平面十次对称准晶中Ⅱ型Griffith裂纹的求解

郭玉翠; 范天佑

平面十次对称准晶中Ⅱ型Griffith裂纹的求解

郭玉翠¹,
范天佑²

1.
北京邮电大学基础科学部, 北京, 100088;
2.
北京理工大学材料科学研究中心, 北京, 100081

详细信息

作者简介:
郭玉翠(1962- ),女,辽宁锦州人,副教授,博士.

中图分类号: O346.1
计量
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- 被引次数: 0
出版历程
- 收稿日期: 1999-02-08
- 修回日期: 2001-07-13
- 刊出日期: 2001-11-15

A Mode-Ⅱ Griffith Crack in Decagonal Quasicrystals

GUO Yu-cui¹,
FAN Tian-you²

1.
Basic Science Department, Beijing University of Post and Telecommunications, Beijing 100088, P R China;
2.
Research Center of Material Science, Beijing Institute of Technology, Beijing 100081, P R China

摘要

摘要: 应用应力函数法,求解了二维十次对称准晶中的Ⅱ型Griffith裂纹问题。特点是把二维准晶的弹性力学问题分解成一个平面应变问题与一个反平面问题的叠加,通过引入应力函数,把平面应变问题的十八个弹性力学基本方程简化成一个八阶偏微分方程,并且求出了其在Ⅱ型Griffith裂纹情况的混合边值问题的解,所有的应力分量和位移分量都用初等函数表示出来,并且由此得出了准晶中Ⅱ型Griffith裂纹问题的应力强度因子和能量释放率。
- 二维准晶 /
- Ⅱ型Griffith裂纹 /
- 应力函数 /
- 应力强度因子 /
- 应变能释放率
Abstract: By using the method of stress functions,the problem of mode-Ⅱ Griffith crack in decagonal quasicrystals was solved.First,the crack problem of two-dimensional quasicrystals was decomposed into a plane strain state problem superposed on anti-plane state problem and secondly,by introducing stress functions,the 18 basic elasticity equations on coupling phonon-phason field of decagonal quasicrystals were reduced to a single higher-order partial differential equations.The solution of this equation under mixed boundary conditions of mode-Ⅱ Griffith crack was obtained in terms of Fourier transform and dual integral equations methods.All components of stresses and displacements can be expressed by elemental functions and the stress intensity factor and the strain energy release rate were determined.
- two-dimensional quasicrystal /
- model-Ⅱ Griffith crack /
- stress function /
- stress intensity factor /
- strain energy release rate

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参考文献(5)

[1]	胡承正,扬文革,王仁卉,等. 准晶的对称性和物理性质[J]. 物理学进展,1997,17(4):345-375.
[2]	DING Di-hua, YANG Wen-ge, HU Cheng-zheng, et al. Generalized elasticity theory of quasicrystals[J]. Phys Rev B,1993,48(10):7003-7010.
[3]	范天佑. 断裂力学基础[M]. 南京: 江苏科学技术出版社,1978.
[4]	范天佑,郭玉翠. 平面五次对称准晶中一类混合边值问题的交替解法和直接积分法[J]. 中国科学(A),1997,27(6):553-565.
[5]	郭玉翠,范天佑. 平面五次对称准晶的应力强度因子[J]. 北京邮电大学学报,1998,21(4):62-65.