# On the Linearity of Contact Area and Reduced Pressure

On the Linearity of Contact Area and Reduced Pressure Computer simulations, Persson theory, and dimensional analysis find that the relative contact area between nominally flat surfaces grows linearly with the reduced pressure $$p^*$$ p ∗ at small loads, where $$p^*$$ p ∗ is the ratio of the macroscopic pressure p to the contact modulus times the root-mean-square height gradient $$\bar{g}$$ g ¯ . Here, we show that it also holds for Hertzian and other harmonic, axisymmetric indenters—as long as $$\bar{g}$$ g ¯ is determined over the true contact area and p is defined as the load divided by an arbitrary but fixed reference area. For a Hertzian indenter, the value for the proportionality coefficient $$\kappa$$ κ turns out to be $$\kappa = 3\pi /\sqrt{32}$$ κ = 3 π / 32 . The analysis explains why mathematically rigorous treatments of Greenwood–Williamson type models identify a sublinear dependence of contact area on load. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Tribology Letters Springer Journals

# On the Linearity of Contact Area and Reduced Pressure

, Volume 65 (4) – Aug 29, 2017
2 pages

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Publisher
Springer Journals
Copyright
Copyright © 2017 by Springer Science+Business Media, LLC
Subject
Materials Science; Tribology, Corrosion and Coatings; Surfaces and Interfaces, Thin Films; Theoretical and Applied Mechanics; Physical Chemistry; Nanotechnology
ISSN
1023-8883
eISSN
1573-2711
D.O.I.
10.1007/s11249-017-0912-y
Publisher site
See Article on Publisher Site

### Abstract

Computer simulations, Persson theory, and dimensional analysis find that the relative contact area between nominally flat surfaces grows linearly with the reduced pressure $$p^*$$ p ∗ at small loads, where $$p^*$$ p ∗ is the ratio of the macroscopic pressure p to the contact modulus times the root-mean-square height gradient $$\bar{g}$$ g ¯ . Here, we show that it also holds for Hertzian and other harmonic, axisymmetric indenters—as long as $$\bar{g}$$ g ¯ is determined over the true contact area and p is defined as the load divided by an arbitrary but fixed reference area. For a Hertzian indenter, the value for the proportionality coefficient $$\kappa$$ κ turns out to be $$\kappa = 3\pi /\sqrt{32}$$ κ = 3 π / 32 . The analysis explains why mathematically rigorous treatments of Greenwood–Williamson type models identify a sublinear dependence of contact area on load.

### Journal

Tribology LettersSpringer Journals

Published: Aug 29, 2017

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