Modeling of Elastic/Plastic Contact Between Nominally Flat Rough Surfaces Using an n-Point Asperity Model

[+] Author and Article Information
A. Hariri

Department of Mechanical and Industrial Engineering, University of Toronto, King's College Road, Toronto, ON, M5S 3G8 Canadahariri@mie.utoronto.ca

J. W. Zu, R. Ben Mrad

Department of Mechanical and Industrial Engineering, University of Toronto, King's College Road, Toronto, ON, M5S 3G8 Canada

J. Tribol 128(4), 876-885 (May 03, 2006) (10 pages) doi:10.1115/1.2345409 History: Received November 17, 2005; Revised May 03, 2006

The asperities of rough surfaces have long been considered to be points higher than their immediate neighbors. Based on this concept, theories were developed for quantitatively understanding the elastic and plastic nature of contact between rough surfaces. Recently it has been recognized that the above model for asperities is inadequate. Consequently, all the models that have been constructed based on that model are inadequate too. In this paper, based on a newly developed multiple-point asperity model, the elastic and plastic contact problem between nominally flat surfaces is reformulated. This leads to finding the deformed area, and load produced by the contact. The model is developed for the general form of isotropic rough surfaces with arbitrary height distribution and autocorrelation function (ACF). The microcontact areas generated by each asperity contact are considered to be circles. The Gaussian distribution of heights and exponential ACF are considered as a benchmark to compare the results of the new model with the existing models. Using results from numerical models developed by other groups, the new model is validated.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 1

A typical equivalent normalized profile of two nominally flat surfaces in contact

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Figure 2

A three-point asperity at level h (consisting of z3 to z5) that will be transformed to a seven-point one at level h2, with an equivalent parabolic asperity fitted to it

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Figure 3

The total number of sample points above a certain level, Mt, compared to the exact values (M=10,000, and nmax=7)

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Figure 4

Comparing Ane for different values of ρ, (a)ρ=0.1 and (b)ρ=0.67

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Figure 5

(a) A possible case of a 2D 11-point asperity viewed in x-y plane and (b) possible cases of a 2D four-point asperity (only points above the given level are shown)

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Figure 6

Comparing various parameters from present model and OA model (a) dimensionless deformed area, A∕A0, against dimensionless separation, h*(b) dimensionless load, FPρ, against h*(c) dimensionless mean pressure, pm, against h*(d)A∕A0 against FPρ

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Figure 7

The percentage of deformed area involving plastic flow, Ap∕A, against the dimensionless separation, h*, at different values of ψ



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