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J. A. Greenwood

Other affiliations: Burndy
Bio: J. A. Greenwood is an academic researcher from University of Cambridge. The author has contributed to research in topics: Contact area & Surface roughness. The author has an hindex of 24, co-authored 31 publications receiving 8591 citations. Previous affiliations of J. A. Greenwood include Burndy.

Papers
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Journal ArticleDOI
TL;DR: In this article, the authors proposed a new theory of elastic contact, which is more closely related to real surfaces than earlier theories, and showed how the contact deformation depends on the topography of the surface, and established the criterion for distinguishing surfaces which touch elastically from those which touch plastically.
Abstract: It is usually assumed that the real area of contact between two nominally flat metal surfaces is determined by the plastic deformation of their highest asperities. This leads at once to the result that the real area of contact is directlyproportional to the load and independent of the apparent area-a result with many applications in the theories of electric contacts and friction. Archard pointed out that plastic deformation could not be the universal rule, and introduced a model which showed that, contrary to earlier ideas, the area of contact could be proportional to the load even with purely elastic contact. This paper describes a new theory of elastic contact, which is more closely related to real surfaces than earlier theories. We show how the contact deformation depends on the topography of the surface, and establish the criterion for distinguishing surfaces which touch elastically from those which touch plastically. The theory also indicates the existence of an 'elastic contact hardness', a composite quantity depending on the elastic properties and the topography, which plays the same role in elastic contact as the conventional hardness does in plastic contact. A new instrument for measuring surface topography has been built; with it the various parameters shown by the theory to govern surface contact can be measured experimentally. The typical radii of surface asperities have been measured. They were found, surprisingly, to be orders of magnitude larger than the heights of the asperities. More generally we have been able to study the distributions of asperity heights and of other surface features for a variety of surfaces prepared by standard techniques. Using these data we find that contact between surfaces is frequently plastic, as usually assumed, but that surfaces which touch elastically are by no means uncommon in engineering practice.

5,371 citations

Journal ArticleDOI
J. A. Greenwood1, J. H. Tripp1
TL;DR: In this article, the Hertzian theory of elastic contact between spheres is extended by considering one of the spheres to be rough, so that contact occurs, as in practice, at a number of discrete microcontacts.
Abstract: The Hertzian theory of elastic contact between spheres is extended by considering one of the spheres to be rough, so that contact occurs, as in practice, at a number of discrete microcontacts. It is found that the Hertzian results are valid at sufficiently high loads, but at lower loads the effective pressure distribution is much lower and extends much further than for smooth surfaces. The relevance to the physical-contact theory of friction and electric contact is considered.

644 citations

Journal ArticleDOI
J. A. Greenwood1
TL;DR: In this paper, a method of finding the resistance of a cluster of micro-contacts is derived, and it is shown that the resistance may be regarded as the sum of the parallel resistance of the microcontacts and an interaction term often related to the extent of the cluster and not to the number or size of individual contacts.
Abstract: The relation between the area of contact and the constriction resistance which holds for a single circular contact spot is widely used in electric contact theory, although the normal mode of contact is by a large number of microcontacts. A method of finding the resistance of a cluster of microcontacts is derived, and it is shown that the resistance may be regarded as the sum of the parallel resistance of the microcontacts and an interaction term often related to the extent of the cluster and not to the number or size of the individual contacts. The resistance is often close to that found by assuming that the entire area covered by the cluster is a single conducting spot. The known agreement between areas of contact found from resistance measurements and by other methods is therefore puzzling - until it is realized that the other methods also give only an apparent area: the real area of contact in, for example, a Brinell indentation is a small fraction of the area of the indentation. Thus from the point of view of electric contact theory the system is self-consistent, although the real area of contact is now seen to play no part in it: the implications for the theory of friction are more profound.

568 citations

Journal ArticleDOI
TL;DR: In this article, the Hertz equations for the contact of elastic spheres are modifed by surface energy, and the force needed to separate the spheres is equal to (3/2)πΔ R γ, which is independent of the elastic modulus and so appears to be universally applicable and therefore to conflict with Bradley9s answer.
Abstract: Bradley (1932) showed that if two rigid spheres of radii R 1 and R 2 are placed in contact, they will adhere with a force 2πΔ R γ, where R is the equivalent radius R 1 R 1 /( R 1 + R 2 ) and Δγ is the surface energy or ‘work of adhesion’ (equal to γ1+γ2-γ12). Subsequently Johnson et al. (1971) (JKR theory) showed by a Griffith energy argument (assuming that contact over a circle of radius a introduces a surface energy -π a 2 Δγ) how the Hertz equations for the contact of elastic spheres are modifed by surface energy, and showed that the force needed to separate the spheres is equal to (3/2)πΔ R γ, which is independent of the elastic modulus and so appears to be universally applicable and therefore to conflict with Bradley9s answer. The discrepancy was explained by Tabor (1977), who identified a parameter 3 Δγ 2 / 3 / E * 2 / 3 \e governing the transition from the Bradley pull-off force 2π R Δ|γ to the JKR value (3/2)π R Δγ. Subsequently Muller et al. (1980) performed a complete numerical solution in terms of surface forces rather than surface energy, (combining the Lennard–Jones law of force between surfaces with the elastic equations for a half-space), and confirmed that Tabor9s parameter does indeed govern the transition. The numerical solution is repeated more accurately and in greater detail, confirming the results, but showing also that the load–;approach curves become S-shaped for values of μ greater than one, leading to jumps into and out of contact. The JKR equations describe the behaviour well for values of μ of 3 or more, but for low values of μ the simple Bradley equation better describes the behaviour under negative loads.

