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一维六方准晶双材料中圆孔边共线界面裂纹的反平面问题

张炳彩 丁生虎 张来萍

张炳彩,丁生虎,张来萍. 一维六方准晶双材料中圆孔边共线界面裂纹的反平面问题 [J]. 应用数学和力学,2022,43(6):639-647 doi: 10.21656/1000-0887.420202
引用本文: 张炳彩,丁生虎,张来萍. 一维六方准晶双材料中圆孔边共线界面裂纹的反平面问题 [J]. 应用数学和力学,2022,43(6):639-647 doi: 10.21656/1000-0887.420202
ZHANG Bingcai, DING Shenghu, ZHANG Laiping. The Anti-Plane Problem of Collinear Interface Cracks Emanating From a Circular Hole in 1D Hexagonal Quasicrystal Bi-Materials[J]. Applied Mathematics and Mechanics. doi: 10.21656/1000-0887.420202
Citation: ZHANG Bingcai, DING Shenghu, ZHANG Laiping. The Anti-Plane Problem of Collinear Interface Cracks Emanating From a Circular Hole in 1D Hexagonal Quasicrystal Bi-Materials[J]. Applied Mathematics and Mechanics. doi: 10.21656/1000-0887.420202

一维六方准晶双材料中圆孔边共线界面裂纹的反平面问题

doi: 10.21656/1000-0887.420202
基金项目: 国家自然科学基金(11762016;11762017;12062021);宁夏自然科学基金(2022AAC03068);2019年宁夏一流基层教学组织项目(NXYLJCJXZ-21)
详细信息
    作者简介:

    张炳彩(1985—),女,讲师,硕士(E-mail:zbc850415@163.com

    丁生虎(1980—),男,教授,博士(通讯作者. E-mail:dshnx2019@nxu.edu.cn

  • 中图分类号: O341

The Anti-Plane Problem of Collinear Interface Cracks Emanating From a Circular Hole in 1D Hexagonal Quasicrystal Bi-Materials

  • 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。
  • 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  2  保角变换示意图

    Figure  2.  The diagram of conformal mapping

    图  3  不同的R, K$ {{{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} $, K$ {{{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  5  不同的R3, GH0的变化情形

    Figure  5.  For different R3 values, the change of G with H0

    图  6  不同的R3, G$ {{{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} $作用下, G$ {H_0} $的变化情形

    Figure  7.  For different $ {\tau _0} $ values, the change of G with $ {H_0} $

    表  1  两种不同一维六方准晶材料的参数取值[25, 30]

    Table  1.   Parameter values of 2 different 1D hexagonal quasicrystals[25, 30]

    parameter QC1QC2
    C44/GPa5035.5
    K2/GPa0.30.15
    R3/GPa 1.21.765
    下载: 导出CSV
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出版历程
  • 收稿日期:  2021-07-14
  • 录用日期:  2021-07-14
  • 修回日期:  2021-10-10
  • 网络出版日期:  2022-05-21

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