Abstract
Understanding the elastoplastic contact loading–unloading behavior between a sphere and a rigid plane is a problem in the field of contact mechanics. In this study, a bilinear strain-hardening material model was used to study the frictionless elastoplastic contact loading–unloading behavior of a sphere in contact with a rigid plane across a large range of interference. A two-dimensional axisymmetric finite element model was established. The effects of the tangent modulus (Et) and the ratio of the reduced elastic modulus to the yield strength (E/Y) on the contact load, residual interference, and contact area of the spherical contact model during loading–unloading were analyzed for a series of different interferences. The effects of Et and E/Y on the elastoplastic contact loading–unloading behavior were amplified with increasing interference. With an increase in Et, the effect of E/Y on the contact behavior was diminished. A new constitutive model for elastoplastic contact loading–unloading is presented. The model accommodates the calculation of the contact load, contact area, and residual interference of the spherical contact model across a large range of interference. The proposed model was verified by comparing its predictions with those of previous models. In the range of material properties considered in this work, the current research results can be applied to particle and contact mechanics.
References
1.
Johnson
, K. L.
, 1985
, Contact Mechanics
, 2nd ed., Cambridge University Press
, New York
.2.
Ghaednia
, H.
, Wang
, X.
, Saha
, S.
, Xu
, Y.
, Sharma
, A.
, and Jackson
, R. L.
, 2017
, “A Review of Elastic–Plastic Contact Mechanics
,” Appl. Mech. Rev.
, 69
(6
), p. 060804
. 3.
Zhang
, W.
, Chen
, J.
, Wang
, C.
, Liu
, D.
, and Zhu
, L.
, 2022
, “Analysis of Elastic–Plastic Loading and Unloading Contact Between Ellipsoid and Rigid Flat
,” Proc. Inst. Mech. Eng. Part J J. Eng. Tribol.
4.
Weng
, P.
, Yin
, X.
, Hu
, W.
, Yuan
, H.
, Chen
, C.
, Ding
, H.
, Yu
, B.
, Xie
, W.
, Jiang
, L.
, and Wang
, H.
, 2021
, “Piecewise Linear Deformation Characteristics and a Contact Model for Elastic–Plastic Indentation Considering Indenter Elasticity
,” Tribol Int.
, 162
, p. 107114
. 5.
Zhao
, B.
, Zhang
, S.
, Wang
, Q.
, Zhang
, Q.
, and Wang
, P.
, 2015
, “Loading and Unloading of a Power-Law Hardening Spherical Contact Under Stick Contact Condition
,” Int. J. Mech. Sci.
, 94–95
, pp. 20
–26
. 6.
Li
, B.
, Li
, P.
, Zhou
, R.
, Feng
, X.
, and Zhou
, K.
, 2022
, “Contact Mechanics in Tribological and Contact Damage-Related Problems: A Review
,” Tribol Int.
, 171
, p. 107534
. 7.
Chen
, J.
, Zhang
, W.
, Wang
, C.
, Liu
, D.
, and Zhu
, L.
, 2022
, “Effect of Strain Hardening and Ellipticity on Elastic–Plastic Contact Behaviour Between Ellipsoids and Rigid Planes
,” Machines
, 10
(6
), p. 488
. 8.
Zhang
, W.
, Chen
, J.
, Wang
, C.
, Liu
, D.
, and Zhu
, L.
, 2022
, “Research on Elastic–Plastic Contact Behavior of Hemisphere Flattened by a Rigid Flat
,” Materials
, 15
(13
), p. 4527
. 9.
Becker
, V.
, and Kamlah
, M.
, 2021
, “A Theoretical Model for the Normal Contact Force of Two Elastoplastic Ellipsoidal Bodies
,” ASME J. Appl. Mech.
, 88
(3
), p. 031006
. 10.
Ghaednia
, H.
, and Jackson
, R. L.
, 2013
, “The Effect of Nanoparticles on the Real Area of Contact, Friction, and Wear
,” ASME J. Tribol.
, 135
(4
), p. 041603
. 11.
Lontin
, K.
, and Khan
, M.
, 2021
, “Interdependence of Friction, Wear, and Noise: A Review
,” Friction
, 9
(6
), pp. 1319
–1345
. 12.
Gholami
, R.
, Ghaemi
, K.
, Silani
, M.
, and Akbarzadeh
, S.
, 2020
, “Experimental and Numerical Investigation of Friction Coefficient and Wear Volume in the Mixed-Film Lubrication Regime With ZnO Nano-Particle
,” J. Appl. Fluid Mech.
, 13
(3
), pp. 993
–1001
. 13.
Gao
, C.
, Proudhon
, H.
, and Liu
, M.
, 2019
, “Three-Dimensional Finite Element Analysis of Shallow Indentation of Rough Strain-Hardening Surface
,” Friction
, 7
(6
), pp. 587
–602
. 14.
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
. 15.
Salari
, S.
, and Beheshti
, A.
, 2021
, “Asperity-Based Contact and Static Friction With Provision for Creep: A Review
,” Surf. Interfaces
, 24
, p. 101144
. 16.
Jackson
, R. L.
, and Streator
, J. L.
, 2006
, “A Multi-scale Model for Contact Between Rough Surfaces
,” Wear
, 261
(11–12
), pp. 1337
–1347
. 17.
