Impression creep of a viscous layer
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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.
I. INTRODUCTION
II. BASIC MODEL
The understanding of plastic deformation processes in thin films and between different materials adhered together requires advanced experimental techniques to examine the mechanical properties in a controlled manner. There are extensive studies on the improvements of experimental capabilities to obtain mechanical information of materials.1–10 Among these improvements, the impression creep test is one of the most successful because of its simplicity and capability to obtain local behavior from a small volume of material. 1 This method has been successfully applied to metals, ionic crystals, molecular crystals, and polymers. Using a viscous-flow model, Yang and Li11 analyzed the impression creep of a semi-infinite medium by using a flatended cylindrical punch. An important conclusion is that the impressing velocity is independent of the slip or stick boundary conditions between the punch and the medium. Recently, their analyses were confirmed by an impression creep test on an acrylonitrile-butadiere-styrene (ABS) polymer at temperatures below and above its glass transition temperature.12 However although the effect of the thickness of the specimen was examined experimentally, it was not shown analytically. So the purpose of this paper is to study the impression creep of a flat-ended cylindrical punch pushed onto a layer of material which deforms by viscous flow. The paper focuses on relating the force to the impressing velocity as a function of layer thickness for different boundary conditions (stick or slip) between the punch and the layer and between the layer and the substrate.
As shown schematically in Fig. 1, a flat-ended cylindrical punch is pushed at constant velocity into an incompressible, viscous layer. This layer is overlaid on a rigid substrate. The equation of motion is governed by
J. Mater. Res., Vol. 16, No. 9, Sep 2001
http://journals.cambridge.org
Downloaded: 18 Mar 2015
ⵜ2V = ⵜp , ⵜ⭈V=0 ,
(1) (2)
where V is the
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