Response to Dr Greenwood\u2019s Comments on \u201cExtending the Double-Hertz Model to Allow Modeling of an Adhesive Elliptical Contact\u201d

Nurul Hilwa Mohd Zini ,M.b De Rooij ,M Bazr Afshan Fadafan,N Ismail ,Dirk J Schipper

doi:10.1007/s11249-018-1050-x

Nurul Hilwa Mohd Zini , M.b De Rooij + Show 3 more

Open Access

https://doi.org/10.1007/s11249-018-1050-x

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Abstract

© 2018, The Author(s). 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

A contact problem with an annular elliptical adhesive region is difficult to solve as a, b, c, and d are unknown a priori
We fully acknowledge that Eq (2) is not correct for adhesive elliptical contacts; it was not our intention to suggest this being the case
Assuming that the ellipticity ratio remains constant throughout the contact, at the pull-off force, both βab and βcd become equal to the ellipticity ratio at the initial loading, β0;

Summary

Introduction

For β0 = 0.8 and β0 = 0.9, the contact shapes are obviously elongated in the major axis direction, and the application of Eq (4) results in inaccurate pull-off force predictions, by assuming βab = βcd for μ values close to the JKR domain.

Results

Conclusion