Hertz
, H.
, 1881
, “Ueber die Berührung Fester Elastischer Körper
,” J. Reine Angew. Math.
, 92
(4
), pp. 156
–171
. 18.
Kogut
, L.
, and Etsion
, I.
, 2002
, “Elastic–Plastic Contact Analysis of a Sphere and a Rigid Flat
,” Int. J. Appl. Mech.
, 69
(5
), pp. 657
–662
. 19.
Green
, I.
, 2004
, “Poisson Ratio Effects and Critical Values in Spherical and Cylindrical Hertzian Contacts
,” Int. J. Appl. Mech. Eng.
, 10
(3
), pp. 451
–462
. 20.
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
. 21.
Sahoo
, P.
, and Chatterjee
, B.
, 2010
, “A Finite Element Study of Elastic–Plastic Hemispherical Contact Behavior Against a Rigid Flat Under Varying Modulus of Elasticity and Sphere Radius
,” Engineering
, 2
(4
), pp. 205
–211
. 22.
Shankar
, S.
, and Mayuram
, M. M.
, 2008
, “Effect of Strain Hardening in Elastic–Plastic Transition Behavior in a Hemisphere in Contact With a Rigid Flat
,” Int. J. Solids Struct.
, 45
(10
), pp. 3009
–3020
. 23.
Shankar
, S.
, and Mayuram
, M. M.
, 2008
, “A Finite Element Based Study on the Elastic–Plastic Transition Behavior in a Hemisphere in Contact With a Rigid Flat
,” ASME J. Tribol.
, 130
(4
), p. 044502
. 24.
Megalingam
, A.
, and Mayuram
, M. M.
, 2014
, “A Comprehensive Elastic–Plastic Single-Asperity Contact Model
,” Tribol Trans.
, 57
(2
), pp. 324
–335
. 25.
Megalingam
, A.
, and Hanumanth
, K. S.
, 2021
, “A Complete Elastic–Plastic Spherical Asperity Contact Model With the Effect of Isotropic Strain Hardening
,” Proc. Inst. Mech. Eng. Part J J. Eng. Tribol.
, 235
(4
), pp. 820
–829
. 26.
Peng
, W.
, and Bhushan
, B.
, 2003
, “Transient Analysis of Sliding Contact of Layered Elastic–Plastic Solids With Rough Surfaces
,” Microsyst. Technol.
, 9
(5
), pp. 340
–345
. 27.
Majumder
, S.
, McGruer
, N. E.
, Adams
, G. G.
, Zavracky
, P. M.
, Morrison
, R. H.
, and Krim
, J.
, 2001
, “Study of Contacts in an Electrostatically Actuated Microswitch
,” Sens. Actuators, A
, 93
(1
), pp. 19
–26
. 28.
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
. 29.
Song
, Z.
, and Komvopoulos
, K.
, 2014
, “An Elastic–Plastic Analysis of Spherical Indentation: Constitutive Equations for Single-Indentation Unloading and Development of Plasticity Due to Repeated Indentation
,” Mech. Mater.
, 76
, pp. 93
–101
. 30.
Zhao
, J. H.
, Nagao
, S.
, and Zhang
, Z. L.
, 2012
, “Loading and Unloading of a Spherical Contact: From Elastic to Elastic–Perfectly Plastic Materials
,” Int. J. Mech. Sci.
, 56
(1
), pp. 70
–76
. 31.
Zhao
, B.
, Zhang
, S.
, Wang
, P.
, and Hai
, Y.
, 2015
, “Loading–Unloading Normal Stiffness Model for Power-Law Hardening Surfaces Considering Actual Surface Topography
,” Tribol Int.
, 90
, pp. 332
–342
. 32.
Sharma
, A.
, and Jackson
, R. L.
, 2017
, “A Finite Element Study of an Elasto-Plastic Disk or Cylindrical Contact Against a Rigid Flat in Plane Stress With Bilinear Hardening
,” Tribol. Lett.
, 65
(3
), p. 112
. 33.
Ghaednia
, H.
, Mifflin
, G.
, Lunia
, P.
, O’Neill
, E. O.
, and Brake
, M. R. W.
, 2020
, “Strain Hardening From Elastic–Perfectly Plastic to Perfectly Elastic Indentation Single Asperity Contact
,” Front. Mech. Eng.
, 6
, p. 60
. 34.
Ghaednia
, H.
, Brake
, M. R. W.
, Berryhill
, M.
, and Jackson
, R. L.
, 2019
, “Strain Hardening From Elastic–Perfectly Plastic to Perfectly Elastic Flattening Single Asperity Contact
,” ASME J. Tribol.
, 141
(3
), p. 031402
. 35.
Ghaednia
, H.
, Pope
, S. A.
, Jackson
, R. L.
, and Marghitu
, D. B.
, 2016
, “A Comprehensive Study of the Elasto-Plastic Contact of a Sphere and a Flat
,” Tribol Int.
, 93
, pp. 78
–90
. 36.
Brizmer
, V.
, Kligerman
, Y.
, and Etsion
, I.
, 2006
, “Elastic–Plastic Spherical Contact Under Combined Normal and Tangential Loading in Full Stick
,” Tribol. Lett.
, 25
(1
), pp. 61
–70
. Copyright © 2022 by ASME
You do not currently have access to this content.
