This paper presents an analytical solution of a coated square hole embedded in an isotropic infinite plate under a remote uniform heat flow. Based on conformal mapping, analytic continuation theorem and the alternation technique, temperature and stress functions are derived in a compact series form. Results of temperature contours and interfacial stresses are validated using the finite element method. The comparison indicates the high accuracy of the proposed method. Numerical results of both the interfacial normal and shear stresses for different properties and geometric parameters of a coated layer are provided in a graphical form. The results indicate that the interfacial stresses are highly dependent on the thermal expansion coefficient, thickness of the coating layer and shape factor of the coated square hole. In conclusion, the interfacial shear stresses exhibit a significant increase at the corners with abrupt geometrical changes, which would cause the delamination of the coating layer system. Furthermore, increasing the thickness of the coating layer and the shape factor results in a higher interfacial stress.

中文翻译：

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远程均匀热流引起的涂层方孔的界面应力

本文提出了在远程均匀热流下嵌入各向同性无限板中的涂层方孔的解析解。基于共形映射、解析延拓定理和交替技术，以紧级数形式导出温度和应力函数。使用有限元方法验证温度等值线和界面应力的结果。比较表明所提出的方法的准确性很高。涂层的不同性质和几何参数的界面法向应力和剪切应力的数值结果以图形形式提供。结果表明，界面应力高度依赖于涂层方孔的热膨胀系数、涂层厚度和形状因子。综上所述，界面剪切应力在拐角处随着几何形状的突然变化而显着增加，这将导致涂层系统的分层。此外，增加涂层的厚度和形状因子会导致更高的界面应力。