A Mode-Ⅱ Griffith Crack in Decagonal Quasicrystals
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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。
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关键词:
- 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. -
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