Elastic solution in a functionally graded coating subjected to a concentrated force

Functionally graded materials are currently being actively explored in coating design to reduce the mismatch of thermomechanical properties at the interface and thus increase the resistance of coatings to fracture mechanisms. Many established and potential applications of graded materials involve contact or impact problems that are primarily load transfer problems; consequently, the goal is to study basic elasticity problems for graded inhomogeneous solids. Here we study the three-dimensional elastic deformation of a graded coating subjected to a point load on the free surface, deposited on a homogeneous elastic half-space. By assuming an isotropic coating for which Young’s modulus depends exponentially on the thickness and Poisson’s ratio is constant, the elastic solution is obtained using Plevako’s representation, which reduces the problem to the construction of a potential function satisfying a linear fourth-order partial differential equation. We explicitly obtain the elastic solution for the coating and the substrate for two different interface conditions: the frictionless case and the perfectly bonded case. A comparative study of FGMs and homogeneous coatings is presented to investigate the effect of the graded coating properties.