Impression creep of a viscous layer

Abstract

Impression creep of a flat-ended cylindrical punch pushed into a viscous layer overlaid on a rigid substrate is analyzed. The method developed here permits us to relate the impression velocity to the punching stress in terms of an auxiliary function, which represents the solution of a set of Fredholm integral equations with a continuous symmetrical kernel. By a series of numerical analysis, the influence of the boundary conditions and the effect of the thickness of the layer on the impression velocity are obtained. For infinite thickness (i.e., h/a →∞, where h is the thickness of the layer and a is the radius of the punch), the impression creep is independent of the stick or slip boundary condition at the indenter/layer interface. For finite thickness such as h/a = 20, the boundary conditions have about 5% effect on the impression velocity. For a thin film, the impressing velocity is very sensitive to the boundary conditions. In fact it suggests a possible experimental way to detect debonding at the interface between the thin film and the substrate.