Hard protective overlayers on viscoelastic-plastic substrates

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 delta(1/2) and delta(3/2) respectively, where delta 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.