Hard protective overlayers on viscoelastic-plastic substrates

Abstract

A simple superposition solution for a point-loaded elastic plate on a soft substrate is proposed. The solution considers a “drumhead” being elastically bent into a compliant substrate that is viscoelastic-plastic. With simplifying assumptions it is found that the drumhead and substrate support loads proportional to δ^1/2 and δ^3/2, respectively, where δ is the vertical point displacement. At fixed displacement, relaxation proceeds at high loads, but if sufficiently unloaded, recovery or increased load results with time. Qualitative verification of the time-dependent drumhead solution is shown by relaxation and recovery data on polycarbonate covered by polysiloxane, composite or diamondlike carbon (DLC) coatings, and films.