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一维六方准晶非周期平面内中心开口裂纹的平面热弹性问题

赵雪芬 卢绍楠 马园园 张保文

赵雪芬, 卢绍楠, 马园园, 张保文. 一维六方准晶非周期平面内中心开口裂纹的平面热弹性问题[J]. 应用数学和力学, 2024, 45(3): 303-317. doi: 10.21656/1000-0887.440302
引用本文: 赵雪芬, 卢绍楠, 马园园, 张保文. 一维六方准晶非周期平面内中心开口裂纹的平面热弹性问题[J]. 应用数学和力学, 2024, 45(3): 303-317. doi: 10.21656/1000-0887.440302
ZHAO Xuefen, LU Shaonan, MA Yuanyuan, ZHANG Baowen. The Plane Thermoelastic Problem of a Central Opening Crack in the 1D Hexagonal Quasicrystal Non-Periodic Plane[J]. Applied Mathematics and Mechanics, 2024, 45(3): 303-317. doi: 10.21656/1000-0887.440302
Citation: ZHAO Xuefen, LU Shaonan, MA Yuanyuan, ZHANG Baowen. The Plane Thermoelastic Problem of a Central Opening Crack in the 1D Hexagonal Quasicrystal Non-Periodic Plane[J]. Applied Mathematics and Mechanics, 2024, 45(3): 303-317. doi: 10.21656/1000-0887.440302

一维六方准晶非周期平面内中心开口裂纹的平面热弹性问题

doi: 10.21656/1000-0887.440302
基金项目: 

国家自然科学基金 12062021

国家自然科学基金 62062057

国家自然科学基金 12262033

国家自然科学基金 12062022

详细信息
    通讯作者:

    赵雪芬(1983—), 女, 副教授, 博士, 硕士生导师(通讯作者. E-mail: snownfen@163.com)

  • 中图分类号: O343.8

The Plane Thermoelastic Problem of a Central Opening Crack in the 1D Hexagonal Quasicrystal Non-Periodic Plane

  • 摘要: 考虑裂纹内部介质的热传导率, 研究了一维六方准晶非周期平面内含中心开口裂纹的平面热弹性问题. 利用Fourier积分变换技术, 得到了热应力、裂纹尖端处的热应力强度因子和应变能密度因子的封闭解. 数值结果讨论了裂纹内部介质的热传导率、外载荷及声子场-相位子场耦合系数对热应力强度因子和应变能密度因子的影响. 结果表明, 声子场-相位子场耦合系数对裂纹扩展影响较大. 当声子场载荷较小或热流密度较大时, 裂纹不易扩展,热流密度在裂纹尖端处会出现集中热效应. 随着裂纹内部介质热传导率的增大, 热流密度逐渐增加而热应力强度因子逐渐减小. 该文所得结果为准晶热力学性质的实际应用提供了理论依据, 进而可用于优化准晶元器件的设计和制备.
  • 图  1  均匀的热流密度q0和外载荷σ0, h0作用下的中心开口裂纹

    Figure  1.  A central opening crack under uniform heat flux density q0 and stress σ0, h0

    图  2  qc/q0, Kσ/Kσmλc/λzσ0的变化趋势

    Figure  2.  Variations of qc/q0, Kσ/Kσm with λc/λz and σ0

    图  3  qc/q0, Kσ/KσmKH/KHmλc/λz的变化趋势

    Figure  3.  Variations of qc/q0, Kσ/Kσm and KH/KHm with λc/λz

    图  4  qc/q0, Kσ/KσmKH/KHmσ0的变化趋势

    Figure  4.  Variations of qc/q0, Kσ/Kσm and KH/KHm with σ0

    图  5  Kσ/Kσmq0变化

    Figure  5.  Variations of Kσ/Kσm with q0

    图  6  KH/KHmq0变化

       为了解释图中的颜色,读者可以参考本文的电子网页版本,后同.

    Figure  6.  Variations of KH/KHm with q0

    图  7  q0不同时, S/Smσ0变化

    Figure  7.  Variations of S/Sm with σ0 for different q0 values

    图  8  z不同时, qz/q0x变化

    Figure  8.  Variations of qz/q0 with x for different z values

    图  9  qz/q0xOz面上的变化趋势

    Figure  9.  Variations of qz/q0 on plane xOz

    表  1  一维六方压电准晶体弹性常数[15]

    Table  1.   1D hexagonal piezoelectric quasicrystal elastic constants[15]

    C11/GPa C12/GPa C13/GPa C33/GPa C44/GPa K1/GPa K2/GPa
    150 55 45 90 50 0.084 0.036
    R1/GPa R2/GPa R3/GPa β1/(MPa/K) β3/(MPa/K) λx/(W/(m·K)) λz/(W/(m·K))
    -1.68 1.2 1.2 1.798 1.383 12.4 12.4
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出版历程
  • 收稿日期:  2023-10-10
  • 修回日期:  2023-11-14
  • 刊出日期:  2024-03-01

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