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.
Department of Civil, Environmental
and Architectural Engineering (DICAT)
and Research Center for Materials Science and Technology
(MaST)
University of Genova
Via Montallegro 1
16145 Genova
Italy