416 citations

Journal ArticleDOI
TL;DR: In this paper, the properties of the peaks and summits of a rough surface are predicted on the assumption that the surface is two-dimensional random noise and the important result is that, in non-dimensional form, the answers depend only to a minor degree on the parameters describing the surface or on the sampling interval used.
Abstract: The properties of the peaks and summits of a rough surface are predicted on the assumption that the surface is two-dimensional random noise. The important result is that, in non-dimensional form, the answers depend only to a minor degree on the parameters describing the surface or on the sampling interval used: on the other hand the absolute values are strongly dependent on the sampling interval. Experimental results on a real surface agree remarkably well with the predictions.

271 citations


Cited by
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Book
25 Jan 1991
TL;DR: The connection between faults and the seismicity generated is governed by the rate and state dependent friction laws -producing distinctive seismic styles of faulting and a gamut of earthquake phenomena including aftershocks, afterslip, earthquake triggering, and slow slip events.
Abstract: This essential reference for graduate students and researchers provides a unified treatment of earthquakes and faulting as two aspects of brittle tectonics at different timescales. The intimate connection between the two is manifested in their scaling laws and populations, which evolve from fracture growth and interactions between fractures. The connection between faults and the seismicity generated is governed by the rate and state dependent friction laws - producing distinctive seismic styles of faulting and a gamut of earthquake phenomena including aftershocks, afterslip, earthquake triggering, and slow slip events. The third edition of this classic treatise presents a wealth of new topics and new observations. These include slow earthquake phenomena; friction of phyllosilicates, and at high sliding velocities; fault structures; relative roles of strong and seismogenic versus weak and creeping faults; dynamic triggering of earthquakes; oceanic earthquakes; megathrust earthquakes in subduction zones; deep earthquakes; and new observations of earthquake precursory phenomena.

3,802 citations

Book
01 Jan 2011
TL;DR: In this article, the authors present basic tools for elasticity and Hooke's law, effective media, granular media, flow and diffusion, and fluid effects on wave propagation for wave propagation.
Abstract: Preface 1. Basic tools 2. Elasticity and Hooke's law 3. Seismic wave propagation 4. Effective media 5. Granular media 6. Fluid effects on wave propagation 7. Empirical relations 8. Flow and diffusion 9. Electrical properties Appendices.

2,007 citations

Reference EntryDOI
15 Nov 2004
TL;DR: The mathematical structure of the contact formulation for finite element methods is derived on the basis of a continuum description of contact, and several algorithms related to spatial contact search and fulfillment of the inequality constraints at the contact interface are discussed.
Abstract: This paper describes modern techniques used to solve contact problems within Computational Mechanics. On the basis of a continuum description of contact, the mathematical structure of the contact formulation for finite element methods is derived. Emphasis is also placed on the constitutive behavior at the contact interface for normal and tangential (frictional) contact. Furthermore, different discretization schemes currently applied to solve engineering problems are formulated for small and finite strain problems. These include isoparametric interpolations, node-to-segment discretizations and also mortar and Nitsche techniques. Furthermore, several algorithms related to spatial contact search and fulfillment of the inequality constraints at the contact interface are discussed. Here, especially the penalty and Lagrange multiplier schemes are considered and also SQP- and linear-programming methods are reviewed. Keywords: contact mechanics; friction; penalty method; Lagrange multiplier method; contact algorithms; finite element method; finite deformations; discretization methods

1,761 citations

Journal ArticleDOI
TL;DR: This paper reviews the work in this area with special reference to the discrete element method and associated theoretical developments, and covers three important aspects: models for the calculation of the particle–particle and particle–fluid interaction forces, coupling of discrete elements method with computational fluid dynamics to describe particle-fluid flow, and the theories for linking discrete to continuum modelling.

1,563 citations

Journal ArticleDOI
01 Jun 1970
TL;DR: In this article, the authors give a general theory of contact between two rough plane surfaces and show that the important results of the previous models are unaffected: in particular, the load and the area of contact remain almost proportional, independently of the detailed mechanical and geometrical properties of the asperities.
Abstract: Most models of surface contact consider the surface roughness to be on one of the contacting surfaces only. The authors give a general theory of contact between two rough plane surfaces. They show that the important results of the previous models are unaffected: in particular, the load and the area of contact remain almost proportional, independently of the detailed mechanical and geometrical properties of the asperities. Further, a single-rough-surface model can always be found which will predict the same laws as a given two-rough-surface model, although the required model may be unrealistic. It does not seem possible to deduce the asperity shape or deformation mode from the load-compliance curve.

1,435 citations