DOI: 10.1098/rspa.1966.0242. Contact of nominally flat surfaces

10.1098/rspa.1966.0242

Crossref journal-article

The Royal Society

Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences (175)

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 directly proportional 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.

Bibliography

Contact of nominally flat surfaces. (1966). Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 295(1442), 300â319.

Authors 0

None

References 15 Referenced 3,787

{'key': 'p_1', 'first-page': '569', 'article-title': 'Mech', 'volume': '55', 'year': '1933', 'journal-title': 'Engng'} / Engng / Mech (1933)
A ntler M. 1964 Wear7 181.
{'key': 'p_3', 'first-page': '190', 'article-title': 'Proc. Roy', 'volume': '243', 'year': '1957', 'journal-title': 'Soc. A'} / Soc. A / Proc. Roy (1957)
Bickel E . 1963 Proc. In t. Conf. Prod. Eng. Res. Pittsburgh.
{'key': 'p_5', 'first-page': '480', 'article-title': 'Proc. R oy', 'volume': '212', 'year': '1952', 'journal-title': 'Soc. A'} / Soc. A / Proc. R oy (1952)
B ow den F . P . & T abor D. 1954 P a r t I 1964 P a r t I I Friction and Iubrication of solids. O xford U n IV ersity Press.
Cocks M. 1962 J . A p p l. P hys. 33 2152. (10.1063/1.1728920)
Cocks M. 1964 J . A p p l. P hys. 35 1807. (10.1063/1.1713746)
G reenwood J . A. 1965 ASME pap er 65-Lub-10 to app ear in J . Basic Engng.
Greenwood J . A. & T ripp J . H . J . A p p l. Mech. (in th e press).
{'key': 'p_11', 'first-page': '777', 'article-title': 'Proc. In st', 'volume': '169', 'year': '1955', 'journal-title': 'Mech. Engrs'} / Mech. Engrs / Proc. In st (1955)
H olm R . 1958 Electric contacts handbook. B erlin: Springer.
Miller J . C. P . 1964 A rticle 19 in Handbook of mathematical functions N ational B ureau of S tandard s W ashington D.C.
T abor D . 1951 The hardness of metals. Oxford U niversity Press.
Tim oshenko S. & Goodier J . N. 1951 Theory of elasticity. New Y ork: McGraw-Hill.

Dates

Type	When
Created	18 years, 8 months ago (Dec. 15, 2006, 3:12 p.m.)
Deposited	4 years, 6 months ago (Feb. 20, 2021, 10:39 p.m.)
Indexed	2 hours, 58 minutes ago (Aug. 22, 2025, 12:47 a.m.)
Issued	58 years, 8 months ago (Dec. 6, 1966)
Published	58 years, 8 months ago (Dec. 6, 1966)
Published Online	28 years, 7 months ago (Jan. 1, 1997)
Published Print	58 years, 8 months ago (Dec. 6, 1966)

Funders 0

None

BibTeX

@article{1966, volume={295}, ISSN={2053-9169}, url={http://dx.doi.org/10.1098/rspa.1966.0242}, DOI={10.1098/rspa.1966.0242}, number={1442}, journal={Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences}, publisher={The Royal Society}, year={1966}, month=dec, pages={300–319} }

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