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Research Papers

Plane Contact and Partial Slip Behaviors of Elastic Layers With Randomly Rough Surfaces

[+] Author and Article Information
Fan Jin, Qiang Wan

Institute of Systems Engineering,
China Academy of Engineering Physics,
Mianyang, Sichuan 621900, China

Xu Guo

State Key Laboratory of Structural Analysis
for Industrial Equipment,
Department of Engineering Mechanics,
Dalian University of Technology,
Dalian 116023, China
e-mail: guoxu@dlut.edu.cn

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received May 5, 2015; final manuscript received May 23, 2015; published online June 19, 2015. Editor: Yonggang Huang.

J. Appl. Mech 82(9), 091006 (Sep 01, 2015) (7 pages) Paper No: JAM-15-1223; doi: 10.1115/1.4030742 History: Received May 05, 2015; Revised May 23, 2015; Online June 19, 2015

A plane contact and partial slip model of an elastic layer with randomly rough surface were established by combining the Greenwood–Williamson (GW) rough contact model and the Cattaneo–Mindlin partial slip model. The rough surface of the elastic layer bonded to a rigid base is modeled as an ensemble of noninteracting asperities with identical radius of curvature and Gaussian-distributed heights. By employing the Hertzian solution and the Cattaneo–Mindlin solution to each individual asperity of the rough surface, we derive the total normal force, the real contact area, and the total tangential force for the rough surface, respectively, and then examine the normal contact and partial slip behaviors of the layer. An effective Coulomb coefficient is defined to account for interfacial friction properties. Furthermore, a typical stick–slip transition for the rough surface was also captured by distinguishing the stick and slip contacting asperities according to their respective indentation depths. Our analysis results show that an increasing layer thickness may result in a larger real contact area, a lower mean contact pressure, and a higher effective Coulomb coefficient.

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References

Figures

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Fig. 1

An elastic layer bonded to a rigid substrate in contact with a rigid cylinder. A normal compressive line force P is first applied followed by a subsequent tangential line force Q with no slip.

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Fig. 2

Comparison between the exact a-δ relations (dots) and the corresponding fitted curves (lines) for (a) ν=0.3 and (b) ν=0.5, respectively

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Fig. 3

Plane contact between a rigid smooth surface and an elastic layer with a randomly rough surface in (a) a real case and (b) a simplified model

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Fig. 4

The dimensionless normal force P/NE*σ versus the dimensionless real contact area A/NRσ for (a) ν=0.3 and (b) ν=0.5, respectively

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Fig. 5

The dimensionless mean real contact pressure versus the dimensionless layer thickness for (a) ν=0.3 and (b) ν=0.5, respectively

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Fig. 6

Variation of the tangential forces contributed by the stick and slip asperities as a function of the tangential displacement for (a) ν=0.3 and (b) ν=0.5, respectively. Here, τcr*=0.01, d*=1, h*=100, and M=2.

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Fig. 7

The effective Coulomb coefficient versus the dimensionless layer thickness for (a) ν = 0.3 and (b) ν = 0.5, respectively

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