Modeling of the Rolling and Sliding Contact Between Two Asperities

[+] Author and Article Information
Vincent Boucly, Daniel Nélias

 LaMCoS, UMR CNRS 5259, INSA Lyon, 69621, Villeurbanne Cedex, France

Itzhak Green

George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0405

J. Tribol 129(2), 235-245 (Nov 27, 2006) (11 pages) doi:10.1115/1.2464137 History: Received April 19, 2006; Revised November 27, 2006

A semi-analytical method for the tridimensional elastic-plastic contact between two hemispherical asperities is proposed. The first part of the paper describes the algorithm used to deal with the normal contact, which can be either load-driven or displacement-driven (dd). Both formulations use the conjugate gradient method and the discrete convolution and fast Fourier transform (DC-FFT) technique. A validation of the code is made in the case of the displacement-driven formulation for an elastic-plastic body in contact with a rigid punch, simulating a nano-indentation test. Another new feature is the treatment of the contact between two elastic-plastic bodies. The model is first validated through comparison with the finite element method. The contact pressure distribution, the hydrostatic pressure and the equivalent plastic strain state below the contacting surfaces are also found to be strongly modified in comparison to the case of an elastic-plastic body in contact with a purely elastic body. The way to consider rolling and sliding motion of the contacting bodies consists of solving the elastic-plastic contact at each time step while upgrading the geometries as well as the hardening state along the moving directions. The derivations concerning the interference calculation at each step of the sliding process are then shown, and an application to the tugging between two spherical asperities in simple sliding (dd formulation) is made. The way to project the forces in the global reference is outlined, considering the macro-projection due to the angle between the plane of contact and the sliding direction, and the micro-projection due to the pile-up induced by the permanent deformation of the bodies due to their relative motion. Finally, a load ratio is introduced and results are presented in terms of forces, displacements, and energy loss in the contact.

Copyright © 2007 by American Society of Mechanical Engineers
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Figure 2

Pressure distribution at the end of the loading phase, in the plane y=0. Load 0.650N

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Figure 3

Updating of the initial geometry with ur at the beginning of a step. (a) Elastic body against elastic-plastic body. (b) Contact between 2 elastic-plastic bodies.

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Figure 4

Pressure distribution at the end of loading in the plane y=0. Load 11,179N, i.e., Ph=8GPa and Hertzian contact radius a=817μm.

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Figure 1

Load (mN) versus interference during the loading∕unloading phases. Max load 0.650N∕Max interference 372nm.

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Figure 5

Hydrostatic pressure at the end of loading at the center of the contact. Load 11,179N, i.e., Ph=8GPa, and Hertzian contact radius a=817μm.

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Figure 6

Maximum contact pressure Pmax (GPa) and equivalent plastic strain ep (%) versus the normal load (N)

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Figure 7

Dimensionless contact pressure versus dimensionless load found at the center of the contact

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Figure 8

Difference between the maximum contact pressures obtained assuming an E̱EP and EP̱EP behavior versus the dimensionless load L∕Lc

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Figure 9

Schematic view of the tugging between two interfering asperities in rolling∕sliding

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Figure 10

Updating at the end of the first loading step. (a) One of the bodies is elastic. (b) Both bodies are elastic-plastic. Case of pure rolling. (c) Both bodies are elastic-plastic. Case of rolling plus sliding contact.

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Figure 11

Displacement δd of body 2

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Figure 12

Correction of the term δd

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Figure 13

Representation of two consecutive states i−1 and i for the determination of θi−1

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Figure 14

Projection in the global reference of the force at a point of the contact surface

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Figure 15

Effect of the pile-up due to the slope of the residual displacement

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Figure 16

Dimensionless tangential force during sliding versus dimensionless sliding direction

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Figure 17

Dimensionless normal force during sliding versus dimensionless sliding direction

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Figure 18

Dimensionless net energy versus dimensionless interference

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Figure 19

Load ratio during sliding versus dimensionless sliding direction

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Figure 20

Dimensionless residual displacement versus dimensionless interference



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