Effect of Tabor parameter on hysteresis losses during adhesive contact.pdfVIP

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Effect of Tabor parameter on hysteresis losses during adhesive contact.pdf

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Effect of Tabor parameter on hysteresis losses during adhesive contact.pdf

J. Mech. Phys. Solids 98 (2017) 236–244 Contents lists available at ScienceDirect Journal of the Mechanics and Physics of Solids journal homepage: /locate/jmps E?ect of Tabor parameter on hysteresis losses during adhesive contact M. Ciavarellaa, J.A. Greenwoodb, J.R. Barberc,? a CEMEC-Politecnico di Bari, 70125 Bari, Italy b Department of Engineering, University of Cambridge,Cambridge CB2 1PZ, UK c Department of Mechanical Engineering, University of Michigan,Ann Arbor, MI 48109-2125, USA cross ARTICLE INFO Keywords: Contact mechanics Hysteresis JKR Adhesion ABSTRACT The Tabor parameter μ is conventionally assumed to determine the range of applicability of the classical ‘JKR’ solution for adhesive elastic contact of a sphere and a plane, with the variation of the contact area and approach with load, and in particular the maximum tensile force (the pullo? force) being well predicted for μ 5. Here we show that the hysteretic energy loss during a contact separation cycle is signi?cantly overestimated by the JKR theory, even at quite large values of μ. This stems from the absence of long-range tensile forces in the JKR theory, which implies that jump into contact is delayed until the separation α = 0. We develop an approximate solution based on the use of Wus solution with van der Waals interactions for jump-in, and the JKR theory for jump out of contact, and show that for μ 5, the predicted hysteresis loss is then close to that found by direct numerical solutions using the Lennard-Jones force law. We also show how the same method can be adapted to allow for contact between bodies with ?nite support sti?ness. 1. Introduction When adhesive forces [e.g. van der Waals forces] are included in the formulation of an elastic contact problem, the normal loading and unloading curves can be di?erent, implying hysteresis losses during a loading/unloading cycle. This e?ect is most pronounced in small scale contacting systems such as the atomic force microscope [AFM]. In particular