0
Research Papers: Contact Mechanics

Model for Elastic–Plastic Contact Between Rough Surfaces

[+] Author and Article Information
Zhiqian Wang

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

Xingna Liu

Henan Key Laboratory of Photovoltaic Materials,
College of Physics and Electronic Engineering,
Henan Normal University,
Xinxiang 453007, China

1Corresponding author.

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received March 21, 2018; final manuscript received May 20, 2018; published online July 12, 2018. Assoc. Editor: Liming Chang.

J. Tribol 140(5), 051402 (Jul 12, 2018) (8 pages) Paper No: TRIB-18-1119; doi: 10.1115/1.4040385 History: Received March 21, 2018; Revised May 20, 2018

This paper studies elastic–plastic contact between Greenwood–Williamson (GW) rough surfaces, on which there are many asperities with the same radius whose height obeys the Gaussian distribution. A new plasticity index is defined as the ratio of the standard deviation of the height of asperities on the rough surface to the single-asperity critical displacement (the transition point from the elastic to the elastic-fully plastic deformation regime), which is linearly proportional to the GW plasticity index to the power of 2. The equations for the load/area–separation relationship of rough surfaces are presented based on Wang and Wang's smooth model of singe-asperity elastic–plastic contact, which is an improvement of the Kogut–Etsion (KE) empirical model based on finite element analysis (FEA) data. The load/area–separation relationship can be described by empirical Gaussian functions. The load–area relationship of rough surfaces is approximately linear. The average pressure is only function of the new plasticity index. According to Wang and Wang's conclusion that Etsion et al. single-asperity elastic–plastic loading (EPL) index is approximately equal to the ratio of the single-asperity residual plastic contact displacement to the single-asperity total elastic–plastic contact displacement, the equations for the relationship between Kadin et al. modified plasticity index (MPI) and separation of rough surfaces are also presented. In addition, the MPI is approximately linearly proportional to the separation between rough surfaces for a given new plasticity index ranging from 5 to 30. When the new plasticity index is smaller than 5, due to the large proportion of the elastic deformation in the total deformation, the MPI slightly deviate from linearity.

FIGURES IN THIS ARTICLE
<>
Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.

References

Greenwood, J. A. , and Williamson, J. B. P. , 1966, “ Contact of Nominally Flat Surfaces,” Proc. R. Soc. London A: Math. Phys. Eng. Sci., 295(1442), pp. 300–319. [CrossRef]
Hertz, H. , 1881, “ Ueber Die Berührung Fester Elastischer Körper,” J. Für Die Reine. Angew. Math., 92(4), pp. 156–171.
Mikic, B. , 1971, “ Analytical Studies of Contact of Nominally Flat Surfaces; Effect of Previous Loading,” ASME J. Lubr. Technol., 93(4), pp. 451–456. [CrossRef]
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]
Jones, R. E. , 2004, “ Models for Contact Loading and Unloading of a Rough Surface,” Int. J. Eng. Sci., 42(17–18), pp. 1931–1947. [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]
Kadin, Y. , Kligerman, Y. , and Etsion, I. , 2006, “ Unloading an Elastic-Plastic Contact of Rough Surfaces,” J. Mech. Phys. Solids, 54(12), pp. 2652–2674. [CrossRef]
Jackson, R. L. , and Green, I. , 2005, “ A Finite Element Study of Elasto-Plastic Hemispherical Contact against a Rigid Flat,” ASME J. Tribol., 127(2), pp. 343–354. [CrossRef]
Jackson, R. L. , and Green, I. , 2006, “ A Statistical Model of Elasto-Plastic Asperity Contact Between Rough Surfaces,” Tribol. Int., 39(9), pp. 906–914. [CrossRef]
Pei, L. , Hyun, S. , Molinari, J. F. , and Robbins, M. O. , 2005, “ Finite Element Modeling of Elasto-Plastic Contact Between Rough Surfaces,” J. Mech. Phys. Solids, 53(11), pp. 2385–2409. [CrossRef]
Wang, Z. Q. , 2013, “ 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]
Wang, Z. Q. , and Wang, J. F. , 2017, “ Model of a Sphere-Flat Elastic-Plastic Adhesion Contact,” ASME J. Tribol., 139(4), p. 041401. [CrossRef]
Greenwood, J. A. , and Tripp, J. H. , 1970, “ The Contact of Two Nominally Flat Rough Surfaces,” Proc. Inst. Mech. Eng., 185(1), pp. 625–633. [CrossRef]
Kogut, L. , and Etsion, I. , 2003, “ A Finite Element Based Elastic-Plastic Model for the Contact of Rough Surfaces,” Tribol. Trans., 46(3), pp. 383–390. [CrossRef]

Figures

Grahic Jump Location
Fig. 2

Area–separation relationship of rough surface at σs/δc of 5, 10, 15, 20, 25, and 30 during loading

Grahic Jump Location
Fig. 3

Relationship between P/P0 and d/σs at σs/δc of 5, 10, 15, 20, 25, and 30 during loading

Grahic Jump Location
Fig. 4

Relationship between A/A0 and d/σs at σs/δc of 5, 10, 15, 20, 25, and 30 during loading

Grahic Jump Location
Fig. 5

Relationship between P/P0 and A/A0 at σs/δc of 5, 10, 15, 20, 25, and 30 during loading

Grahic Jump Location
Fig. 6

Load–separation relationship of rough surface at σs/δc of 0.5, 1.5, 2.5, 3.5, and 4.5 during loading

Grahic Jump Location
Fig. 7

Area–separation relationship of rough surface at σs/δc of 0.5, 1.5, 2.5, 3.5, and 4.5 during loading

Grahic Jump Location
Fig. 8

Relationship between P/P0 and d/σs at σs/δc of 0.5, 1.5, 2.5, 3.5, and 4.5 during loading

Grahic Jump Location
Fig. 9

Relationship between A/A0 and d/σs at σs/δc of 0.5, 1.5, 2.5, 3.5, and 4.5 during loading

Grahic Jump Location
Fig. 10

Relationship between P/P0 and A/A0 at σs/δc of 0.5, 1.5, 2.5, 3.5, and 4.5 during loading

Grahic Jump Location
Fig. 11

Relationship between P0/A0 and σs/δc during loading

Grahic Jump Location
Fig. 1

Load–separation relationship of rough surface at σs/δc of 5, 10, 15, 20, 25, and 30 during loading

Grahic Jump Location
Fig. 12

MPI–separation relationship of rough surface at σs/δc of 5, 10, 15, 20, 25, and 30

Grahic Jump Location
Fig. 13

MPI–separation relationship of rough surface at σs/δc of 1, 1.5, 2.5, 3.5, and 4.5

Tables

Errata

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