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TECHNICAL PAPERS

# A Three-Dimensional Semianalytical Model for Elastic-Plastic Sliding Contacts

[+] Author and Article Information
Daniel Nélias

LaMCoS,  INSA Lyon, CNRS UMR 5259, Villeurbanne F69621, Francedaniel.nelias@insa-lyon.fr

Eduard Antaluca

LaMCoS,  INSA Lyon, CNRS UMR 5259, Villeurbanne F69621, France; Technical University “Gh. Asachi,” Iasi 700050, Romania

Vincent Boucly

LaMCoS,  INSA Lyon, CNRS UMR 5259, Villeurbanne F69621, France

Spiridon Cretu

Technical University “Gh. Asachi,” Iasi 700050, Romania

J. Tribol 129(4), 761-771 (May 24, 2007) (11 pages) doi:10.1115/1.2768076 History: Received May 12, 2006; Revised May 24, 2007

## Abstract

A three-dimensional numerical model based on a semianalytical method in the framework of small strains and small displacements is presented for solving an elastic-plastic contact with surface traction. A Coulomb’s law is assumed for the friction, as commonly used for sliding contacts. The effects of the contact pressure distribution and residual strain on the geometry of the contacting surfaces are derived from Betti’s reciprocal theorem with initial strain. The main advantage of this approach over the classical finite element method (FEM) is the computing time, which is reduced by several orders of magnitude. The contact problem, which is one of the most time-consuming procedures in the elastic-plastic algorithm, is obtained using a method based on the variational principle and accelerated by means of the discrete convolution fast Fourier transform (FFT) and conjugate gradient methods. The FFT technique is also involved in the calculation of internal strains and stresses. A return-mapping algorithm with an elastic predictor∕plastic corrector scheme and a von Mises criterion is used in the plasticity loop. The model is first validated by comparison with results obtained by the FEM. The effect of the friction coefficient on the contact pressure distribution, subsurface stress field, and residual strains is also presented and discussed.

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## Figures

Figure 1

Comparison of numerical results (SAM versus FEM, elastic solution, contact pressure distribution) for various friction coefficients: (a) μ=0, (b) μ=0.2, and (c) μ=0.4

Figure 2

Comparison of numerical results (SAM versus FEM, elastic solution, von Mises stress under load (profile at x=y=0)) for various friction coefficients: (a) μ=0, (b) μ=0.2, and (c) μ=0.4

Figure 3

Comparison of numerical results (SAM versus FEM, elastic-plastic solution, contact pressure distribution) for various friction coefficients: (a) μ=0, (b) μ=0.2, and (c) μ=0.4

Figure 4

Comparison of numerical results (SAM versus FEM, elastic-plastic solution, von Mises stress under load (profile at x=y=0)) for various friction coefficients: (a) μ=0, (b) μ=0.2, and (c) μ=0.4

Figure 5

Comparison of numerical results (SAM versus FEM, elastic-plastic solution, equivalent plastic strain (profile at x=y=0)) for various friction coefficients: (a) μ=0, (b) μ=0.2, and (c) μ=0.4

Figure 6

Influence of the friction coefficient on the critical load (circle symbols) and interference (square symbols) at the onset of yielding, normalized by the values for the frictionless contact

Figure 7

Maximum of the equivalent plastic strain versus the corresponding Hertzian contact pressure normalized by the microyield stress for various friction coefficients

Figure 8

Pressure distribution for various friction coefficients. Normal load of 5000N.

Figure 9

Figure 10

Value and location of the maximum von Mises stress (under load) versus the friction coefficient

Figure 11

Residual von Mises stress profile in the plane y=0. Normal load of 5000N; frictionless contact.

Figure 12

Equivalent plastic strain profile versus depth at x=y=0. (a) Regular view. (b) Zoom of (a).

Figure 13

Hydrostatic pressure after unloading (residual), profile at x=y=0, frictionless contact, for various normal loads ranging from 1000Nto5000N

Figure 14

Hydrostatic pressure after unloading (residual), profile at x=y=0, normal load of 5000N, for various friction coefficients ranging from 0 to 0.5

## Errata

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