Abstract In this manuscript, the interface crack problem is investigated for a functionally graded coating-substrate structure under steady heat flux. The general thermal-elastic properties of the functionally graded material (FGM) coating are considered. A piecewise-exponential model (PE model) is developed for the thermal fracture problem. In the PE model, the piecewise-exponential function is used to approach the generally continuous variation of coating’s material properties, including shear modulus, thermal conductivity and thermal expansion coefficient, and then the problem is turned into solving three singular integral equations after a series of mathematical manipulation. The thermal insulation coefficient of the crack is considered, which can indicate the influence of the crack on the heat flux. With the present PE model, the mixed-mode thermal stress intensity factors (TSIFs) are obtained for the crack problem of FGMs with general thermal-elastic property distributions. After analyzing the calculation results, the influences of the thermal-elastic property distributions of the FGM coating and the geometric parameters of the structure on the thermal stresses and the mixed-mode TSIFs are discussed comprehensively. The present study can provide a method for the fracture behavior evaluation and the design of FGM coating-substrate structures.

中文翻译：

---

具有一般涂层特性的功能梯度涂层-基材结构在稳定热通量下的界面裂纹问题

摘要 在本手稿中，研究了稳定热通量下功能梯度涂层-基材结构的界面裂纹问题。考虑了功能梯度材料 (FGM) 涂层的一般热弹性特性。针对热断裂问题开发了分段指数模型（PE 模型）。在PE模型中，利用分段指数函数来逼近涂层材料特性的一般连续变化，包括剪切模量、热导率和热膨胀系数，然后经过一系列的求解，问题转化为求解三个奇异积分方程。数学运算。考虑裂纹的绝热系数，可以表示裂纹对热通量的影响。用现在的 PE 模型，针对具有一般热弹性特性分布的 FGM 的裂纹问题，获得了混合模式热应力强度因子 (TSIF)。通过对计算结果的分析，综合讨论了FGM涂层的热弹性分布和结构几何参数对热应力和混合模式TSIF的影响。本研究可为断裂行为评估和 FGM 涂层-基材结构的设计提供一种方法。综合讨论了FGM涂层的热弹性分布和结构几何参数对热应力和混合模式TSIF的影响。本研究可为断裂行为评估和 FGM 涂层-基材结构的设计提供一种方法。综合讨论了FGM涂层的热弹性分布和结构几何参数对热应力和混合模式TSIF的影响。本研究可为断裂行为评估和 FGM 涂层-基材结构的设计提供一种方法。