Roof Deformation and Collapse of Stamps With Isolated Grooves: A Contact Mechanics Approach

Abstract

This paper has revisited the roof deformation and collapse of stamps with isolated grooves based on a contact mechanics approach, with emphasis on establishing the nonadhesive and adhesive contact solutions for surfaces containing a shallow rectangular groove with the effects of applied load and interfacial adhesion taken into account. By solving singular integral equations and using the energy release rate approach, closed-form solutions are derived analytically for the deformed groove shapes, interfacial stress distributions, and equilibrium relations between load and contact size, which reduce to the previously proposed solutions without adhesion or without applied load. Finite element (FE) analysis is performed to validate the nonadhesion solutions, while experiment results of stamp collapse reported in the literature are adopted to examine the adhesion solutions. By introducing the Johnson parameter α to represent a competition between surface energy and elastic strain energy of the groove, four kinds of contact behaviors of the groove roof can be characterized appropriately: nonadhesion, weak adhesion, intermediate adhesion, and strong adhesion. Hysteresis loop and energy loss due to distinct load/unloading paths are revealed in the cases of intermediate and strong adhesion. We have also provided the critical applied pressure to achieve roof collapse and the corresponding equilibrium contact size for full range of α.