Dynamic Problems of Mode Ⅱ Cracks in 2D Octagonal Quasicrystals
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摘要: 依据准晶弹性流体动力学模型,采用有限差分方法,探讨了八次对称二维准晶Ⅱ型单边裂纹的动力学问题.首先分析了相同载荷的不同加载时间、不同的加载位置以及不同的试样尺寸对裂纹尖端处声子场应力强度因子的影响;其次分析了不同的声子场相位子场耦合弹性常数对相位子场位移分量的影响;最后分析了板端加载与裂纹面加载对动态应力强度因子的影响.计算结果表明:大小相同的脉冲载荷,加载的时间越长,无量纲化的应力强度因子越大,其曲线逐渐趋近于阶跃载荷下的曲线;试样宽度越宽,应力强度因子由零到非零需要的时间越长,无量纲化的应力强度因子值越小,说明应力强度因子与试样的尺寸有关系;声子场相位子场耦合弹性常数越大相位子场的位移分量也越大,这是因为相位子场的边界没有载荷,相位子场位移的作用力来自声子场,声子场起主导作用;而裂纹面加载和板端加载是不等价的,前者的无量纲化应力强度因子的变化幅度比后者大,这与板端加载更容易导致材料断裂的事实相一致.
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关键词:
- 弹性-流体动力学模型 /
- 有限差分格式 /
- Ⅱ型裂纹 /
- 应力强度因子
Abstract: Based on the elasto-hydrodynamic model, the dynamic problems of mode Ⅱ cracks in octagonal 2D quasicrystals were investigated with the finite difference scheme. The dynamic responses of stress intensity factors to different loading periods and different specimen sizes were analyzed, respectively. Then the influence of different phonon-phason coupling elastic constants on the displacement component of the phason field was demonstrated. The results indicate that, the stress intensity factor increases with the loading period, while the curve approaches the curve under the step load. The wider the specimen size is, the longer the time will be for the stress wave to reach the crack tip, and the smaller the stress intensity factor will be. The crack loading is different from the board loading, for the change of the stress intensity factor under the former is greater than that under the latter. With the increasing phonon-phason coupling constant, the displacement component of the phason field rises. Because of the influence of the phonon and phonon-phason coupling effect, the displacement component of the phason field equals zero when the phonon-phason coupling constant is zero. -
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