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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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References

Johnson, K. L. , 1985, Contact Mechanics, Cambridge University Press, Cambridge, UK. [CrossRef]
Johnson, K. L. , Kendall, K. , and Roberts, A. D. , 1971, “ Surface Energy and the Contact of Elastic Solids,” Proc. R. Soc. London A, 324(1558), pp. 301–313. [CrossRef]
Greenwood, J. A. , and Williamson, J. B. P. , 1966, “ Contact of Nominally Flat Surfaces,” Proc. R. Soc. London A, 295(1442), pp. 300–319. [CrossRef]
Fuller, K. N. G. , and Tabor, D. , 1975, “ The Effect of Surface Roughness on the Adhesion of Elastic Solids,” Proc. R. Soc. London A, 345(1642), pp. 327–342. [CrossRef]
Bradley, R. S. , 1932, “ The Cohesive Force Between Solid Surfaces and the Surface Energy of Solids,” Philos. Mag., 13(86), pp. 853–862. [CrossRef]
Derjaguin, B. V. , 1934, “ Theorie des Anhaftens kleiner Teilchen,” Kolloid Z., 69(2), pp. 155–164. [CrossRef]
Derjaguin, B. V. , Muller, V. M. , and Toporov, Yu. P. , 1975, “ Effect of Contact Deformations on the Adhesion of Particles,” J. Colloid Interface Sci., 53(2), pp. 314–326. [CrossRef]
Tabor, D. , 1977, “ Surface Forces and Surface Interactions,” J. Colloid Interface Sci., 58(1), pp. 2–13. [CrossRef]
Persson, B. N. J. , 2002, “ Adhesion Between an Elastic Body and a Randomly Rough Hard Surface,” Eur. Phys. J. E, 8(4), pp. 385–401. [CrossRef]
Persson, B. N. J. , and Scaraggi, M. , 2014, “ Theory of Adhesion: Role of Surface Roughness,” J. Chem. Phys., 141(12), p. 124701. [CrossRef] [PubMed]
Krick, B. A. , Vail, J. R. , Persson, B. N. , and Sawyer, W. G. , 2012, “ Optical In Situ Micro Tribometer for Analysis of Real Contact Area for Contact Mechanics, Adhesion, and Sliding Experiments,” Tribol. Lett., 45(1), pp. 185–194. [CrossRef]
Johnson, K. L. , 1995, “ The Adhesion of Two Elastic Bodies With Slightly Wavy Surfaces,” Int. J. Solids Struct., 32(3–4), pp. 423–430. [CrossRef]
Guduru, P. R. , 2007, “ Detachment of a Rigid Solid From an Elastic Wavy Surface: Theory,” J. Mech. Phys. Solids, 55(3), pp. 445–472. [CrossRef]
Guduru, P. R. , and Bull, C. , 2007, “ Detachment of a Rigid Solid From an Elastic Wavy Surface: Experiments,” J. Mech. Phys. Solids, 55(3), pp. 473–488. [CrossRef]
Waters, J. F. , Lee, S. , and Guduru, P. R. , 2009, “ Mechanics of Axisymmetric Wavy Surface Adhesion: JKR–DMT Transition Solution,” Int. J. Solids Struct., 46(5), pp. 1033–1042. [CrossRef]
Ciavarella, M. , 2015, “ Adhesive Rough Contacts Near Complete Contact,” Int. J. Mech. Sci., 104, pp. 104–111. [CrossRef]
Xu, Y. , Jackson, R. L. , and Marghitu, D. B. , 2014, “ Statistical Model of Nearly Complete Elastic Rough Surface Contact,” Int. J. Solids Struct., 51(5), pp. 1075–1088. [CrossRef]
Ciavarella, M. , 2016, “ Rough Contacts Near Full Contact With a Very Simple Asperity Model,” Tribol. Int., 93(Pt. A), pp. 464–469. [CrossRef]
Persson, B. N. J. , 2001, “ Theory of Rubber Friction and Contact Mechanics,” J. Chem. Phys., 115(8), pp. 3840–3861. [CrossRef]
McCool, J. I. , 1987, “ Relating Profile Instrument Measurements to the Functional Performance of Rough Surfaces,” ASME J. Tribol., 109(2), pp. 264–270. [CrossRef]
Xu, Y. , and Jackson, R. L. , 2017, “ Statistical Models of Nearly Complete Elastic Rough Surface Contact-Comparison With Numerical Solutions,” Tribol. Int., 105, pp. 274–291. [CrossRef]
Nayak, P. R. , 1973, “ Random Process Model of Rough Surfaces in Plastic Contact,” Wear, 26(3), pp. 305–333. [CrossRef]
Carbone, G. , and Bottiglione, F. , 2015, “ Asperity Contact Theories: Do They Predict Linearity Between Contact Area and Load?” J. Mech. Phys. Solids, 56(8), pp. 2555–2572. [CrossRef]
Afferrante, L. , Ciavarella, M. , and Demelio, G. , 2015, “ Adhesive Contact of the Weierstrass Profile,” Proc. R. Soc. A, 471(2182), p. 20150248. [CrossRef]
Carbone, G. , Pierro, E. , and Recchia, G. , 2015, “ Loading-Unloading Hysteresis Loop of Randomly Rough Adhesive Contacts,” Phys. Rev. E, 92(6), p. 062404. [CrossRef]

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).

Grahic Jump Location
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.

Grahic Jump Location
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

Grahic Jump Location
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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