A new numerical model for the three-dimensional contact analysis of a layered elastic–perfectly plastic half space with another rough surface is presented. The model is based on a variational principle in which the real area of contact and contact pressure distribution are those which minimize the total complementary potential energy. A quasi-Newton method is used to find the minimum. The influence coefficients matrix is determined using the Papkovich–Neuber potentials with fast Fourier transformation. The model is extended to elastic–perfectly plastic contacts in dry and wet conditions. Contact analyses have been performed to predict contact statistics of layered elastic/plastic solids with rough surfaces using this model. The effects of the stiffness of the layer and the substrate, layer thickness, as well as normal load are studied. Optimum layer parameters are identified to provide low friction/stiction and wear.
Issue Section:
Technical Papers
Keywords:
mechanical contact,
surface topography,
rough surfaces,
elasticity,
plasticity,
wear,
tribology,
friction,
numerical analysis,
Contact Analysis,
Multilayered Solid Deformation,
Real Area of Contact,
Friction
Topics:
Pressure,
Solids,
Stress,
Surface roughness,
Variational principles,
Friction,
Deformation,
Wear
1.
Bhushan
, B.
, 1998
, “Contact Mechanics of Rough Surfaces in Tribology: Multiple Asperity Contact
,” Tribol. Lett.
, 4
, pp. 1
–35
.2.
Bhushan, B., 1999, Principles and Applications of Tribology, Wiley, New York.
3.
Bhushan
, B.
, 1996
, “Contact Mechanics of Rough Surfaces in Tribology: Single Asperity Contact
,” Appl. Mech. Rev.
, 49
, pp. 275
–298
.4.
Plumet
, S.
, and Dubourg
, M.-C.
, 1998
, “A 3-D Model for a Multilayered Body Loaded Normally and Tangentially Against a Rigid Body: Application to Specific Coatings
,” ASME J. Tribol.
, 120
, pp. 668
–676
.5.
Kral
, E. R.
, and Komvopoulos
, K.
, 1997
, “Three-Dimensional Finite Element Analysis of Subsurface Stress and Strain Fields Due to Sliding Contact on an Elastic-Plastic Layered Medium
,” ASME J. Tribol.
, 119
, pp. 332
–341
.6.
Merriman
, T.
, and Kannel
, J.
, 1989
, “Analyses of the Role of Surface Roughness on Contact Stresses Between Elastic Cylinders with and without Soft Surface Coating
,” ASME J. Tribol.
, 111
, pp. 87
–94
.7.
Cole
, S. J.
, and Sayles
, R. S.
, 1991
, “A Numerical Model for the Contact of Layered Elastic Bodies with Real Rough Surfaces
,” ASME J. Tribol.
, 114
, pp. 334
–340
.8.
Mao
, K.
, Bell
, T.
, and Sun
, Y.
, 1997
, “Effect of Sliding Friction on Contact Stresses for Multilayered Elastic Bodies with Rough Surfaces
,” ASME J. Tribol.
, 119
, pp. 476
–480
.9.
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.
, 119
, pp. 493
–500
.10.
Hestenes
, M. R.
, and Stiefel
, E.
, 1952
, “Methods of Conjugate Gradients for Solving Linear Systems
,” J. Res. Nat. Bur. Stand.
, 49
, pp. 409
–436
.11.
Winther
, R.
, 1980
, “Some Superlinear Convergence Results for the Conjugate Gradient Method
,” SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal.
, 17
, pp. 14
–17
.12.
Tian
, X.
, and Bhushan
, B.
, 1996
, “A Numerical Three-dimensional Model for the Contact of Rough Surfaces by Variational Principle
,” ASME J. Tribol.
, 118
, pp. 33
–41
.13.
Tian
, X.
, and Bhushan
, B.
, 1996
, “The Micro-Meniscus Effect of a Thin Liquid Film on the Static Friction of Rough Surface Contact
,” J. Phys. D: Appl. Phys.
, 29
, pp. 163
–178
.14.
Hu
, Y. Z.
, and Tonder
, K.
, 1992
, “Simulation of 3-D Random Surface by 2-D Digital Filter and Fourier Analysis
,” Int. J. Mach. Tools Manuf.
, 32
, pp. 82
–90
.15.
Chilamakuri
, S. K.
, and Bhushan
, B.
, 1998
, “Contact Analysis of non-Gaussian random surfaces
,” Proc. Inst. Mech. Eng. Part J: J. Eng. Tribol.
, 212
, pp. 19
–32
.16.
Johnson, K. L., 1985, Contact Mechanics, Cambridge University Press, Cambridge, UK.
17.
Richards, T. H., 1977, Energy Methods in Stress Analysis: With an Introduction to Finite Element Techniques, Halsted Press, New York.
18.
Kalker
, J. J.
, and van Randen
, Y.
, 1972
, “A Minimum Principle for Frictionless Elastic Contact with Application to Non-Hertzian Half-Space Contact Problems
,” J. Eng. Math.
, 6
, pp. 193
–206
.19.
Love
, A. E. H.
, 1929
, “The Stress Produced in a Semi-Infinite Solid by Pressure on Part of the Boundary
,” Proc. R. Soc. London, Ser. A
, 228
, pp. 377
–420
.20.
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.
, 110
, pp. 235
–240
.21.
Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P., 1999, Numerical Recipes in FORTRAN, the Art of Scientific Computing, 2nd ed., Cambridge University Press, Cambridge, UK.
22.
Ju
, Y.
, and Farris
, T. N.
, 1996
, “Special Analysis of Two-dimensional Contact Problems
,” ASME J. Tribol.
, 118
, pp. 320
–328
.23.
Stanley
, H. M.
, and Kato
, T.
, 1997
, “An FFT-Based Method for Rough Surface Contact
,” ASME J. Tribol.
, 119
, pp. 481
–485
.24.
Ai
, X.
, and Sawamiphakdi
, K.
, 1999
, “Solving Elastic Contact Between Rough Surfaces as an Unconstrained Strain Energy Minimization by Using CGM and FFT Techniques
,” ASME J. Tribol.
, 121
, pp. 639
–647
.25.
Bhattacharya
, A. K.
, and Nix
, W. D.
, 1988
, “Analysis of Elastic and Plastic Deformation Associated with Indentation Testing of Thin Films on Substrates
,” Int. J. Solids Struct.
, 24
, pp. 1287
–1298
.26.
Oliver
, W. C.
, and Pharr
, G. M.
, 1992
, “An Improved Technique for determining Hardness and Elastic Modulus Using Load and Displacement Sensing Indentation Experiments
,” J. Mater. Res.
, 7
, pp. 1564
–1583
.27.
Gao
, C.
, Tian
, X.
, and Bhushan
, B.
, 1995
, “A Meniscus Model for Optimization of Texturing and Liquid Lubrication of Magnetic Thin-Film Rigid Disks
,” Tribol. Trans.
, 38
, pp. 201
–212
.28.
Stewart, J., 1995, Calculus, 3rd ed., Brooks/Cole, Pacific Grove, CA.
Copyright © 2001
by ASME
You do not currently have access to this content.
