表面效应对热电材料中纳米孔周围热应力的影响

赵婕燕; 杨海兵

doi:10.21656/1000-0887.440151

表面效应对热电材料中纳米孔周围热应力的影响

doi: 10.21656/1000-0887.440151

赵婕燕^1,,
杨海兵^2, ,

1.
华南理工大学土木与交通学院，广州 510641
2.
河海大学力学与材料学院，南京 211100

基金项目:

国家自然科学基金项目 11902116

广东省自然科学基金项目 2022A1515011773

详细信息

作者简介:
赵婕燕(1998—)，女，硕士生(E-mail: 18768174161@163.com)

通讯作者:
杨海兵(1988—)，男，讲师，博士(通讯作者. E-mail: yanghb@scut.edu.cn)

中图分类号: TB332;O39
计量
- 文章访问数: 217
- HTML全文浏览量: 72
- PDF下载量: 43
- 被引次数: 0
出版历程
- 收稿日期: 2023-05-15
- 修回日期: 2023-06-15
- 刊出日期: 2023-11-01

Surface Effects on Thermal Stresses Around the Nanohole in Thermoelectric Material

ZHAO Jieyan^1
,,
YANG Haibing^{2
, ,}

1.
School of Civil Engineering and Transportation, South China University of Technology, Guangzhou 510641, P.R.China
2.
College of Mechanics and Materials, Hohai University, Nanjing 211100, P.R.China

摘要

摘要: 基于完整Gurtin-Murdoch(G-M)低阶表面能模型，进一步探讨了纳米尺度下表面效应的影响. 建立了合理考虑构型变化的应力边界条件，实现了研究尺度从宏观到微观的转变. 利用复变函数理论和保角映射技术，构建了用于纳米尺度下的热-电-力理论框架模型，得到了热电基体中纳米孔周围热场、温度场以及应力场的半解析解. 数值结果表明，相对于完整G-M模型，简化G-M模型(忽略孔洞构型变化的影响)往往会高估表面效应和远场热电载荷对热应力分布的影响. 此外，表面效应的存在将在一定程度上缓解纳米孔周围的热应力集中.
- 热电材料 /
- 完整Gurtin-Murdoch模型 /
- 表面效应 /
- 复变函数理论 /
- 纳米孔
Abstract: Based on the complete Gurtin-Murdoch (G-M) low-order surface energy model, the surface effects at nanoscale were further explored. The transition from macroscale to microscale was achieved through construction of reasonable stress boundary conditions in view of the change of hole geometry configuration. With the series expansion techniques and complex variable methods, the semi-analytic solutions for the electric field, the temperature field, and the full stress field in the vicinity of the nanohole within the thermoelectric matrix were derived eventually with a built thermal-electrical-force theoretical framework model at nanoscale. Numerical results show that, compared with the complete G-M model, the simplified G-M model (neglecting the effects of nanohole geometry changes) would overestimate the surface effects and far-field thermoelectric loading effects on the thermal stress distributions. In addition, the surface effects can relieve the thermal stress concentration around the nanohole to some extent.
- thermoelectric material /
- complete Gurtin-Murdoch model /
- surface effect /
- complex function theory /
- nanohole

HTML全文

图 1 包含纳米孔的无限大热电基体

Figure 1. The infinite thermoelectric matrix with a nanohole

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图 2 微观尺度下，本文工作与前人工作的比较

Figure 2. Comparison of this work with previous work at microscale

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图 3 表面张力对圆孔周围环向热应力的影响

Figure 3. Effects of surface tensions on hoop thermal stresses around the circular hole

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图 4 环向热应力随表面张力的线性变化

Figure 4. Linear variations of hoop thermal stresses with the surface tension

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图 5 纳米孔周围的环向热应力

Figure 5. Hoop thermal stresses around the nanohole

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图 6 孔周残余应力分布

Figure 6. The residual hoop stress distributions around the nanohole

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图 7 表面张力的引入对环向热应力和由热电外载引起的环向热应力的影响

Figure 7. The influences of the surface tension on the hoop thermal stress and the hoop thermal stress induced by thermoelectric external loading

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图 8 表面效应对由热电外载引起的环向热应力的影响

Figure 8. The surface effects on the hoop thermal stress induced by thermoelectric external loading

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表 1 Bi₂Te₃和PbTe的材料性能

Table 1. Properties of the Bi₂Te₃ material and the PbTe material

	δ/(S/m)	E/GPa	ε/(V/K)	κ/(W/(m·K))	λ/K^-1	ν
Bi₂Te₃	1.1×10⁵	47	2×10^－4	1.6	2.7×10^－5	0.4
PbTe	1×10⁴	58	3×10^－4	1.5	2×10^－5	0.29

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表 2 不同表面弹性与表面张力共同作用下的环向应力值(单位：MPa)

Table 2. Hoop stresses under the combined actions of different surface elasticities and surface tensions (unit: MPa)

surface elasticity γ/(N/m)	δ_tt/MPa
surface elasticity γ/(N/m)	τ_s=0.2 N/m	τ_s=0.6 N/m	τ_s=1.0 N/m
0	138.587 0	136.587 0	134.587 0
0.2	138.573 3	136.573 3	134.573 4
0.6	138.545 8	136.546 0	134.546 1
1.0	138.518 3	136.518 6	134.518 9

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