Abstract
An elastic contact model for three-dimensional layered or coated materials under coupled normal and tangential loads, with consideration of partial slip effects, has been developed in this paper. The response functions for calculating the displacements and stresses were determined in the frequency domain by using the Papkovich–Neuber potentials. The partial slip contact problem was solved by a numerical procedure based on the conjugate Gradient method and fast Fourier transform technique. The contact pressure, surface shear tractions, stick ratios, rigid body displacements, and subsurface stresses are analyzed under different conditions with variations in the material properties and coating thickness. Results show that stiffer coatings tend to decrease the stick ratios and the rigid ball tangential displacements in comparison to those with compliant coatings under the same contact conditions. For stiffer coatings, the values of the von Mises stress and compressive surface stress increase and the positions of maximum von Mises stress move up to the surface; meanwhile, the distributions of the compressive stress become asymmetric due to the action of the tangential load.
Issue Section:
Contact Mechanics
1.
Johnson
, K. L.
, 1985, Contact Mechanics
, Cambridge University Press
, Cambridge, UK
.2.
Hills
, D. A.
, and Nowell
, D.
, 1994, Mechanics of Fretting Fatigue
, Kluwer
, Boston, MA
.3.
Giannakopoulos
, A. E.
, and Suresh
, S.
, 1998, “A Three-Dimensional Analysis of Fretting Fatigue
,” Acta Mater.
1359-6454, 46
(1
), pp. 177
–192
.4.
Cattaneo
, C.
, 1938, “Sul Contatto Di Due Corpi Elastici: Distribuzione Locale Degli Sforzi
,” Rend. Accad. Naz. Lincei
0392-7881, 27
, pp. 342
–348
, 474–478, 434–436.5.
Mindlin
, R. D.
, 1949, “Compliance of Elastic Bodies in Contact
,” ASME J. Appl. Mech.
0021-8936, 16
, pp. 259
–268
.6.
Ciavarella
, M.
, 1998, “The Generalized Cattaneo Partial Slip Plane Contact Problem. I—Theory
,” Int. J. Solids Struct.
0020-7683, 35
(18
), pp. 2349
–2362
.7.
Ciavarella
, M.
, 1998, “The Generalized Cattaneo Partial Slip Plane Contact Problem. II—Examples
,” Int. J. Solids Struct.
0020-7683, 35
(18
), pp. 2363
–2378
.8.
Ciavarella
, M.
, Hills
, D. A.
, and Moobola
, R.
, 1999, “Analysis of Plane and Rough Contacts, Subject to a Shearing Force
,” Int. J. Mech. Sci.
0020-7403, 41
(1
), pp. 107
–120
.9.
Kasarekar
, A. T.
, Bolander
, N. W.
, Sadeghi
, F.
, and Tseregounis
, S.
, 2007, “Modeling of Fretting Wear Evolution in Rough Circular Contacts in Partial Slip
,” Int. J. Mech. Sci.
0020-7403, 49
(6
), pp. 690
–703
.10.
Dini
, D.
, and Hills
, D. A.
, 2009, “Frictional Energy Dissipation in a Rough Hertzian Contact
,” ASME J. Tribol.
0742-4787, 131
(2
), p. 021401
.11.
Spence
, D. A.
, 1968, “Self-Similar Solutions to Adhesive Contact Problems With Incremental Loading
,” Proc. R. Soc. London, Ser. A
0950-1207, A305
(55
), pp. 55
–80
.12.
Spence
, D. A.
, 1973, “Eigenvalue Problem for Elastic Contact With Finite Friction
,” Proc. Cambridge Philos. Soc.
0068-6735, 73
, pp. 249
–268
.13.
Nowell
, D.
, Hills
, D. A.
, and Sackfield
, A.
, 1988, “Contact of Dissimilar Elastic Cylinders Under Normal and Tangential Loading
,” J. Mech. Phys. Solids
0022-5096, 36
(1
), pp. 59
–75
.14.
Kosior
, F.
, Guyot
, N.
, and Maurice
, G.
, 1999, “Analysis of Frictional Contact Problem Using Boundary Element Method and Domain Decomposition Method
,” Int. J. Numer. Methods Eng.
0029-5981, 46
(1
), pp. 65
–82
.15.
Guyot
, N.
, Kosior
, F.
, and Maurice
, G.
, 2000, “Coupling of Finite Elements and Boundary Elements Methods for Study of the Frictional Contact Problem
,” Comput. Methods Appl. Mech. Eng.
