Volume 42 Issue 6
Jun.  2021
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ZHU Mingming, LI Lianhe. Fracture Mechanics Analysis of Thermoelectric Materials With Equilateral Triangle Holes[J]. Applied Mathematics and Mechanics, 2021, 42(6): 656-664. doi: 10.21656/1000-0887.410232
Citation: ZHU Mingming, LI Lianhe. Fracture Mechanics Analysis of Thermoelectric Materials With Equilateral Triangle Holes[J]. Applied Mathematics and Mechanics, 2021, 42(6): 656-664. doi: 10.21656/1000-0887.410232

Fracture Mechanics Analysis of Thermoelectric Materials With Equilateral Triangle Holes

doi: 10.21656/1000-0887.410232
Funds:

12002175)

The National Natural Science Foundation of China(11962026

  • Received Date: 2020-08-05
  • Rev Recd Date: 2021-01-18
  • The fracture mechanics for thermoelectric materials with equilateral triangle holes subjected to uniform electric current densities and uniform energy fluxes at infinity was studied by means of the complex variable method. The analytic expressions of temperature fields and stress fields were obtained under the boundary conditions of electric insulation and thermal insulation. Effects of the triangle size, the applied electric current density and the energy flux on the thermoelectric material were analyzed. The results show that, the variations of the current density and the triangle size have obvious influences on the annular energy flux, the annular stress and the annular heat flux.
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  • [2]SCHMIDT R D, CASE E D, GILES I I I J, et al. Room-temperature mechanical properties and slow crack growth behavior of Mg2Si thermoelectric materials[J]. Journal of Electronic Materials,2012,41: 1210-1216.
    GAO J L, DU Q G, ZHANG X D, et al. Thermal stress analysis and structure parameter selection for a Bi2Te3-based thermoelectric module[J]. Journal of Electronic Materials,2011, 40(5): 884-888.
    [3]ZHANG A B, WANG B L. Crack tip field in thermoelectric media[J]. Theoretical and Applied Fracture Mechanics,2013,66: 33-36.
    [4]SONG H P, GAO C F, LI J Y. Two-dimensional problem of a crack in thermoelectric materials[J]. Journal of Thermal Stresses,2015,38: 325-337.
    [5]YU C B, GAO C F. Analysis of a circular arc-crack in thermoelectric media[C]//National Doctoral Academic Forum on Aeronautical Science and Technology. Xi’an, 2016: 207-212.
    [6]SONG H P, SONG K. Electric and heat conductions across a crack in a thermoelectric material[J]. Journal of Theoretical and Applied Mechanics,2016,46(1): 83-98.
    [7]锁娟. 热电材料中共线裂纹问题的复变方法研究[D]. 硕士学位论文. 银川: 宁夏大学, 2018.(SUO Juan. Complex variable method of collinear cracks in thermoelectric materials[D]. Master Thesis. Yinchuan: Ningxia University, 2018.(in Chinese))
    [8]杜昕鲲, 丁生虎. 热电材料中含椭圆夹杂问题的精确解[J]. 数学的实践与认识, 2019,49(17): 213-218.(DU Xinkun, DING Shenghu. Exact solutions of elliptical inclusion in thermoelectric materials[J]. Mathematics in Practice and Theory,2019,49(17): 213-218.(in Chinese))
    [9]郭怀民. 带正三角形孔口的平面弹性问题的解析解[J]. 阴山学刊(自然科学版), 2009,23(1): 9-11.(GUO Huaimin. Analytic solutions for a finite plane with an equilateral triangle hole[J]. Yinshan Academic Journal (Natural Science),2009, 23(1): 9-11.(in Chinese))
    [10]王玮华, 郭俊宏, 邢永明. 压电弹性体中光滑顶点的正三角形孔边裂纹的反平面问题分析[J]. 复合材料学报, 2015,32(2): 601-607.(WANG Weihua, GUO Junhong, XING Yongming. Anti-plane problem analysis of edge crack emanating from regular triangle hole with smooth vertices in piezoelectroelastic solids[J]. Acta Materiae Compositae Sinica,2015,32(2): 601-607.(in Chinese))
    [11]王永健, 高存法. 含等边三角形孔孔边裂纹横观各向同性压电弹性体的反平面问题研究[J]. 应用力学学报, 2015,32(6): 973-979.(WANG Yongjian, GAO Cunfa. The anti-plane solution for the crackedequilateral triangle hole in transverse isotropic piezoelectric materials[J]. Chinese Journal of Applied Mechanics,2015,32(6): 973-979.(in Chinese))
    [12]肖俊华, 韩彬, 徐耀铃, 等. 考虑表面弹性效应时正三角形孔边裂纹反平面剪切问题的断裂力学分析[J]. 固体力学学报, 2017〖STHZ〗, 38(6): 530-536.(XIAO Junhua, HAN Bin, XU Yaoling, et al. Fracture analysis of cracked equilateral triangular hole with surface elasticcity effect under antiplane shear[J]. Chinese Journal of Solid Mechanics,2017,38(6): 530-536.(in Chinese))
    [13]樊世旺, 郭俊宏. 一维六方压电准晶三角形孔边裂纹反平面问题[J]. 应用力学学报, 2016,33(3): 421-426.(FAN Shiwang, GUO Junhong. Anti-plane problem of an edge crack emanating from a triangle hole in one-dimensional hexagonal piezoelectric quasicrystals[J]. Chinese Journal of Applied Mechanics,2016,33(3): 421-426.(in Chinese))
    [14]高媛媛, 刘官厅. 一维六方压电准晶中三角形孔边快速传播裂纹的解析解[J]. 数学的实践与认识, 2019,49(11): 206-213.(GAO Yuanyuan, LIU Guanting. Analytic solutions of a fast propagatingcrack from triangular hole in 1D hexagonal piezoelectric quasicrystals[J]. Mathematics in Practice and Theory,2019,49(11): 206-213.(in Chinese))
    [15]刘兴伟, 李星, 汪文帅. 一维六方压电准晶中正n边形孔边裂纹的反平面问题[J]. 应用数学和力学, 2020,41(7): 713-724.(LIU Xingwei, LI Xing, WANG Wenshuai. The anti-plane problem of regular n-polygon holes with radial edge cracks in 1D hexagonal piezoelectric quasicrystals[J]. Applied Mathematics and Mechanics,2020,41(7): 713-724.(in Chinese))
    [16] PEREZ-APARICIO J L, TAYLOR R L, GAVELA D. Finite element analysis of nonlinear fully coupled thermoelectric materials[J]. Computational Mechanics,2007,40: 35-45.
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