Contact between representative rough surfaces

Yastrebov, Vladislav; Anciaux, Guillaume; Molinari, Jean‐François

doi:10.1103/physreve.86.035601

Cited by 51 publications

(69 citation statements)

References 29 publications

(85 reference statements)

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“…1B shows the complex spatial distribution of A rep for nonadhesive interactions ðN att = 0Þ. Analytic and numerical studies find that A rep is much smaller than the nominal area A 0 and rises linearly with the external load N pushing the surfaces together for small A rep (15,17,18,(20)(21)(22)(23). This implies a constant mean repulsive pressure p rep in contacting regions.…”

Section: Resultsmentioning

confidence: 99%

“…This implies a constant mean repulsive pressure p rep in contacting regions. Steeper and stiffer surfaces are harder to bring into contact, and both numerical and analytic calculations find (15,17,18,(20)(21)(22)(23) A The root-mean-square slope, h′ rms , is the rms average of the local height gradient, j∇hj, as indicated on the right. The attractive length d att is the distance from the contact perimeter at which the surface separation equals the interaction range Δr.…”

Section: Resultsmentioning

confidence: 99%

“…Persson has developed a scaling theory that includes an approximate treatment of asperity interactions (17,18). At the same time, large-scale numerical calculations of contact between rough surfaces have become feasible (19)(20)(21)(22)(23). Both approaches reveal limitations in the GW treatment of nonadhesive surfaces.…”

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Contact between rough surfaces and a criterion for macroscopic adhesion

Pastewka

Robbins

2014

Proc. Natl. Acad. Sci. U.S.A.

265

238

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At the molecular scale, there are strong attractive interactions between surfaces, yet few macroscopic surfaces are sticky. Extensive simulations of contact by adhesive surfaces with roughness on nanometer to micrometer scales are used to determine how roughness reduces the area where atoms contact and thus weakens adhesion. The material properties, adhesive strength, and roughness parameters are varied by orders of magnitude. In all cases, the area of atomic contact is initially proportional to the load. The prefactor rises linearly with adhesive strength for weak attractions. Above a threshold adhesive strength, the prefactor changes sign, the surfaces become sticky, and a finite force is required to separate them. A parameter-free analytic theory is presented that describes changes in these numerical results over up to five orders of magnitude in load. It relates the threshold adhesive strength to roughness and material properties, explaining why most macroscopic surfaces do not stick. The numerical results are qualitatively and quantitatively inconsistent with classical theories based on the Greenwood−Williamson approach that neglect the range of adhesion and do not include asperity interactions.surface roughness | contact mechanics S urfaces are adhesive or "sticky" if breaking contact requires a finite force. At the atomic scale, surfaces are pulled together by van der Waals interactions that produce forces per unit area that are orders of magnitude larger than atmospheric pressure (1). This leads to strong adhesion of small objects, such as Gecko setae (2, 3) [capillary forces may also contribute to Gecko adhesion in humid environments (4, 5)] and engineered mimics (6), and unwanted adhesion is the main failure mechanism in microelectromechanical systems with moving parts (7). Although tape and gecko feet maintain this strong adhesion at macroscopic scales, few of the objects we encounter are sticky. Indeed, our world would come to a halt if macroscopic objects adhered with an average pressure equal to that from van der Waals interactions.The discrepancy between atomic and macroscopic forces has been dubbed the adhesion paradox (8). Experiments show that a key factor underlying this paradox is surface roughness, which reduces the fraction of surface atoms that are close enough to adhere (8-11). Quantitative calculations of this reduction are extremely challenging because of the complex topography of typical surfaces, which have bumps on top of bumps on a wide range of scales (12, 13). In many cases, they can be described as self-affine fractals from a lower wavelength λ s of order nanometers to an upper wavelength λ L in the micrometer to millimeter range (10,14).The traditional Greenwood−Williamson (GW) (15) approach for calculating nonadhesive contact of rough surfaces approximates their complex topography by a set of spherical asperities of radius R. The distribution of asperity heights is assumed to be either exponential or Gaussian, and the long-range elastic interactions between different asperities...

