Thermal stresses for a coated irregularly shaped hole embedded in an infinite substrate subject to a remote uniform heat flow

• Published in: Archive of applied mechanics (1991) Vol. 93; no. 6; pp. 2511 - 2531
• Main Authors: Liao, Yi-Lun, Tseng, Shao-Chen, Chao, Ching-Kong
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2023; Springer Nature B.V
• Subjects: Classical Mechanics; Conformal mapping; Engineering; Error correction; Exact solutions; Heat transfer; Heat transmission; Interfacial stresses; Mathematical analysis; Original; Shear modulus; Stress functions; Substrates; Tensile stress; Theoretical and Applied Mechanics; Thermal conductivity; Thermal expansion; Thermal stress; Trial and error methods; Trial-and-error method; Conformal mapping; Analytical continuation theorem; Coated polygonal hole
• ISSN: 0939-1533; 1432-0681
• DOI: 10.1007/s00419-023-02393-5

This article presents analytical solutions for a coated irregularly shaped void embedded in an infinite substrate subject to remote uniform heat flow. Both the temperature and stress functions are expressed in general form for composites based on conformal mapping, the analytic continuation theorem, and the alternation method. The iterations of the trial-and-error method were utilized to obtain the solution for the correction terms. The results show that a lower temperature gradient occurs on the adjacent matrix, which is caused by the coating layer with a higher thermal conductivity. Moreover, the interfacial stresses were significantly concentrated toward the shaper corner. The thermal expansion coefficient ratio between the coating and matrix has a greater influence on the interfacial stresses than the shear modulus or heat conductivity coefficient ratio. Meanwhile, the coatings produced interfacial tensile stress during the cooling stage, causing irregular voids to gradually increase at the interface.