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Article

A Mechanics Approach to Static Friction of Elastic–Plastic Fractal Surfaces

[+] Author and Article Information
J. Yang, K. Komvopoulos

Department of Mechanical Engineering, University of California, Berkeley, CA 94720

J. Tribol 127(2), 315-324 (Apr 07, 2005) (10 pages) doi:10.1115/1.1828080 History: Received February 16, 2004; Revised July 26, 2004; Online April 07, 2005
Copyright © 2005 by ASME
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Figures

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Schematic showing the separation distance, d, between two rough surfaces, 1 and 2
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Schematic log–log plot of approximate continuous power spectra of two fractal surfaces P̄1(ω) and P̄2(ω) with different fractal dimension (D1<D2) intersecting at a critical frequency ω*, and power spectrum of the surface separation distance P̄(ω)
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Schematic illustration of the truncation of two asperities on surfaces i and j with contact angle θ
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(a) Schematic showing a line segment of projected length l, and (b) probability density function of the secant slope of line segments with l=10 nm (obtained from a two-dimensional fractal surface profile with L=4379 nm,L0=2 nm,D=1.44, and G=9.46×10−4 nm) and normal distributions with standard deviations equal to the rms of the secant slope of the simulation data, σsim, and the square root of the values estimated from Eqs. (6) and (10)
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Schematics of asperity contacts and associated normal load versus interference response: (a) both asperities deform elastically and the contact opposes the onset of relative movement; (b) both asperities deform elastically and tend to separate at the inception of sliding; (c) at least one asperity deforms plastically and the contact opposes the onset of relative movement; and (d) at least one asperity deforms plastically and the asperities tend to separate at the inception of sliding
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Schematic showing the local forces acting on a single spherical asperity. The local normal force Fnl passes through the sphere center, while the local friction force Ffl is tangent to the circle on χ plane, which is parallel to the direction of the relative movement at the inception of sliding.
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Static coefficient of friction versus normal load for (a) Ds1=2.3 and Ds2=2.5, and (b) Ds1=Ds2=2.3 and 2.5 (L=10 μm,L0=2 nm,G1=2.109×10−5 nm,G2=1.055×10−4 nm,E=129.8 GPa,Sy=300 MPa,ν=0.343,H=900 MPa, and τ/k=0.8)
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Static coefficient of friction versus normal load for τ/k=0.2 and 0.8 (L=10 μm,L0=2 nm,Ds1=2.3,Ds2=2.5,G1=2.109×10−5 nm,G2=1.055×10−4 nm,E=129.8 GPa,Sy=300 MPa,ν=0.343, and H=900 MPa)
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Static coefficient of friction versus normal load for surfaces with fractal dimension Ds1 and Ds2, height standard deviation rms1 and rms2, and fractal roughness G1=G2=2.109×10−5 nm(L=10 μm,L0=2 nm,E=129.8 GPa,Sy=300 MPa,ν=0.343,H=900 MPa, and τ/k=0.8)
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Static coefficient of friction versus normal load for surfaces with fractal dimension Ds1 and Ds2, fractal roughness G1 and G2, and height standard deviation rms1=rms2=1.9 nm(L=10 μm,L0=2 nm,E=129.8 GPa,Sy=300 MPa,ν=0.343,H=900 MPa, and τ/k=0.8)

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