Elastic shakedown analysis of two-dimensional thermo-elastic rolling/sliding contact for a functionally graded coating/substrate structure with arbitrarily varying thermo-elastic properties

The elastic shakedown analysis of rolling/sliding contact with friction heat is essential for the safety evaluation of tribological components with a functionally graded (FG) coating. However, the corresponding works are still lacking due to the complexity of thermo-elastic contact stress calculation and residual stress optimization induced by the non-homogeneity of material properties. An effective multi-layered model for the thermo-elastic rolling/sliding contact of two similar elastic cylinders with the FG coating involving arbitrarily distributed thermo-elastic properties is established, and the corresponding thermo-elastic stress field is obtained subsequently by using the conjugate gradient method and fast Fourier transform algorithm. Then, a specific bisection iteration procedure is applied to evaluate the elastic shakedown limit (ESL), and the effects of friction coefficient, rolling speed, distribution gradient indexes of various thermo-mechanical properties, and FG coating thickness on the ESL are discussed, respectively. The results show that the increases of friction coefficient and rolling speed can cause the decrease of ESL, the ESL can be improved significantly by adjusting the distribution gradients of shear modulus and yield stress appropriately, and the relations between the ESL and various heat conduction parameters show a strong dependence on the sliding velocity.