Relation between Interfacial Separation and Load: A General Theory of Contact Mechanics

Persson, B. N. J.

doi:10.1103/physrevlett.99.125502

Cited by 241 publications

(218 citation statements)

References 29 publications

(39 reference statements)

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“…Conventional studies into contact mechanics generally assume single distributions of asperity heights, often with spherical contacts (Greenwood & Williamson, 1966). These models and associated descriptors of roughness are inadequate for the interpretation of interfacial resistance to shear and indeed, under divergent conditions, increasing contact roughness may result in either higher or lower values of static friction (Persson, 2006(Persson, , 2007. Much of the complexity of surfaces arises from their fractal structures, with self-similar features present at ever-finer scales (Sammis & Biegel, 1989;Majumdar & Tien, 1990;Yan & Komvopoulos, 1998).…”

Section: Introductionmentioning

confidence: 99%

Effects of surface structure deformation on static friction at fractal interfaces

Hanaor

Gan

Einav

2013

Géotechnique Letters

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The evolution of fractal surface structures with flattening of asperities was investigated using isotropically roughened aluminium surfaces loaded in compression. It was found that asperity amplitude, mean roughness and fractal dimension decrease through increased compressive stress and number of loading events. Of the samples tested, surfaces subjected to an increased number of loading events exhibited the most significant surface deformation and were observed to exhibit higher levels of static friction at an interface with a single-crystal flat quartz substrate. This suggests that the frequency of grain reorganisation events in geomaterials plays an important role in the development of intergranular friction. Fractal surfaces were numerically modelled using WeierstrassMandelbrot-based functions. From the study of frictional interactions with rigid flat opposing surfaces it was apparent that the effect of surface fractal dimension is more significant with increasing dominance of adhesive mechanisms.

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Section: Introductionmentioning

confidence: 99%

Effects of surface structure deformation on static friction at fractal interfaces

Hanaor

Gan

Einav

2013

Géotechnique Letters

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“…The results provide a numerical test of recent continuum theories [8,9] and their applicability to real solids. The contact area and normal stiffness approach continuum predictions rapidly as system size increases.…”

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“…Experiments [17,18] and calculations [5,8,19] show an exponential rise in load with decreasing u, F N = cA 0 E ′ exp[−u/γh rms ], where h rms is the root mean squared (rms) variation in surface height and γ a constant of order 1. Differentiating leads to an expression for the normal interfacial stiffness:…”

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confidence: 99%

Stiffness of Contacts between Rough Surfaces

2011

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The effect of self-affine roughness on solid contact is examined with molecular dynamics and continuum calculations. The contact area and normal and lateral stiffnesses rise linearly with the applied load, and the load rises exponentially with decreasing separation between surfaces. Results for a wide range of roughnesses, system sizes and Poisson ratios can be collapsed using Persson's contact theory for continuous elastic media. The atomic scale response at the interface between solids has little affect on the area or normal stiffness, but can greatly reduce the lateral stiffness. The scaling of this effect with system size and roughness is discussed. PACS numbers: 46.55.+d, 62.20.Qp, 81.40.Pq The presence of roughness on a wide range of length scales has profound effects on contact and friction between experimental surfaces. Under a broad range of conditions [1][2][3][4][5][6], the area of intimate contact between rough surfaces A c is orders of magnitude smaller than the apparent surface area A 0 . As discussed below, this provides the most common explanation for Amontons' laws that friction is proportional to load and independent of A 0 . Because A c is small, the interfacial region is very compliant. In a range of applications the interfacial compliance can significantly reduce the stiffness of macroscopic joints formed by holding two components together under pressure [1,7].In this paper, we examine the effect of surface roughness on the normal and lateral stiffness of contacts between elastic solids using molecular dynamics (MD) and continuum calculations. The results provide a numerical test of recent continuum theories [8,9] and their applicability to real solids. The contact area and normal stiffness approach continuum predictions rapidly as system size increases. Continuum theory also captures the internal deformations in the solid under tangential load, but the total lateral stiffness may be greatly reduced by atomic scale displacements between contacting atoms on the opposing surfaces. This makes it a sensitive probe of the forces underlying friction and may help to explain unexpectedly small experimental results [10].The topography of many surfaces can be described as a self-affine fractal [2,11]. Over a wide range of lengths, the root mean squared (rms) change in height dh over a lateral distance ℓ scales as a power law: dh ∼ ℓ H , where the roughness or Hurst exponent H is typically between 0.5 and 0.9. Greenwood and Williamson (GW) considered the peaks of rough landscapes as independent asperities and found that A c rose linearly with normal load F N for nonadhesive surfaces [2]. This explains Amontons's laws if there is a constant shear stress at the interface. A linear scaling of area with load is also obtained from Persson's scaling theory, which includes elastic coupling between contacts approximately [12,13].Dimensional analysis implies that the linear relation between load and area must have the form( 1) where a modulus like the contact modulus E ′ is the only dimensional quantity char...

