无限弹性基底上热电薄膜的屈曲行为研究
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摘要
本文研究了热电薄膜粘合到弹性基底结构的屈曲行为.将界面剪切应力和薄膜的轴向应力结合起来,建立了热电薄膜的计算模型,利用边界条件将所求问题转化为一个奇异积分方程.通过使用切比雪夫多项式展开求解奇异积分方程,得到归一化应力强度因子.确定了膜厚度和基材与膜刚度比对薄膜应力和界面应力强度因子的影响.讨论了薄膜长度和厚度比对薄膜应力和界面应力强度因子的影响.结果显示薄膜和基底之间的刚度比对薄膜的应力水平有着较明显的影响.
In this paper, the buckling behavior of thermoelectric thin film bonded to elastic substrates is studied. Combining the interface shear stress with the axial stress of the thin film, the calculation model of the thermoelectric thin film is established and the problem is transformed into a singular integral equation by using boundary conditions. The singular integral equation is separated by using Chebyshev polynomials, and the normalized stress intensity factors are obtained. The effects of film stress and interfacial stress intensity factors are determined by the film thickness and the stiffness ratio of substrate to film. The influence of the film length and the thickness ratio on film stress and interface stress intensity factors is discussed.The result shows that the stiffness ratio between the film and the substrate has a significant effect on the stress level of the film.
In this paper, the buckling behavior of thermoelectric thin film bonded to elastic substrates is studied. Combining the interface shear stress with the axial stress of the thin film, the calculation model of the thermoelectric thin film is established and the problem is transformed into a singular integral equation by using boundary conditions. The singular integral equation is separated by using Chebyshev polynomials, and the normalized stress intensity factors are obtained. The effects of film stress and interfacial stress intensity factors are determined by the film thickness and the stiffness ratio of substrate to film. The influence of the film length and the thickness ratio on film stress and interface stress intensity factors is discussed.The result shows that the stiffness ratio between the film and the substrate has a significant effect on the stress level of the film.
引文
[1]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
[2]Zhang A B,Wang B L.Temperature and electric potential fields of an interface crack in a layered thermoelectric or metal/thermoelectric material[J].International Journal of Thermal Sciences,2016,104(1):396-403
[3]Song H P,Gao C F,Li J.Two-dimensional problem of a crack in thermoelectric materials[J].Journal of Thermal Stresses,2015,38(3):325-337
[4]Zhang A B,Wang B L.Crack tip field in thermoelectric media[J].Theoretical and Applied Fracture Mechanics,2013,66(16):33-36
[5]Ding S H,Zhou Y T.Heat conduction in multilayered thermoelectric materials with multiple cracks[J].Acta Mechanica Solida Sinica,2018,31(4):512-522
[6]Ding S H,Liu Q N.A multi-layered model for heat conduction analysis of thermoelectric material strip[J].Computer Modeling in Engineering and Sciences,2018,114(3):335-349
[7]Hertz H.On the contact of elastic solids[J].Journal f¨ur die Reine und Angewandte Mathematik,1882,92(3):156-171
[8]Harding J W,Sneddon I N.The elastic stresses produced by the indentation of a plane surface of a semiinfinite elastic solid by a rigid punch[J].Mathematical Proceedings of the Cambridge Philosophical Society,1945,41(1):16-26
[9]Sneddon I N.Boussinesq’s problem for a flat-ended cylinder[J].Mathematical Proceedings of the Cambridge Philosophical Society,1946,42(1):29-39
[10]Sneddon I N.The relation between load and penetration in the axisymmetric Boussinesq problem for a punch of arbitrary profile[J].International Journal of Engineering Science,1965,3(1):47-57
[11]Mahajan R,Erdogan F,Chou Y T.The crack problem for an orthotropic half-plane stiffened by elastic films[J].International Journal of Engineering Science,1993,31(3):403-424
[12]Fabrikant V I.Elastic field around a circular punch[J].Journal of Applied Mechanics,1988,55(3):604-610
[13]Sosa H.Plane problems in piezoelectric media with defects[J].International Journal of Solids and Structures,1991,28(4):491-505
[14]Erdogan F,Civelek M B.Contact problem for an elastic reinforcement bonded to an elastic plate[J].Journal of Applied Mechanics,1974,41(4):1014-1018
[15]钟万勰.弹性接触问题的势能原理及其算法[J].计算力学学报,1985,2(1):25-33Zhong W X.The potential energy principle and its algorithm for elastic contact problems[J].Chinese Journal of Computational Mechanics,1985,2(1):25-33
[16]Yao D.In-plane MEMS Thermoelectric Microcooler[M].America:Lambert Academic Publishing,2010:90-91
[2]Zhang A B,Wang B L.Temperature and electric potential fields of an interface crack in a layered thermoelectric or metal/thermoelectric material[J].International Journal of Thermal Sciences,2016,104(1):396-403
[3]Song H P,Gao C F,Li J.Two-dimensional problem of a crack in thermoelectric materials[J].Journal of Thermal Stresses,2015,38(3):325-337
[4]Zhang A B,Wang B L.Crack tip field in thermoelectric media[J].Theoretical and Applied Fracture Mechanics,2013,66(16):33-36
[5]Ding S H,Zhou Y T.Heat conduction in multilayered thermoelectric materials with multiple cracks[J].Acta Mechanica Solida Sinica,2018,31(4):512-522
[6]Ding S H,Liu Q N.A multi-layered model for heat conduction analysis of thermoelectric material strip[J].Computer Modeling in Engineering and Sciences,2018,114(3):335-349
[7]Hertz H.On the contact of elastic solids[J].Journal f¨ur die Reine und Angewandte Mathematik,1882,92(3):156-171
[8]Harding J W,Sneddon I N.The elastic stresses produced by the indentation of a plane surface of a semiinfinite elastic solid by a rigid punch[J].Mathematical Proceedings of the Cambridge Philosophical Society,1945,41(1):16-26
[9]Sneddon I N.Boussinesq’s problem for a flat-ended cylinder[J].Mathematical Proceedings of the Cambridge Philosophical Society,1946,42(1):29-39
[10]Sneddon I N.The relation between load and penetration in the axisymmetric Boussinesq problem for a punch of arbitrary profile[J].International Journal of Engineering Science,1965,3(1):47-57
[11]Mahajan R,Erdogan F,Chou Y T.The crack problem for an orthotropic half-plane stiffened by elastic films[J].International Journal of Engineering Science,1993,31(3):403-424
[12]Fabrikant V I.Elastic field around a circular punch[J].Journal of Applied Mechanics,1988,55(3):604-610
[13]Sosa H.Plane problems in piezoelectric media with defects[J].International Journal of Solids and Structures,1991,28(4):491-505
[14]Erdogan F,Civelek M B.Contact problem for an elastic reinforcement bonded to an elastic plate[J].Journal of Applied Mechanics,1974,41(4):1014-1018
[15]钟万勰.弹性接触问题的势能原理及其算法[J].计算力学学报,1985,2(1):25-33Zhong W X.The potential energy principle and its algorithm for elastic contact problems[J].Chinese Journal of Computational Mechanics,1985,2(1):25-33
[16]Yao D.In-plane MEMS Thermoelectric Microcooler[M].America:Lambert Academic Publishing,2010:90-91