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Research Papers: Contact Mechanics

Some Closed-Form Results for Adhesive Rough Contacts Near Complete Contact on Loading and Unloading in the Johnson, Kendall, and Roberts Regime

[+] Author and Article Information
Michele Ciavarella

Center of Excellence in
Computational Mechanics,
Politecnico di BARI,
Viale Gentile 182,
Bari 70126, Italy
e-mail: Mciava@poliba.it

Yang Xu, Robert L. Jackson

Mechanical Engineering Department,
Auburn University,
Auburn, AL 36849

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received December 26, 2016; final manuscript received April 27, 2017; published online July 21, 2017. Assoc. Editor: James R. Barber.

J. Tribol 140(1), 011402 (Jul 21, 2017) (6 pages) Paper No: TRIB-16-1401; doi: 10.1115/1.4036915 History: Received December 26, 2016; Revised April 27, 2017

Recently, generalizing the solution of the adhesiveless random rough contact proposed by Xu, Jackson, and Marghitu (XJM model), the first author has obtained a model for adhesive contact near full contact, under the Johnson, Kendall, and Roberts (JKR) assumptions, which leads to quite strong effect of the fractal dimension. We extend here the results with closed-form equations, including both loading and unloading which were not previously discussed, showing that the conclusions are confirmed. A large effect of hysteresis is found, as was expected. The solution is therefore competitive with Persson's JKR solution, at least in the range of nearly full contact, with an enormous advantage in terms of simplicity. Two examples of real surfaces are discussed.

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Figures

Grahic Jump Location
Fig. 1

Adhesionless contact. The area of gaps (Anc(p¯″))/A0 as a function of applied pressure for αp=2,10,50 (black, red, and magenta curves), where pressure is normalized to RMS full contact pressure, as compared with Persson's solution (blue solid line).

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Fig. 2

The area of gaps (Anc(p¯″))/A0 as a function of applied pressure and for p0″=1 and αp=2, where pressure is normalized to RMS full contact pressure. Blue solid line is Persson's “shifted” solution of Ciavarella [15], black solid line is the present solution, and dashed lines are unloading curves from p¯max″=1,2.

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Fig. 3

Area of contact for αp=2,10,50 (a)–(c), for p0″=0.01 and unloading curves from p¯max″=0,0.2,..,1

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Fig. 4

Pull-off value extrapolated as pressure for which area of contact (A(p¯″))/A0 on unloading seems to go to zero, depending on the pressure reaches during loading p¯max″. The arrow indicates p¯0″=0.1,0.2...,1. (a) αp=2 and (b) αp=10.

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