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Review Article

A Review of Elastic–Plastic Contact Mechanics

[+] Author and Article Information
Hamid Ghaednia, Xianzhang Wang, Swarna Saha, Yang Xu, Aman Sharma

Department of Mechanical Engineering,
Auburn University,
Auburn, AL 36849

Robert L. Jackson

Department of Mechanical Engineering,
Auburn University,
Auburn, AL 36849
e-mail: robert.jackson@eng.auburn.edu

Manuscript received September 16, 2016; final manuscript received October 4, 2017; published online November 14, 2017. Editor: Harry Dankowicz.

Appl. Mech. Rev 69(6), 060804 (Nov 14, 2017) (30 pages) Paper No: AMR-16-1072; doi: 10.1115/1.4038187 History: Received September 16, 2016; Revised October 04, 2017

In typical metallic contacts, stresses are very high and result in yielding of the material. Therefore, the study of contacts which include simultaneous elastic and plastic deformation is of critical importance. This work reviews the current state-of-the-art in the modeling of single asperity elastic–plastic contact and, in some instances, makes comparisons to original findings of the authors. Several different geometries are considered, including cylindrical, spherical, sinusoidal or wavy, and axisymmetric sinusoidal. As evidenced by the reviewed literature, it is clear that the average pressure during heavily loaded elastic–plastic contact is not governed by the conventional hardness to yield strength ratio of approximately three, but rather varies according to the boundary conditions and deformed geometry. For spherical contact, the differences between flattening and indentation contacts are also reviewed. In addition, this paper summarizes work on tangentially loaded contacts up to the initiation of sliding. As discussed briefly, the single asperity contact models can be incorporated into existing rough surface contact model frameworks. Depending on the size of a contact, the material properties can also effectively change, and this topic is introduced as well. In the concluding discussion, an argument is made for the value of studying hardening and other failure mechanisms, such as fracture as well as the influence of adhesion on elastic–plastic contact.

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Angadi, S. V. , Jackson, R. L. , Choe, S. Y. , Flowers, G. T. , Lee, B. Y. , and Zhong, L. , 2012, “ A Multiphysics Finite Element Model of a 35A Automotive Connector Including Multiscale Rough Surface Contact,” ASME J. Electron. Packag., 134(1), p. 011001. [CrossRef]
Jackson, R. L. , Malucci, R. D. , Angadi, S. , and Polchow, J. R. , 2009, “ A Simplified Model of Multiscale Electrical Contact Resistance and Comparison to Existing Closed Form Models,” 55th IEEE Holm Conference on Electrical Contacts (Holm), Vancouver, BC, Canada, Sept. 14--16, pp. 27–34.
Zhang, X. , and Jackson, R. L. , 2014, “ The Influence of Multiscale Roughness on the Real Contact Area and Contact Resistance Between Real Reference Surfaces,” 27th International Conference on Electrical Contacts (ICEC), Dresden, Germany, June 22–26, pp. 1–6. http://ieeexplore.ieee.org/document/6857137/
Wilson, W. E. , Angadi, S. V. , and Jackson, R. L. , 2008, “ Electrical Contact Resistance Considering Multi-Scale Roughness,” IEEE Holm Conference on Electrical Contacts (Holm), Orlando, FL, Oct. 27–29, pp. 190–197.
Jackson, R. L. , Liu, H. , and Leray, D. , 2013, “ A Comparison of the Predictions of a Finite Element Model and Multiscale Model for a Rough MEMS Electrical Contact,” 59th IEEE Holm Conference on Electrical Contacts (Holm), Newport, RI, Sept. 22–25, pp. 1–9.
Morag, Y. , and Etsion, I. , 2007, “ Resolving the Contradiction of Asperities Plastic to Elastic Mode Transition in Current Contact Models of Fractal Rough Surfaces,” Wear, 262(5–6), pp. 624–629. [CrossRef]
Chung, J. C. , and Lin, J. F. , 2004, “ Fractal Model Developed for Elliptic Elastic-Plastic Asperity Microcontacts of Rough Surfaces,” ASME J. Tribol., 126(4), pp. 646–654. [CrossRef]
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Almeida, L. , Ramadoss, R. , Jackson, R. , Ishikawa, K. , and Yu, Q. , 2007, “ Laterally Actuated Multicontact MEMS Relay Fabricated Using Metal MUMPS Process: Experimental Characterization and Multiscale Contact Modeling,” J. Micro/Nanolithogr. MEMS MOEMS, 6(2), p. 023009. [CrossRef]
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Figures

Grahic Jump Location
Fig. 1

Schematic of the contact between a cylinder and a flat surface. Here, b is the width of the contact area (often referred to as contact width), and L is the length of the cylinder.

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Fig. 2

Comparison between Eqs. (6) and (10) for indentation (a) and flattening (b) and with FEM results

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Fig. 3

In the indentation models, the sphere is rigid and the flat is deforming

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Fig. 4

In the flattening models, the flat is rigid and the sphere is deforming

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Fig. 5

Contact radius versus the yield strength ratio for a constant deflection

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Fig. 6

Average pressure or hardness versus the yield strength ratio for spherical contact

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Fig. 7

Contact force versus the yield strength ratio for spherical contact

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Fig. 8

Comparison between predicted contact radii during indentation for different contact models

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Fig. 9

Comparison between predicted contact forces during indentation for different contact models

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Fig. 10

Comparison between predicted contact radii during flattening for different contact models

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Fig. 11

Comparison between predicted contact forces during flattening for different contact models

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Fig. 12

Schematic of an axisymmetric sinusoidal asperity loaded with a rigid flat

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Fig. 13

Dimensionless contact pressure area relation for different values of E/Sy at E=100 and Δ/λ=0.0125

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Fig. 14

Relation between pep*/pe* and E′/Sy·Δ/λ for all the cases analyzed

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Fig. 15

Prediction of the critical pressure required to induce complete contact relative to the yield strength for an elastic–plastic axisymmetric sinusoidal asperity

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Fig. 16

Contour plot of the sinusoidal surface geometry

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Fig. 17

The dimensionless tangential load versus the dimensionless tangential displacement for different parameters

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Fig. 18

The effects of different parameters on the static friction coefficient

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