0
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.

FIGURES IN THIS ARTICLE
<>
Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.

References

Hertz, H. , 1881, “ Ueber die Berührung Fester Elastischer Körper,” J. Reine Angew. Math., 92(4), pp. 156–171.
Tabor, D. , 1951, The Hardness of Metals (Oxford Classic Texts), Clarendon, London.
Chang, W. R. , Etsion, I. , and Bogy, D. B. , 1987, “ An Elastic-Plastic Model for the Contact of Rough Surfaces,” ASME J. Tribol., 109(2), pp. 257–263. [CrossRef]
Zhao, Y. , Maietta, D. M. , and Chang, L. , 2000, “ An Asperity Microcontact Model Incorporating the Transition From Elastic Deformation to Fully Plastic Flow,” ASME J. Tribol., 122(1), pp. 86–93. [CrossRef]
Kogut, L. , and Etsion, I. , 2002, “ Elastic-Plastic Contact Analysis of a Sphere and a Rigid Flat,” ASME J. Appl. Mech., 69(5), pp. 657–662. [CrossRef]
Etsion, I. , Kligerman, Y. , and Kadin, Y. , 2005, “ Unloading of an Elastic-Plastic Loaded Spherical Contact,” Int. J. Solids Struct., 42(13), pp. 3716–3729. [CrossRef]
Wang, Z. Q. , 2012, “ A Compact and Easily Accepted Continuous Model for the Elastic-Plastic Contact of a Sphere and a Flat,” ASME J. Appl. Mech., 80(1), p. 014506. [CrossRef]
Chang, W. R. , Etsion, I. , and Bogy, D. B. , 1988, “ Static Friction Coefficient Model for Metallic Rough Surfaces,” ASME J. Tribol., 110(1), pp. 57–63. [CrossRef]
Brizmer, V. , Kligerman, Y. , and Etsion, I. , 2006, “ The Effect of Contact Conditions and Material Properties on the Elasticity Terminus of a Spherical Contact,” Int. J. Solids Struct., 43(18–19), pp. 5736–5749. [CrossRef]
Johnson, K. L. , Kendall, K. , and Roberts, A. D. , 1971, “ Surface Energy and the Contact of Elastic Solids,” Proc. R. Soc. A, 324(1558), pp. 301–313. [CrossRef]
Derjaguin, B. V. , Muller, V. M. , and Toporov, Y. P. , 1975, “ Effect of Contact Deformations on the Adhesion of Particles,” J. Colloid Interface Sci., 53(75), pp. 314–326. [CrossRef]
Maugis, D. , 1992, “ Adhesion of Spheres: The JKR-DMT Transition Using a Dugdale Model,” J. Colloid Interface Sci., 150(92), pp. 243–269. [CrossRef]
Carpick, R. W. , Ogletree, D. F. , and Salmeron, M. , 1999, “ A General Equation for Fitting Contact Area and Friction vs Load Measurements,” J. Colloid Interface Sci., 211(2), pp. 395–400. [CrossRef] [PubMed]
Schwarz, U. D. , 2003, “ A Generalized Analytical Model for the Elastic Deformation of an Adhesive Contact Between a Sphere and a Flat Surface,” J. Colloid Interface Sci., 261(1), pp. 99–106. [CrossRef] [PubMed]
Chowdhury, S. K. R. , and Pollock, H. M. , 1981, “ Adhesion Between Metal Surfaces: The Effect of Surface Roughness,” Wear, 66(3), pp. 307–321. [CrossRef]
Chang, W. R. , Etsion, I. , and Bogy, D. B. , 1988, “ Adhesion Model for Metallic Rough Surfaces,” ASME J. Tribol., 110(1), pp. 50–56. [CrossRef]
Kogut, L. , and Etsion, I. , 2003, “ Adhesion in Elastic-Plastic Spherical Microcontact,” J. Colloid Interface Sci., 261(2), pp. 372–378. [CrossRef] [PubMed]
Majumder, S. , 2003, “ Contact Properties of a Micro Electromechanical Switch With Gold On-Gold Contacts,” Ph.D. thesis, Electrical and Computer Engineering, Northeastern University, Boston, MA.
Du, Y. , Chen, L. , McGruer, N. E. , Adams, G. G. , and Etsion, I. , 2007, “ A Finite Element Model of Loading and Unloading of an Asperity Contact With Adhesion and Plasticity,” J. Colloid Interface Sci., 312(2), pp. 522–528. [CrossRef] [PubMed]
Kadin, Y. , Kligerman, Y. , and Etsion, I. , 2008, “ Jump-In Induced Plastic Yield Onset of Approaching Microcontacts in the Presence of Adhesion,” J. Appl. Phys., 103(1), p. 013513. [CrossRef]
Kadin, Y. , Kligerman, Y. , and Etsion, I. , 2008, “ Loading-Unloading of an Elastic-Plastic Adhesive Spherical Microcontact,” J. Colloid Interface Sci., 321(1), pp. 242–250. [CrossRef] [PubMed]

Figures

Grahic Jump Location
Fig. 1

Schematic of the elastic–plastic regime

Grahic Jump Location
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).

Grahic Jump Location
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).

Grahic Jump Location
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).

Grahic Jump Location
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).

Grahic Jump Location
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).

Grahic Jump Location
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.

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In