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“…The main problem is the influence of surface roughness on the contact mechanics at the seal-substrate interface. Most surfaces of engineering interest have surface roughness on a wide range of length scales [3], e.g, from cm to nm, which will influence the leak rate and friction of seals, and accounting for the whole range of surface roughness is impossible using standard numerical methods, such as the Finite Element Method.In this paper we present experimental results for the leak-rate of rubber seals, and compare the results to a novel theory [3,4,5], which is based on percolation theory and a recently developed contact mechanics theory [6,7,8,9,10,11,12], which accurately takes into account the elastic coupling between the contact regions in the nominal rubber-substrate contact area. Earlier contact mechanics models, such as the GreenwoodWilliamson[13] model or the model of Bush et al [14], neglect this elastic coupling, which results in highly incorrect results [15,16], in particular for the relations between the squeezing pressure and the interfacial separation [17].…”

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Leak rate of seals: Comparison of theory with experiment

2009

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Seals are extremely useful devices to prevent fluid leakage. We present experimental results for the leak-rate of rubber seals, and compare the results to a novel theory, which is based on percolation theory and a recently developed contact mechanics theory. We find good agreement between theory and experiment.A seal is a device for closing a gap or making a joint fluid tight [1]. Seals play a crucial role in many modern engineering devices, and the failure of seals may result in catastrophic events, such as the Challenger disaster. In spite of its apparent simplicity, it is not easy to predict the leak-rate and (for dynamic seals) the friction forces [2] for seals. The main problem is the influence of surface roughness on the contact mechanics at the seal-substrate interface. Most surfaces of engineering interest have surface roughness on a wide range of length scales [3], e.g, from cm to nm, which will influence the leak rate and friction of seals, and accounting for the whole range of surface roughness is impossible using standard numerical methods, such as the Finite Element Method.In this paper we present experimental results for the leak-rate of rubber seals, and compare the results to a novel theory [3,4,5], which is based on percolation theory and a recently developed contact mechanics theory [6,7,8,9,10,11,12], which accurately takes into account the elastic coupling between the contact regions in the nominal rubber-substrate contact area. Earlier contact mechanics models, such as the GreenwoodWilliamson[13] model or the model of Bush et al [14], neglect this elastic coupling, which results in highly incorrect results [15,16], in particular for the relations between the squeezing pressure and the interfacial separation [17]. We assume that purely elastic deformation occurs in the solids, which is the case for rubber seals.Consider the fluid leakage through a rubber seal, from a high fluid pressure P a region, to a low fluid pressure P b region, as in Fig. 1. Assume that the nominal contact region between the rubber and the hard countersurface is rectangular with area L x × L y . We assume that the high pressure fluid region is for x < 0 and the low pressure region for x > L x . We "divide" the contact region into squares with the side L x = L and the area A 0 = L 2 (this assumes that N = L y /L x is an integer, but this restriction does not affect the final result). Now, let us study the contact between the two solids within one of the squares as we change the magnification ζ. We define ζ = L/λ, where λ is the resolution. We study how the

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Relation between Interfacial Separation and Load: A General Theory of Contact Mechanics

Cited by 241 publications

References 29 publications

Effects of surface structure deformation on static friction at fractal interfaces

Effects of surface structure deformation on static friction at fractal interfaces

Stiffness of Contacts between Rough Surfaces

Leak rate of seals: Comparison of theory with experiment

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