Fretting contact problem of functionally graded piezoelectric material (FGPM) coating bonded to the piezoelectric substrate under the rigid conducting indenter is considered. The laminated model is used to simulate the nonhomogeneous piezoelectric coating with electromechanical properties varying arbitrarily along the thickness direction. The spherical indenter is applied under the normal force and cyclic torque to generate the slip and stick region on the surface of FGPM coating. The problem was described mathematically according to the singular integral equations which are transferred to a system of linear equations by employing the numerical method. The stress distribution, the stick/slip region, torsion angle, surface displacement, and electrical displacement are obtained for different gradient value of FGPM coating under the cyclic torque loading. The present results will provide the theoretical basis for the design to FGPM coating.

The contact problem with adhesion for a functionally graded coated half-space indented by a rigid spherical punch is considered. The whole contact region is stick assuming the interfacial friction sufficient to prevent any slip taking place between the indenter and the coated half-space. The linear multi-layered model is used to model functionally graded materials with arbitrarily varying shear modulus and constant Poisson’s ratio under axisymmetric loads. By using the transfer matrix method and Hankel integral transform technique, the problem is reduced to a set of Cauchy singular integral equations. An iterative method is developed to numerically solve singular integral equations. The contact stress and indentation are calculated for different variations in elastic modulus. It is found that appropriate gradual variation in the shear modulus can improve the resistance to contact damage at the contact surfaces.

This paper deals with the contact problem for a coating-graded layer-substrate structure subjected to a rigid spherical punch on its surface. The coating and substrate are homogeneous materials with the different shear modulus. It is assumed that the shear modulus of the graded interfacial layer varies as exponential function along the thickness direction. The contact problem of a coating-graded layer-substrate structure is reduced to a singular integral equation with the method of Hankel integral transform. The stress components in the coating-graded layer-substrate structure are calculated by solving the equation numerically. The results show that the stiffness ratio has a significant effect on the stress components.

Axisymmetric indentation problem of a rigid perfect electrical insulator indenter on a functionally graded piezoelectric coating bonded to a piezoelectric substrate is investigated. The electromechanical properties of the functionally graded piezoelectric coating are assumed to vary as an exponential function along the thickness direction. The technique of the Hankel integral transform is applied to reduce the indentation problem to a singular integral equation. The numerical methods are developed and applied to compute the contact pressure for a cylindrical indenter and a spherical indenter. The effects of the material property gradient on the contact pressure, contact region, indentation depth, and electrical potential are analyzed. The numerical results are also obtained for the indentation responses of three different piezoelectric substrates.