Models of discrete contact of elastic bodies taking into account adhesion forces

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Abstract

The paper presents formulations and solutions of periodic contact problems for an elastic half-plane and an elastic half-space taking into account the adhesive interaction of contacting bodies’ surfaces. To describe the adhesive forces in the gap between the surfaces, an approximation of the adhesive potential in the form of a piecewise constant function (the Maugis–Dugdale approximation) is used. The dependences of the real contact area, as well as the approach of bodies on the nominal pressure, the parameters of adhesive potential, and the surface relief parameters of the indenting body are investigated. The obtained solutions are compared with the results following from the Johnson, Kendall, Roberts (JKR) model based on the use of a simplified form of the adhesive potential. An analysis of energy dissipation in the surfaces approach–retraction cycle is carried out, and the influence of the parameters of surface microrelief on this contact interaction characteristic is estimated.

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About the authors

I. G. Goryacheva

Ishlinsky Institute for Problems in Mechanics of the RAS

Author for correspondence.
Email: goryache@ipmnet.ru
Russian Federation, Moscow

Yu. Y. Makhovskaya

Ishlinsky Institute for Problems in Mechanics of the RAS

Email: makhovskaya@mail.ru
Russian Federation, Moscow

I. Y. Tsukanov

Ishlinsky Institute for Problems in Mechanics of the RAS

Email: ivan.yu.tsukanov@gmail.com
Russian Federation, Moscow

References

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Supplementary files

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2. Fig. 1. Diagram of contact of elastic bodies, one of which is limited by a wavy surface, taking into account adhesive interaction within the framework of the DKR model

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3. Fig. 2. Diagram of contact of elastic bodies, one of which is limited by a wavy surface, taking into account adhesive interaction within the framework of the MD model

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4. Fig. 3. Dependences of the contact area size on the nominal pressure for the MD (curves 1, 2) and DKR (curve 3) models at Δ/L = 0.16; w = 0.01 N/m; w/p0 = 0.5, p0/p* = 0.04 (curve 1), w/p0 = 0.1, p0/p* = 0.2 (curve 2), αp* = 0.06 (curve 3)

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5. Fig. 4. Diagram of contact between a rigid surface covered with protrusions and an elastic half-space

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6. Fig. 5. Dependence of the dimensionless nominal pressure on the distance between the surfaces at L = 50 (curves 1 and 1′) and L = 3.3 (curve 2); λ = 2 (curves 1 and 2) and λ = 0.5 (curve 1′)

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7. Fig. 6. Energy dissipation per unit area in the cycle of surface approach–retraction with discrete contact for L = 3, 5 and 50 – curves 1–3, respectively

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8. Fig. 7. Dependence of energy dissipation on the dimensionless specific work of adhesion for different shapes of protrusions described by the function f (r) = Ar2n for n = 1 (curve 1), n = 2 (curve 2) and n = 3 (curve 3)

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