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Research Papers

Adhesive Contact on Randomly Rough Surfaces Based on the Double-Hertz Model

[+] Author and Article Information
Wei Zhang, Fan Jin

State Key Laboratory of Structural Analysis
for Industrial Equipment,
Department of Engineering Mechanics,
Dalian University of Technology,
Dalian 116023, China

Sulin Zhang

Department of Engineering Science
and Mechanics,
Department of Materials Science
and Engineering,
The Pennsylvania State University,
University Park, PA 16802

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.

Manuscript received October 15, 2013; final manuscript received November 10, 2013; accepted manuscript posted November 14, 2013; published online December 12, 2013. Editor: Yonggang Huang.

J. Appl. Mech 81(5), 051008 (Dec 12, 2013) (7 pages) Paper No: JAM-13-1430; doi: 10.1115/1.4026019 History: Received October 15, 2013; Accepted November 10, 2013; Revised November 10, 2013

A cohesive zone model for rough surface adhesion is established by combining the double-Hertz model (Greenwood, J. A., and Johnson, K. L., 1998, “An Alternative to the Maugis Model of Adhesion Between Elastic Spheres,” J. Phys. D: Appl. Phys., 31, pp. 3279–3290) and the multiple asperity contact model (Greenwood, J. A., and Williamson, J. B. P., 1966, “Contact of Nominally Flat Surfaces,” Proc. R. Soc. Lond. A, 295, pp. 300–319). The rough surface is modeled as an ensemble of noninteracting asperities with identical radius of curvature and Gaussian distributed heights. By applying the double-Hertz theory to each individual asperity of the rough surface, the total normal forces for the rough surface are derived for loading and unloading stages, respectively, and a prominent adhesion hysteresis associated with dissipation energy is revealed. A dimensionless Tabor parameter is also introduced to account for general material properties. Our analysis results show that both the total pull-off force and the energy dissipation due to adhesive hysteresis are influenced by the surface roughness only through a single adhesion parameter, which measures statistically a competition between compressive and adhesive forces exerted by asperities with different heights. It is also found that smoother surfaces with a small adhesion parameter result in higher energy dissipation and pull-off force, while rougher surfaces with a large adhesion parameter lead to lower energy dissipation and pull-off force.

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Figures

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Fig. 1

Schematic illustration of an elastic spherical asperity in adhesive contact with a rigid half-space under a normal force P (negative when tensile). The surface traction consists of two terms: the Hertz pressure pH acting on the contact zone of radius a and an adhesive traction pA acting on the interaction zone of radius c, respectively.

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Fig. 2

The variations of a* and c* with respect to P* in the double-Hertz model with μ=1. The corresponding JKR and DMT limiting solutions are also shown for comparison. The noncontact extension in the c* curve is shown (dashed line) for completeness.

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Fig. 3

The equilibrium P-δ curves in the double-Hertz model for a single contact asperity under different values of the Tabor parameter. Here Pc represents the pull-off force and δc corresponds to the maximum extension.

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Fig. 4

Comparison between the exact double-Hertz solutions (lines) and the corresponding fitted curves (triangles)

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Fig. 5

Adhesive contact between a rigid smooth surface and a randomly rough elastic surface in (a) a real case and (b) a simplified model

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Fig. 6

The variation of normalized loading forces with respect to the normalized separation during a loading/unloading cycle for (a) μ=0.3 and (b) μ=5, respectively

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Fig. 7

Energy dissipation due to adhesion hysteresis as a function of the adhesion parameter 1/Δ¯ in a loading/unloading cycle

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Fig. 8

Total pull-off force for rough surfaces versus the adhesion parameter 1/Δ¯ for different values of μ

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