The work is devoted to modelling thermal fracture of functionally graded coatings which are used in different engineering applications to protect metallic or composite components from extremely high temperatures. For this purpose a semi-infinite plate made of a functionally graded material (FGM) layer on a homogeneous semi-infinite substrate is considered and it is supposed that a system of arbitrary inclined cracks is located in the FGM; the FGM properties are described by a continues function. The heat conduction problem with special thermal boundary conditions for cracks with thermally permeable surfaces has been formulated by means of the singular integral equation technique. Solution methods (numerical for a more general case and asymptotic for some special cases) of the obtained equations are presented. The thermal solution is used to evaluate the effect of crack locations and orientations and its interaction with the influence of non-homogeneity parameter of thermal conductivity on the thermal flux intensity factors in the vicinity of cracks.
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