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Research Papers: Contact Mechanics

Model for a Sphere–Flat Elastic–Plastic Adhesion Contact

[+] Author and Article Information
Zhi Qian Wang

Henan Key Laboratory of Photovoltaic Materials,
College of Physics and Electronic Engineering,
Henan Normal University,
Xinxiang 453007, China
e-mail: wangzhiqian@cntv.cn

Jin Feng Wang

Henan Key Laboratory of Photovoltaic Materials,
College of Physics and Electronic Engineering,
Henan Normal University,
Xinxiang 453007, China
e-mail: wangjinfeng0418@sina.com

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received April 30, 2016; final manuscript received September 17, 2016; published online March 20, 2017. Assoc. Editor: James R. Barber.

J. Tribol 139(4), 041401 (Mar 20, 2017) (10 pages) Paper No: TRIB-16-1143; doi: 10.1115/1.4034767 History: Received April 30, 2016; Revised September 17, 2016

This paper presents a cubic model for the sphere–flat elastic–plastic contact without adhesion. In the cubic model, the applied load and the contact area are described by the cubic polynomial functions of the displacement to the power of 1/2 during loading and unloading, and the applied load is also expressed as the cubic polynomial function of the contact area to the power of 1/3 during loading. Utilizing these cubic polynomial functions, the elastic–plastic load (EPL) index, which is defined by the ratio between the dissipated energy due to plastic deformations and the work done to deform the sphere during loading, is calculated analytically. The calculated EPL index is just the ratio between the residue displacement after unloading and the maximum elastic–plastic displacement after loading. Using the cubic model, this paper extends the Johnson–Kendall–Roberts (JKR) model from the elastic regime to the elastic–plastic regime. Introducing the Derjaguin–Muller–Toporov (DMT) adhesion, the unified elastic–plastic adhesion model is obtained and compared with the simplified analytical model (SAM) and Kogut–Etsion (KE) model.

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References

Figures

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Fig. 2

Relationship between A/Ac and δ/δc. The circles are the data calculated from Eq. (6), the short dashed line is depicted by Eq. (8), the long dashed line is depicted by Eq. (14), and the solid line is depicted by Eq. (20).

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Fig. 3

Relationship between A/Ac and F/Fc. The dots are the data calculated from Eq. (6), and the solid line is depicted by Eq. (21).

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Fig. 4

Relationship between FUL/Fc and δULc during unloading. The dots are the data calculated from Eq. (10), the dashed line is depicted by Eq. (5), and the solid line is depicted by Eq.(22).

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Fig. 5

Relationship between AUL/Ac and δULc during unloading. The dots are the data calculated from Eq. (11), the dashed line is depicted by Eq. (6), and the solid line is depicted by Eq.(23).

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Fig. 1

Schematic of the elastic–plastic regime

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Fig. 6

Relationship between EPL and δ/δc. The dots are the data calculated from Eq. (24), and the solid line is depicted by δp from Eq. (15).

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Fig. 7

Comparisons of the present analysis (PA) model with the SAM model and KE model for Ru (up) and Au (down) under large loads. The dimensionless external force and contact radius are predicted by the SAM (short dashed line), KE (long dashed line), and PA (solid line) models, respectively.

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