Elastic and viscoelastic contact mechanics of coating/substrate composites in axisymmetric indentation

Indentation contact mechanics of coating/substrate composites is addressed in elastic and viscoelastic regimes. An analytical solution for the elastic Boussinesq problems is examined first using an appropriate contact pressure distribution. The analytical expression for the elastic modulus E-eff of layered composites is then converted to the corresponding stress relaxation modulus Y-eff(t) using the correspondence principle of linear elastic and linear viscoelastic deformations. Several numerical simulations for the stress relaxation behaviour of layered composites, i.e., a viscoelastic coating on an elastic substrate, an elastic coating on a viscoelastic substrate, etc., are demonstrated to obtain rheological insights into the contact behaviour of coating/substrate composites for flat-ended cylindrical indentation. The assumptions and approximations included in the theoretical considerations are carefully addressed. The viscous squeezing flow, in a thin coating film, out of the geometrically constrained space beneath the indenter is also examined.