Contact of Nominally Flat Surfaces
06 Dec 1966-Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences (The Royal Society)-Vol. 295, Iss: 1442, pp 300-319
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.
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25 Jan 1991TL;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
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01 Jan 2011TL;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
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
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
09 Jan 2020
TL;DR: The third edition of the reference book as discussed by the authors has been thoroughly updated while retaining its comprehensive coverage of the fundamental theory, concepts, and laboratory results, and highlights applications in unconventional reservoirs, including water, hydrocarbons, gases, minerals, rocks, ice, magma and methane hydrates.
Abstract: Responding to the latest developments in rock physics research, this popular reference book has been thoroughly updated while retaining its comprehensive coverage of the fundamental theory, concepts, and laboratory results. It brings together the vast literature from the field to address the relationships between geophysical observations and the underlying physical properties of Earth materials - including water, hydrocarbons, gases, minerals, rocks, ice, magma and methane hydrates. This third edition includes expanded coverage of topics such as effective medium models, viscoelasticity, attenuation, anisotropy, electrical-elastic cross relations, and highlights applications in unconventional reservoirs. Appendices have been enhanced with new materials and properties, while worked examples (supplemented by online datasets and MATLAB® codes) enable readers to implement the workflows and models in practice. This significantly revised edition will continue to be the go-to reference for students and researchers interested in rock physics, near-surface geophysics, seismology, and professionals in the oil and gas industries.
1,387 citations
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01 Jan 1934
TL;DR: The theory of the slipline field is used in this article to solve the problem of stable and non-stressed problems in plane strains in a plane-strain scenario.
Abstract: Chapter 1: Stresses and Strains Chapter 2: Foundations of Plasticity Chapter 3: Elasto-Plastic Bending and Torsion Chapter 4: Plastic Analysis of Beams and Frames Chapter 5: Further Solutions of Elasto-Plastic Problems Chapter 6: Theory of the Slipline Field Chapter 7: Steady Problems in Plane Strain Chapter 8: Non-Steady Problems in Plane Strain
20,724 citations
TL;DR: In this article, a hemispherically ended copper rider was observed sliding against the surface of a large cylindrical copper drum, and it was found that the shearing of the metal by which the sliding proceeds occurs in a direction slightly inclined to the drum surface.
Abstract: The friction of sliding metal surfaces is often attributed to the formation and shearing of welded junctions between the surfaces. This paper describes a more detailed investigation of the phenomena which occur in the junctions. Experiments were performed with a hemispherically ended copper rider sliding against the surface of a large cylindrical copper drum. Observation of the sliding contact through the microscope shows that most of the time during sliding, the drum and rider are held apart by a wedge of displaced metal from the drum, which becomes trapped between them. Whenever a wedge escapes from between the drum and rider, another wedge forms rapidly to replace it. The wedges are also observed with several other combinations of metals, and with pairs of flat copper surfaces. Sections cut through the wedges and adjacent copper contact members were examined. It is found that the shearing of the metal by which the sliding proceeds occurs in a direction slightly inclined to the drum surface. This causes...
129 citations
TL;DR: In this article, the interaction between pairs of flat metal surfaces sliding against one another was investigated, and it was shown that the junctions which are formed when the surfaces are first placed in contact do not break when surfaces begin to slide.
Abstract: This paper describes an investigation of the interaction between pairs of flat metal surfaces sliding against one another. The experiments show that the junctions which are formed when the surfaces are first placed in contact do not break when the surfaces begin to slide. The relative motion of sliding is accommodated by plastic deformation of the metal near the contact areas. The plastic shearing takes place in a direction slightly inclined to the surfaces and causes the formation of wedges of displaced metal in much the same manner as was observed in a previous investigation with hemispherical riders sliding against cylindrical drums. With a pair of flat surfaces several wedges are formed simultaneously at various places between the surfaces. The wedges force the surfaces apart, and the separation is often as much as 0.1 to 0.4 mm. The variations in the distance of separation during sliding were measured with a dial indicator. The wedges and the gap between the surfaces were also observed visually with and without the microscope. Metallographic sections cut through the wedges were examined. Differences in the phenomena observed with various metals indicate that with some metals the plastic shearing by which the wedges are generated continues to occur during extended periods of sliding, while with others it occurs mainly during an initial period of sliding, though the wedges once formed remain between the surfaces.
53 citations