Abstract Thermoelectric materials and devices have wide applications in micro/nano-structured materials and structures. Under the time-varying thermal loadings, the thermoelectric devices can failure by fatigue accumulation. Fatigue crack propagations at the interface of the thermoelectric pn-junction and at the interface between the thermoelectric layer and the elastic substrate are analyzed in this paper. Influence of the temperature dependence of material properties on the fatigue life is discussed. The fatigue crack is more prone to propagation at the interface between thermoelectric layer and substrate rather than at the interface of the thermoelectric pn-junction. The fatigue life gradually increases to a constant with the external electrical resistance. Fatigue lives of the thermoelectric devices with temperature-dependent material properties are much shorter than those with constant material properties. A simplified but useful expression of the fatigue life as functions of the thermal loadings and the crack length is presented.

中文翻译：

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结合在弹性衬底上的热电 pn 结疲劳裂纹扩展的理论模型

摘要 热电材料和器件在微/纳米结构材料和结构中有着广泛的应用。在随时间变化的热载荷下，热电装置会因疲劳累积而失效。分析了热电pn结界面和热电层与弹性基板界面的疲劳裂纹扩展。讨论了材料特性的温度依赖性对疲劳寿命的影响。疲劳裂纹更容易在热电层和基板之间的界面处而不是在热电 pn 结的界面处扩展。随着外部电阻的增加，疲劳寿命逐渐增加到一个常数。具有温度相关材料特性的热电器件的疲劳寿命比具有恒定材料特性的热电器件的疲劳寿命短得多。疲劳寿命的简化但有用的表达式作为热载荷和裂纹长度的函数。