Abstract Cracking is a critical issue in the preparation and application of thermoelectric materials. Traditional models for thermoelectric fracture predict infinite electric current and heat flux at the crack tip. However, it is impossible since infinite electric current and heat cannot be sustained at the atomic level. To give a physically reasonable fracture prediction of thermoelectric materials, this paper proposes an analytical model of thermoelectric fracture based on the concept of electrical and thermal field saturation along a strip at the crack front, in which we assume the electric current and heat flux cannot exceed a saturation limit. Firstly, based on the complex variable method, we derive the thermoelectric field solutions with electrical and thermal field saturation at the crack tip. Then, the thermally induced stresses and the fracture criterions are given. The results show that the thermoelectric field predicted by the saturation model exhibits no singularity at the crack tip, which may give better agreement with the experimental observations and thus shows better application potential.

中文翻译：

---

热电材料的断裂：电热条饱和模型

摘要 裂解是热电材料制备和应用中的一个关键问题。传统的热电断裂模型预测裂纹尖端的无限电流和热通量。然而，这是不可能的，因为在原子水平上无法维持无限大的电流和热量。为了对热电材料进行物理上合理的断裂预测，本文提出了一种基于裂纹前沿带的电场和热场饱和的概念的热电断裂分析模型，其中我们假设电流和热通量不能超过饱和极限。首先，基于复变量法，推导出裂纹尖端电场和热场饱和的热电场解。然后，给出了热致应力和断裂准则。结果表明，饱和模型预测的热电场在裂纹尖端不表现出奇异性，这可能与实验观察结果更加吻合，从而显示出更好的应用潜力。