This paper investigates two axisymmetric thermoelastic contact problems of functionally graded materials (FGMs) with arbitrarily varying material properties. A rigid, insulated spherical punch slides/rotates on the surface of the FGM coating at a constant velocity. The primary novelty of this study lies in developing a comprehensive semi-analytical framework capable of evaluating the complex thermoelastic behaviors of FGM coatings with arbitrarily varying properties under both sliding and rotating frictional heating conditions. It is assumed that there is no coupling between the tangential stress and the normal stress, but the tangential stress on the surface cannot be ignored. The frictional heating is generated in the contact region by a sliding/rotating spherical punch. A homogeneous multi-layered model is employed to simulate the thermoelastic properties of FGM coatings. By making use of the transfer matrix method and the Hankel integral transform, the two axisymmetric thermoelastic problems are reduced to Cauchy singular integral equations, which are then numerically solved to obtain the normal contact stress, radial stress and surface temperature. The key findings demonstrate that (1) tailoring the coating gradient index and gradient type can effectively mitigate thermal stress concentrations under these frictional heating modes; (2) higher sliding or angular velocities significantly amplify the thermoelastic effects, leading to elevated surface temperatures and radial tensile stresses; and (3) the proposed arbitrary gradient model provides a more flexible and accurate tool for optimizing FGM coatings against surface failure in extreme thermal-mechanical environments.
Liu et al. (Sun,) studied this question.