Elastic Shakedown Analysis of Graded Coatings in Lubricated Contact Considering Interfacial Strength

Abstract Functionally graded coatings are increasingly employed to alleviate interfacial stress concentrations and enhance surface durability. However, the elastic shakedown behavior of graded coating–substrate systems under lubricated conditions remains insufficiently understood, particularly when constrained by limited interfacial strength. To address this gap, a three-dimensional numerical model is developed for graded coatings in lubricated line contacts. The framework integrates a mixed-lubrication solver with a semi-analytical model based on the discrete convolution-fast Fourier transform algorithm and influence coefficients summation. The elastic shakedown limit is determined via Melan's static theorem coupled with a bisection iteration scheme. Numerical results indicate that increasing the coating stiffness and optimizing the gradient index effectively enhance the shakedown limit, whereas the improvement is strongly thickness-dependent. Conversely, weak interfacial adhesion significantly reduces the load-bearing capacity, acting as a primary failure trigger. Furthermore, higher entrainment speeds are found to decrease the shakedown limit and shift the critical failure location toward the surface. These findings offer theoretical guidance for the design of graded coatings in heavy-duty lubricated systems.