi-Permeable Regular n-Polygon Nano-Hole

LIU Xinyu^1
,,
WU Zhilin¹,
LIU Guanting^{1, 2
, ,}

1.
School of Mathematics Science, Inner Mongolia Normal University, Hohhot 010022, P.R.China
2.
Center for Applied Mathematics Inner Mongolia, Hohhot 010022, P.R.China

摘要

摘要: 研究了具有表面效应的电半渗透下正n边形纳米孔在远场反平面机械载荷和面内电载荷作用下的断裂行为. 根据Gurtin-Murdoch表面模型理论，采用保角映射技术对应力、电位移场进行解析，得到了裂纹尖端应力强度因子(SIF)和电位移强度因子(EDIF)的解析解. 构造了一个新的保角映射，从正n边形纳米孔发出的s条纳米裂纹的外部到圆形纳米孔的内部. 结果表明，SIF和EDIF均受到远场机械载荷和电载荷耦合的影响，且正n边形边长越小，表面效应的影响越明显.
- 压电材料 /
- 半渗透 /
- 表面效应 /
- 纳米级
Abstract: The fracture behaviors of electrically semi-permeable regular n-polygon nano-holes with surface effects under far-field anti-plane mechanical loading and in-plane electric loading, were investigated. Based on the Gurtin-Murdoch surface model theory, the conformal mapping technique was adopted to analytically solve the stress and electric displacement fields, to obtain the analytical solutions for the stress intensity factor (SIF) and the electric displacement intensity factor (EDIF) at the crack tip. A new conformal mapping was constructed, from the exterior of s nano-cracks emanating from the regular n-polygon nano-hole to the interior of the circular nano-hole. The results indicate that, both the SIF and the EDIF are influenced by the coupling of far-field mechanical and electric loadings. Additionally, the smaller the side length of the regular n-polygon is, the more prominent the surface effect will be.
- piezoelectric material /
- semi-permeable /
- surface effect /
- nanoscale

HTML全文

图 1 压电材料中带s条纳米裂纹的正n边形纳米孔

Figure 1. Regular n-polygon nano-holes with s nano-cracks in piezoelectric materials

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图 2 保角映射(从z平面到ζ平面)

Figure 2. The conformal mapping (from plane z to plane ζ)

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图 3 K随a的变化

Figure 3. Variations of K with a

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图 4 K随τ₃₂^∞的变化

Figure 4. Variations of K with τ₃₂^∞

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图 5 K随D₂^∞的变化

注为了解释图中的颜色，读者可以参考本文的电子网页版本，后同.

Figure 5. Variations of K with D₂^∞

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图 6 K随lg(L/a)的变化

Figure 6. Variations of K with lg(L/a)

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图 7 K随n的变化

Figure 7. Variations of K with n

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图 8 K随s的变化

Figure 8. Variations of K with s

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A1 z平面

A1. A1 Plane z

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A2 z₁平面

A2. Plane z₁

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A3 z₁平面，0＜θ＜π/3

A3. Plane z₁, 0 < θ < π/3

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A4 z₂平面

A4. Plane z₂

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A5 z₃平面

A5. Plane z₃

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A6 z₄平面

A6. Plane z₄

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A7 z₅平面

A7. Plane z₅

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A8 z₆平面

A8. Plane z₆

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A9 ζ₁平面

A9. Plane ζ₁

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A10 ζ平面

A10. A10 Plane ζ

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