Two-dimensional Green’s function for isotropic thermoelastic coating structure

• Published in: Zeitschrift für angewandte Mathematik und Physik 2021-12, Vol.72 (6), Article 199
• Main Authors: Tong, Jie, Su, Jiang, Liu, Ying-jie, Li, Qiu-hua
• Format: Article
• Language: English
• Subjects: Boundary conditions; Conduction heating; Conductive heat transfer; Engineering; Harmonic functions; Image acquisition; Interfacial stresses; Mathematical Methods in Physics; Method of images; Theoretical and Applied Mechanics; Thermal barrier coatings; Thermal stress
• ISSN: 0044-2275; 1420-9039
• DOI: 10.1007/s00033-021-01634-3

A two-dimensional Green’s function suitable for a coated isotropic thermoelastic semi-infinite plane with a line heat source above the surface has been obtained using the method of images. Firstly, based on the control equations of the isotropic thermoelastic materials and the two-dimensional heat conduction equations, the general solutions to three harmonic functions have been obtained. Secondly, six potential function equations have been acquired using the method of images. Finally, three equations that are expressed by three harmonic functions have been obtained by substituting six series of harmonic functions into the boundary conditions of the coated surface. In this way, nine recursive equations have been determined. By taking Green’s function of the isotropic semi-infinite thermoelastic plane with a line heat source above the surface as the first term, the thermoelastic coupling field for the coated semi-infinite plane has been calculated using the recursive formula. The interface temperature increment component and the interface stress components of the coating structures have been calculated numerically. By analyzing the thermal stress of different coated materials, valuable conclusions such as the interface effect, tensile failure, and shear delamination have been obtained, which can provide a reliable basis for the design and analysis of thermal barrier coating structures.