Abstract
Currently existing finite element (FE) Lagrangian models of elastic–plastic spherical contact are costly in terms of computing time to reach vanishing tangential stiffness at sliding inception. A coupled Eulerian–Lagrangian (CEL) model with explicit dynamic analysis and power-law hardening is proposed to resolve this problem. The CEL model also avoids convergence problem caused by excessive distortion of elements in Lagrangian models. Static friction coefficient at sliding inception is investigated and compared with available experimental results. It is found that the proposed new CEL model is more efficient and accurate compared to previously published results of Lagrangian models.
Issue Section:
Technical Brief
References
1.
Ogilvy
, J. A.
, 1992
, “Numerical Simulation of Elastic-Plastic Contact Between Anisotropic Rough Surfaces
,” J. Phys. D. Appl. Phys.
, 25
(12
), pp. 1798
–1809
. 10.1088/0022-3727/25/12/0162.
Kogut
, L.
, and Etsion
, I.
, 2004
, “A Static Friction Model for Elastic-Plastic Contacting Rough Surfaces
,” ASME J. Tribol.
, 126
(1
), pp. 34
–40
. 10.1115/1.16094883.
Karamiş
, M. B.
, and Selçuk
, B.
, 1993
, “Analysis of the Friction Behaviour of Bolted Joints
,” Wear
, 166
(1
), pp. 73
–83
. 10.1016/0043-1648(93)90281-P4.
Gao
, H.
, and Barber
, G. C.
, 2002
, “Microcontact Model for Paper-Based Wet Friction Materials
,” ASME J. Tribol.
, 124
(2
), pp. 414
–419
. 10.1115/1.14306745.
Li
, M.
, Khonsari
, M. M.
, McCarthy
, D. M. C.
, and Lundin
, J.
, 2014
, “Parametric Analysis for a Paper-Based Wet Clutch With Groove Consideration
,” Tribol. Int.
, 80
(12
), pp. 222
–233
. 10.1016/j.triboint.2014.06.0236.
Lumbantobing
, A.
, and Komvopoulos
, K.
, 2005
, “Static Friction in Polysilicon Surface Micromachines
,” J. Microelectromech. Syst.
, 14
(4
), pp. 651
–663
. 10.1109/JMEMS.2005.8507197.
Subhash
, G.
, Corwin
, A. D.
, and De Boer
, M. P.
, 2011
, “Evolution of Wear Characteristics and Frictional Behavior in MEMS Devices
,” Tribol. Lett.
, 41
(1
), pp. 177
–189
. 10.1007/s11249-010-9696-z8.
Mindlin
, R. D.
, 1949
, “Compliance of Elastic Bodies in Contact
,” ASME J. Appl. Mech. ASME
, 16
, pp. 259
–268
.9.
Mindlin
, R. D.
, and Deresiewicz
, H.
, 1953
, “Elastic Spheres in Contact Under Varying Oblique Forces
,” ASME J. Appl. Mech.
, 20
, pp. 327
–344
. 10.1007/978-1-4613-8865-4_3510.
Cattaneo
, C.
, 1938
, “Sul Contatto Di Due Corpi Elastici: Distribuzione Locale Deglisforzi
,” Rend. dell’Accademia Naz. dei Lincei
, 27
(1
), pp. 342
–348
. 434–6, and 74–78.11.
Ovcharenko
, A.
, Halperin
, G.
, and Etsion
, I.
, 2008
, “Experimental Study of Adhesive Static Friction in a Spherical Elastic-Plastic Contact
,” ASME J. Tribol.
, 130
(2
), p. 021401
. 10.1115/1.284224712.
Bowden
, F. P.
, and Tabor
, D.
, 1954
, The Friction and Lubrication of Solids
, Oxford University Press
, Oxford
.13.
Etsion
, I.
, 2010
, “Revisiting the Cattaneo-Mindlin Concept of Interfacial Slip in Tangentially Loaded Compliant Bodies
,” ASME J. Tribol.
, 132
(2
), p. 020801
. 10.1115/1.400123814.
Hamilton
, G. M.
, 1983
, “Explicit Equations for the Stresses Beneath a Sliding Spherical Contact
,” Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci.
, 197
(1
), pp. 53
–59
. 10.1243/PIME_PROC_1983_197_076_0215.
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
. 10.1115/1.326157516.
Kogut
, L.
, and Etsion
, I.
, 2003
, “A Semi-Analytical Solution for Sliding Inception of a Spherical Contact
,” ASME J. Tribol.
, 125
(3
), pp. 499
–506
. 10.1115/1.153819017.
Brizmer
, V.
, Kligerman
, Y.
, and Etsion
, I.
, 2007
, “Elastic-Plastic Spherical Contact Under Combined Normal and Tangential Loading in Full Stick
,” Tribol. Lett.
, 25
(1
), pp. 61
–70
. 10.1007/s11249-006-9156-y18.
Ovcharenko
, A.
, Halperin
, G.
, and Etsion
, I.
, 2008
, “In Situ and Real-Time Optical Investigation of Junction Growth in Spherical Elastic-Plastic Contact
,” Wear
, 264
(11–12
), pp. 1043
–1050
. 10.1016/j.wear.2007.08.00919.
Tabor
, D.
, 1959
, “Junction Growth in Metallic Friction: The Role of Combined Stresses and Surface Contamination
,” Proc. R. Soc. London. Ser. A. Math. Phys. Sci.
, 251
(1266
), pp. 378
–393
. 10.1098/rspa.1959.011420.
