Abstract
An adhesive elliptical contact is normally found in microscale applications that involve cylindrical solids, crossing at an angle between 0° and 90°. Currently, only one model is available to describe the elliptical contact’s surface interaction: the approximate Johnson–Kendall–Roberts (JKR) model which is limited to soft materials. In this paper, a new adhesive elliptical model is developed for a wide range of adhesive contacts by extending the double-Hertz theory, where adhesion is modeled by the difference between two Hertzian pressure distributions. Both Hertzian pressures are assumed to have an equivalent shape of contact areas, the only difference being in size. Assuming that the annular adhesive region is obtained by the area difference between the two Hertzian contact areas, the pull-off force curves can be calculated. In the limiting case of an adhesive circular contact, the results are very close to results from the existing models. However, for an adhesive elliptical contact in the JKR domain, lower pull-off forces are predicted when compared to the JKR values. Unlike the developed model, the shape of the JKR contact area varies throughout contact. Results show, particularly for conditions close to the JKR domain, that it is important to take into account that the adhesive region is the result of the two Hertzian contact areas having a non-equivalent shape.
Highlights
Surface adhesion is important in the mechanics of surface contacts, in particular at microscale [1,2,3,4], as a result of high surface area-to-volume ratios [5]
In the case of a circular contact, the JKR model relies on the assumption that short-range adhesion forces act within the contact area
We developed the adhesive elliptical contact model by extending the DH theory by [11], originally created for an adhesive circular contact
Summary
Surface adhesion is important in the mechanics of surface contacts, in particular at microscale [1,2,3,4], as a result of high surface area-to-volume ratios [5]. Various models have been developed to describe the adhesive contact between surfaces. In the context of modeling smooth surfaces, three important adhesive contact theories exist: (1) the Johnson–Kendall–Roberts (JKR) model [6]; (2) the Derjaguin–Muller–Toporov (DMT) model [7], which was later corrected by Muller et al [8]; and (3) the Maugis–Dugdale (MD) model [9]. In the case of a circular contact, the JKR model relies on the assumption that short-range adhesion forces act within the contact area. In the DMT model, long-range adhesion forces are assumed to act outside the contact area. It was found that the DMT model and the JKR model had different pull-off predictions.
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