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

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Contact between rough surfaces and a criterion for macroscopic adhesion

Pastewka

Robbins

2014

Proc. Natl. Acad. Sci. U.S.A.

265

238

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“…In this case, the material time-dependent behavior , in general, require to consider also the time domain and this really increases the simulation computational cost. Recently, thanks to new computational techniques and more powerful computational resources getting widely available, significant steps forward have been done both for elastic and viscoelastic contacts ( [34], [63], [55], [31] ), but a lot of work remains to be done.…”

Section: Introductionmentioning

confidence: 99%

Mechanics of rough contacts in elastic and viscoelastic thin layers

Putignano

Carbone

Dini

2015

International Journal of Solids and Structures

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Contact mechanics between rough solids usually relies on the half-space approximation, which assumes that the contact area dimension is much smaller than the thickness of the layers of materials that characterise the surfaces of the contacting bodies. However, such simplifying assumption is often inadequate when industrially relevant applications are considered, in particular those of biomechanical interest. Indeed, a large variety of systems, including not only classical engineering applications such as gear boxes, shafts, tyres, etc., but also biological tissues such as human skin, is characterised by superficial coatings; very often the mechanical properties of these coatings are very different from those of the bulk region of the bodies in contact. The aim of this paper is to shed light on the role played by the thickness of the layer of material used as a coating, with specific focus on the contact between a rigid rough surface and a thin deformable layer bonded to a rigid substrate. * Corresponding author. Phone: +44 020 7594 7064Email address: c.putignano12@imperial.ac.uk (C. Putignano) Preprint submitted to International Journal of Solids and Structures March 25, 2015Starting from a recently developed Boundary Element formulation (Carbone and Putignano, 2013), we derive a methodology which accounts for finite thickness by a corrective coefficient modulating the classical Greens function, and extends our analyses to periodic domains. This enables to avoid border effects and provides an innovative tool to tackle viscoelastic contacts with realistic roughness. This is exploited to perform a thorough investigation of the mechanisms responsible for frictional losses in layered systems characterised by different materials, thickness and loading conditions. Results show that decreasing the layer thickness corresponds to an increase in the contact stiffness. Furthermore, in the case of viscoelastic layer, particular attention has to be paid to the changes in the viscoelastic dissipation due to the finite thickness of the surface layer.

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“…The area of true contact is thus generally much smaller than the nominal interfacial contact area between the two surfaces [19,20]. Following pioneering work by Archard [21], it has been shown through analytical models and experimentation that the true contact area at the interface of two self-affine surfaces is linearly proportional to the normal force applied on the two solids [22][23][24][25][26][27]. Frictional force is often considered as linearly proportional to the true contact area [28][29][30].…”

Section: Introductionmentioning

confidence: 99%

Static friction between rigid fractal surfaces

et al. 2015

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Using spheropolygon-based simulations and contact slope analysis, we investigate the effects of surface topography and atomic scale friction on the macroscopically observed friction between rigid blocks with fractal surface structures. From our mathematical derivation, the angle of macroscopic friction is the result of the sum of the angle of atomic friction and the slope angle between the contact surfaces. The latter is obtained from the determination of all possible contact slopes between the two surface profiles through an alternative signature function. Our theory is validated through numerical simulations of spheropolygons with fractal Koch surfaces and is applied to the description of frictional properties of Weierstrass-Mandelbrot surfaces. The agreement between simulations and theory suggests that for interpreting macroscopic frictional behavior, the descriptors of surface morphology should be defined from the signature function rather than from the slopes of the contacting surfaces.

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Contact between representative rough surfaces

Cited by 51 publications

References 29 publications

Contact between rough surfaces and a criterion for macroscopic adhesion

Contact between rough surfaces and a criterion for macroscopic adhesion

Mechanics of rough contacts in elastic and viscoelastic thin layers

Static friction between rigid fractal surfaces

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