Rabinowicz
, E.
, 1965
, Friction and Wear of Materials
, Wiley
, New York
.21.
Wu
, A.
, Shi
, X.
, and Polycarpou
, A. A.
, 2012
, “An Elastic-Plastic Spherical Contact Model Under Combined Normal and Tangential Loading
,” ASME J. Appl. Mech.
, 79
(5
), p. 051001
. 10.1115/ijtc2011-6112622.
ABAQUS
, 2017
, User’s Manual and Theory Manual
, Hibbitt, Karlsson and Sorensen, Inc
, Providence, RI
.23.
Abdelhafeez
, A. M.
, Soo
, S. L.
, Aspinwall
, D.
, Dowson
, A.
, and Arnold
, D.
, 2016
, “A Coupled Eulerian Lagrangian Finite Element Model of Drilling Titanium and Aluminium Alloys
,” SAE Int. J. Aerosp.
, 9
(1
), pp. 198
–207
. 10.4271/2016-01-212624.
Al-Badour
, F.
, Merah
, N.
, Shuaib
, A.
, and Bazoune
, A.
, 2013
, “Coupled Eulerian Lagrangian Finite Element Modeling of Friction Stir Welding Processes
,” J. Mater. Process. Technol.
, 213
(8
), pp. 1433
–1439
. 10.1016/j.jmatprotec.2013.02.01425.
Gao
, W. M.
, Wang
, L.
, Coffey
, J. K.
, and Daver
, F.
, 2018
, “Understanding the Scratch Behaviour of Polymeric Materials With Surface Texture
,” Mater. Des.
, 146
(10
), pp. 38
–48
. 10.1016/j.matdes.2018.02.07426.
Ducobu
, F.
, Rivière-Lorphèvre
, E.
, and Filippi
, E.
, 2016
, “Application of the Coupled Eulerian-Lagrangian (CEL) Method to the Modeling of Orthogonal Cutting
,” Eur. J. Mech. A/Solids
, 59
(5
), pp. 58
–66
. 10.1016/j.euromechsol.2016.03.00827.
Bonetto
, A.
, Nélias
, D.
, Chaise
, T.
, and Zamponi
, L.
, 2019
, “A Coupled Euler-Lagrange Model for More Realistic Simulation of Debris Denting in Rolling Element Bearings
,” Tribol. Trans.
, 62
(5
), pp. 760
–778
. 10.1080/10402004.2019.161791528.
Gao
, W. M.
, Wang
, L.
, Coffey
, J. K.
, and Daver
, F.
, 2018
, “Finite Element Simulation of Scratch on Polypropylene Panels
,” Mater. Des.
, 140
(4
), pp. 400
–408
. 10.1016/j.matdes.2017.12.01829.
ASM International
, 2002
, Atlas of Stress-Strain Curves
, ASM International
, Materials Park, OH
.30.
Zhao
, B.
, Zhang
, S.
, and Keer
, L. M.
, 2017
, “Spherical Elastic-Plastic Contact Model for Power-Law Hardening Materials Under Combined Normal and Tangential Loads
,” ASME J. Tribol.
, 139
(2
), p. 021401
. 10.1115/1.403364731.
Hammelmuller
, F.
, and Zehetner
, C.
, 2015
, “Increasing Numerical Efficiency in Coupled Eulerian-Lagrangian Metal Forming Simulations
,” Proceedings of the 8th International Conference on Computational Plasticity—Fundamentals and Applications, CIMNE
, Barcelona, Spain
, Sept. 1–3
, pp. 727
–733
.32.
Wu
, A.
, and Shi
, X.
, 2013
, “Numerical Investigation of Adhesive Wear and Static Friction Based on the Ductile Fracture of Junction
,” ASME J. Appl. Mech.
, 80
(4
), p. 041032
. 10.1115/1.402310933.
Hertz
, H.
, 1882
, “Ueber Die Beruhrung Fester Elastischer Korper
,” J. Reine Angew. Math.
, 1882
(92
), pp. 156
–171
. 10.1515/crll.1882.92.15634.
Brizmer
, V.
, Zait
, Y.
, Kligerman
, Y.
, and Etsion
, I.
, 2006
, “The Effect of Contact Conditions and Material Properties on Elastic-Plastic Spherical Contact
,” J. Mech. Mater. Struct.
, 1
(5
), pp. 865
–879
. 10.2140/jomms.2006.1.86535.
Zolotarevskiy
, V.
, Kligerman
, Y.
, and Etsion
, I.
, 2011
, “The Evolution of Static Friction for Elastic-Plastic Spherical Contact in Pre-Sliding
,” ASME J. Tribol.
, 133
(3
), p. 034502
. 10.1115/1.400430436.
Ovcharenko
, A.
, Halperin
, G.
, Verberne
, G.
, and Etsion
, I.
, 2007
, “In Situ Investigation of the Contact Area in Elastic–Plastic Spherical Contact During Loading–Unloading
,” Tribol. Lett.
, 25
(2
), pp. 153
–160
. 10.1007/s11249-006-9164-y37.
Rice
, J. R.
, 1976
, Localization of Plastic Deformation
, Brown University
, Providence, RI
38.
Chen
, Z.
, and Etsion
, I.
, 2019
, “Model for the Static Friction Coefficient in a Full Stick Elastic-Plastic Coated Spherical Contact
,” Friction
, 7
(6
), pp. 613
–624
. 10.1007/s40544-018-0251-5Copyright © 2020 by ASME
You do not currently have access to this content.
