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Research Papers

Micro/Nanocontact Between a Rigid Ellipsoid and an Elastic Substrate With Surface Tension

[+] Author and Article Information
W. K. Yuan, J. M. Long, Y. Ding

Department of Engineering Mechanics,
SVL,
Xi'an Jiaotong University,
Xi'an 710049, China

G. F. Wang

Department of Engineering Mechanics,
SVL,
Xi'an Jiaotong University,
Xi'an 710049, China
e-mail: wanggf@mail.xjtu.edu.cn

1Corresponding author.

Manuscript received September 18, 2016; final manuscript received October 15, 2016; published online November 7, 2016. Assoc. Editor: Harold S. Park.

J. Appl. Mech 84(1), 011012 (Nov 07, 2016) (7 pages) Paper No: JAM-16-1460; doi: 10.1115/1.4035032 History: Received September 18, 2016; Revised October 15, 2016

For micro/nanosized contact problems, the influence of surface tension becomes prominent. Based on the solution of a point force acting on an elastic half space with surface tension, we formulate the contact between a rigid ellipsoid and an elastic substrate. The corresponding singular integral equation is solved numerically by using the Gauss–Chebyshev quadrature formula. When the size of contact region is comparable with the elastocapillary length, surface tension significantly alters the distribution of contact pressure and decreases the contact area and indent depth, compared to the classical Hertzian prediction. We generalize the explicit expression of the equivalent contact radius, the indent depth, and the eccentricity of contact ellipse with respect to the external load, which provides the fundament for analyzing nanoindentation tests and contact of rough surfaces.

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Figures

Grahic Jump Location
Fig. 1

Indentation of a rigid ellipsoid on an elastic half space

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Fig. 2

The schematic of the elliptical contact region

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Fig. 3

Variation of semimajor a with respect to η for different values of θ

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Fig. 4

The pressure distribution within the contact region

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Fig. 9

Variation of normalized eccentricity with respect to the ratio of χ to s

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Fig. 8

Variation of normalized load with respect to the ratio of re to s

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Fig. 7

Variation of normalized load with respect to (ABδ/C)1/2/s

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Fig. 6

The surface normal bulk stress along the x-axis

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Fig. 5

The surface normal displacement along the x-axis

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