0045-7825, 181
(1–3
), pp. 147
–159
.16.
Xu
, B. Q.
, and Jiang
, Y. Y.
, 2002, “Elastic-Plastic Finite Element Analysis of Partial Slip Rolling Contact
,” ASME J. Tribol.
0742-4787, 124
(1
), pp. 20
–26
.17.
Li
, J.
, and Berger
, E. J.
, 2003, “A Semi-Analytical Approach to Three-Dimensional Normal Contact Problems With Friction
,” Comput. Mech.
0178-7675, 30
(4
), pp. 310
–322
.18.
Kalker
, J. J.
, 1977, “Variational Principles in Contact Elastostatics
,” J. Inst. Math. Appl.
0020-2932, 20
, pp. 199
–219
.19.
Nogi
, T.
, and Kato
, T.
, 1997, “Influence of a Hard Surface Layer on the Limit of Elastic Contact—Part I: Analysis Using a Real Surface Model
,” ASME J. Tribol.
0742-4787, 119
(3
), pp. 493
–500
.20.
Hu
, Y. Z.
, Barber
, G. C.
, and Zhu
, D.
, 1999, “Numerical Analysis for the Elastic Contact of Real Rough Surfaces
,” Tribol. Trans.
1040-2004, 42
(3
), pp. 443
–452
.21.
Polonsky
, I. A.
, and Keer
, L. M.
, 1999, “A Numerical Method for Solving Rough Contact Problems Based on the Multi-Level Multi-Summation and Conjugate Gradient Techniques
,” Wear
0043-1648, 231
(2
), pp. 206
–219
.22.
Liu
, S. B.
, Wang
, Q.
, and Liu
, G.
, 2000, “A Versatile Method of Discrete Convolution and FFT (DC-FFT) for Contact Analyses
,” Wear
0043-1648, 243
(1–2
), pp. 101
–111
.23.
Chen
, W. W.
, and Wang
, Q.
, 2008, “A Numerical Model for the Point Contact of Dissimilar Materials Considering Tangential Tractions
,” Mech. Mater.
0167-6636, 40
(11
), pp. 936
–948
.24.
Chen
, W. W.
, and Wang
, Q.
, 2009, “A Numerical Static Friction Model for Spherical Contacts of Rough Surfaces, Influence of Load, Material, and Roughness
,” ASME J. Tribol.
0742-4787, 131
(2
), p. 021402
.25.
Gallego
, L.
, Nélias
, D.
, and Jacq
, C.
, 2006, “A Comprehensive Method to Predict Wear and to Define the Optimum Geometry of Fretting Surfaces
,” ASME J. Tribol.
0742-4787, 128
(3
), pp. 476
–485
.26.
Gallego
, L.
, and Nélias
, D.
, 2007, “Modeling of Fretting Wear Under Gross Slip and Partial Slip Conditions
,” ASME J. Tribol.
0742-4787, 129
(3
), pp. 528
–535
.27.
Burmister
, D. M.
, 1945, “The General Theory of Stresses and Displacement in Layered System
,” J. Appl. Phys.
0021-8979, 16
, pp. 89
–94
.28.
Hannah
, M.
, 1951, “Contact Stress and Deformation in a Thin Elastic Layer
,” Q. J. Mech. Appl. Math.
0033-5614, 4
, pp. 94
–105
.29.
Meijers
, P.
, 1968, “The Contact Problem of a Rigid Cylinder on an Elastic Layer
,” Appl. Sci. Res.
0003-6994, 18
, pp. 353
–383
.30.
O’Sullivan
, T. C.
, and King
, R. B.
, 1988, “Sliding Contact Stress Field Due to a Spherical Indenter on a Layered Elastic Half-Space
,” ASME J. Tribol.
0742-4787, 110
, pp. 235
–240
.31.
Komvopoulos
, K.
, Saka
, N.
, and Suh
, N. P.
, 1987, “The Role of Hard Layers in Lubricated and Dry Sliding
,” ASME J. Tribol.
0742-4787, 109
, pp. 223
–231
.32.
Komvopoulos
, K.
, 1988, “Finite Element Analysis of a Layered Elastic Solid in Normal Contact With a Rigid Surface
,” ASME J. Tribol.
0742-4787, 110
, pp. 477
–485
.33.
Nowell
, D.
, and Hills
, D. A.
, 1988, “Contact Problems Incorporating Elastic Layers
,” Int. J. Solids Struct.
0020-7683, 24
(1
), pp. 105
–115
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