The Anti-Plane Problem of Collinear Interface Cracks Emanating From a Circular Hole in 1D Hexagonal Quasicrystal Bi-Materials
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摘要: 研究了一维六方准晶双材料中圆孔边不对称共线界面裂纹的反平面问题。利用Stroh公式和复变函数方法得到了声子场和相位子场耦合作用下的复势函数，给出了裂纹尖端应力强度因子和能量释放率的解析表达式。通过数值算例，讨论了圆孔半径和裂纹长度对应力强度因子的影响，以及耦合系数、声子场应力和相位子场应力对能量释放率的影响。结果表明：当圆孔半径不变时，应力强度因子随右裂纹长度的增大趋向稳定值。当相位子场应力取一定值时，能量释放率达到最小值，说明特定的相位子场应力可以抑制裂纹的扩展。Abstract: The anti-plane problem of asymmetric collinear interface cracks emanating from a circular hole in 1D hexagonal quasicrystal bi-materials was studied. With the Stroh formula and the complex function method, the complex potential functions under the coupling action of the phonon field and the phason field were obtained. The analytical expressions of the stress intensity factor (SIF) and the energy release rate (ERR) at the crack tip were given. The effects of the circular hole radius and the crack length on the SIF, and the effects of the coupling coefficient, the phonon field stress and the phason field stress on the ERR, were discussed. The results show that, the SIF tends to be stable with the increase of the right crack length for a constant circular hole radius. For a certain phason field stress value, the ERR reaches the minimum value, which indicates that a specific phason field stress can inhibit the crack growth.
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Key words:
- quasicrystal bi-material /
- circular hole /
- interface crack /
- complex function method
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图 1 含圆孔孔边界面裂纹的一维六方准晶双材料
Figure 1. One dimensional hexagonal quasicrystal bi-materials with interface cracks emanating from a circular hole
图 3 不同的R, K随
$ {{{L_1}} / R} $ 的变化情形Figure 3. For different R values, the change of K with
$ {{{L_1}} /R} $ 
图 4 不同
$ {{{L_2}}/ R} $ , K随$ {{{L_1}} /R} $ 的变化情形Figure 4. For different
$ {{{L_2}} / R} $ values, the change of K with$ {{{L_1}} /R} $ 
图 6 不同的R3, G随
$ {{{L_1}}/ R} $ 的变化情形Figure 6. For different R3 values, the change of G with
$ {{{L_1}}/R} $ 
图 7 不同
$ {\tau _0} $ 作用下, G随$ {H_0} $ 的变化情形Figure 7. For different
$ {\tau _0} $ values, the change of G with$ {H_0} $ -
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