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TECHNICAL PAPERS

# An Elliptical Elastic-Plastic Microcontact Model Developed for an Ellipsoid in Contact With a Smooth Rigid Flat

[+] Author and Article Information
Li Po Lin

Department of Mechanical Engineering, Southern Taiwan University of Technology, Tainan, Taiwan, 710, Republic of China

Jen Fin Lin1

Department of Mechanical Engineering, National Cheng Kung University, Tainan, Taiwan 701, Republic of Chinajflin@mail.ncku.edu.tw

1

Corresponding author.

J. Tribol 129(4), 772-782 (Jun 10, 2007) (11 pages) doi:10.1115/1.2768077 History: Received December 05, 2006; Revised June 10, 2007

## Abstract

The determination of the elastoplastic deformation regime arising at the microcontact of a deformable ellipsoid and a rigid smooth flat was the main purpose of this study. One-eighth of an ellipsoid and a flat plate were taken as the contact bodies in the finite element analysis, and a mesh scheme of multisize elements was applied. Two observed phenomena regarding the contact pressures and the equivalent von Mises stresses formed at the contact area are given in order to identify the inception of the fully plastic deformation regime of an ellipsoid with an ellipticity $ke$. If the ellipticity $(k)$ of an elliptical contact area is defined as the length ratio of the minor axis to the major axis, it is asymptotic to the $ke$ value when the interference is sufficiently increased, irrespective of the $ke$ value. The dimensionless interference regime associated with the elastoplastic deformation regime is narrowed by increasing the ellipticity of the ellipsoid $(ke)$. Significant differences in the microcontact parameters such as the contact pressure, the contact area, and the contact load were found to be a function of the interference and the $ke$ parameter of an ellipsoid. The interferences corresponding to the inceptions of the elastoplastic and fully plastic deformation regimes are both increased if the $ke$ value is lowered. The interference, the contact area, and the contact load predicted by the present model for the behavior demonstrated at the inception of the elastoplastic deformation regime are lower than those obtained from the Horng model (Horng, J. H., 1998, “An Elliptical Elastic-Plastic Asperity Microcontact Model for Rough Surfaces  ,” ASME J. Tribol., 120, pp. 82–88) and the Jeng-Wang model (Jeng, Y. R., and Wang, P. Y., 2003, “An Elliptical Microcontact Model Considering Elastic, Elastoplastic, and Plastic Deformation  ,” ASME J. Tribol., 125, pp. 232–240). Big differences in the results of the average contact pressure, the contact area, and the contact load among the above microcontact models are discussed. The discrepancies are also explained from the developments of these models and boundary conditions set for the elastoplastic deformation regime.

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## Figures

Figure 1

The contact schematic diagram of a rigid flat with an ellipsoid (1∕8 volume)

Figure 2

The FEA and the meshed model for simulations (There is no need of meshing for the rigid flat)

Figure 3

The distribution of the dimensionless contact pressure on the 1∕4 contact surface for ke=1∕5, and δ∕δec=40

Figure 4

The distribution of the dimensionless equivalent von Mises stress on the 1∕4 contact surface for ke=1∕5, and δ∕δec=40

Figure 5

Variations of the dimensionless critical interference formed at the inception of the elastoplastic deformation and the fully plastic deformation regimes, respectively, with ke

Figure 6

Variations of the ellipticity of contact area with the dimensionless interference in the elastoplastic deformation regime

Figure 7

Variations of the dimensionless average contact pressure with the dimensionless interference

Figure 8

Variations of the dimensionless contact area with the dimensionless interference

Figure 12

Comparisons of the dimensionless average contact pressures obtained using the Horng model, the JW model, and the present model

Figure 14

Comparisons of the dimensionless contact loads obtained using the Horng model, the JW model, and the present model

Figure 9

Variations of the dimensionless contact load with the dimensionless interference

Figure 10

Variations of the dimensionless contact area with the dimensionless contact load

Figure 11

Comparisons of contact parameters evaluated at yielding for the Horng model, the JW model, and the present model: (a) the maximum contact pressure, (b) the critical interference, (c) the critical contact area, and (d) the critical contact load

Figure 13

Comparisons of the dimensionless contact areas obtained using the Horng model, the JW model, and the present model

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