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RESEARCH PAPERS

# A New Method for Elastic-Plastic Contact Analysis of a Deformable Sphere and a Rigid Flat

[+] Author and Article Information
Li Po Lin

Department of Mechanical Engineering, National Cheng Kung University, Tainan, 701, Taiwan R.O.C.

Jen Fin Lin1

Department of Mechanical Engineering, National Cheng Kung University, Tainan, 701, Taiwan R.O.C.jflin@mail.ncku.edu.tw

1

Corresponding author.

J. Tribol 128(2), 221-229 (Oct 18, 2005) (9 pages) doi:10.1115/1.2164469 History: Received May 02, 2005; Revised October 18, 2005

## Abstract

A new method is developed in the present study to determine the elastoplastic regime of a spherical asperity in terms of the interference of two contact surfaces. This method provides an efficient way to solve the problem of discontinuities often present in the reported solutions for the contact load and area or the gradients of these parameters obtained at either the inception or the end of the elastoplastic regime. The well-established solutions for the elastic regime and experimental data of metal materials using indentation tests are provided as the references to determine the errors of these contact parameters due to the use of the finite-element method. These numerical errors provide the basis to adjust the contact area and contact load of a rigid sphere in contact with a flat such that the dimensionless mean contact pressure $Pave∕Y$ ($Y$: the yielding strength) and the dimensionless contact load $Fpc∕Fec$ ($Fec$, $Fpc$: the contact loads corresponding to the inceptions of the elastoplastic and fully plastic regimes, respectively) reaches the criteria arising at the inception of the fully plastic regime, which are available from the reports of the indentation tests for metal materials. These two criteria are however not suitable for the present case of a rigid flat in contact with a deformable sphere. In the case of a rigid flat in contact with a deformable sphere, the proportions in the adjustments of these contact parameters are given individually the same as those arising in the indentation case. The elastoplastic regime for each of these two contact mechanisms can thus be determined independently. By assuming that the proportion of adjustment in the elastoplastic regime is a linear function, the discontinuities appearing in these contact parameters are absent from the two ends of the elastoplastic regime in the present study. These results are presented and compared with the published results.

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## Figures

Figure 1

The contact of a spherical asperity and a rigid flat

Figure 2

The simplified contact mechanism used in the simulation of a rigid flat contacts with a deformable sphere

Figure 3

Four meshing schemes shown in the RF case: (a) A2 type; (b) A5 type.

Figure 4

(a) The meshing scheme shown in the RS case; (b) the local magnification of (a) nearby the contact region. (b) the local magnification of (a) nearby the contact region.

Figure 7

Variations of Pave∕Pec with δ∕δec. They are evaluated by five types of meshing schemes and compared with the theoretical solutions of the RF case in the elastic regime.

Figure 6

Variations of F∕Fec with δ∕δec. They are evaluated by five types of meshing schemes and compared with the theoretical solutions of the RF case in the elastic regime.

Figure 9

Variations of A∕Aec with δ∕δec at three deformation regimes

Figure 10

Variations of F∕Fec with δ∕δec at three deformation regimes

Figure 11

Variations of Pave∕Y with δ∕δec at three deformation regimes

Figure 12

Variations of A∕Aec with F∕Fec at three deformation regimes

Figure 8

(a)Variations of P∕Y with r∕a as well as δ∕δec. They are shown for (a) the RS case, and (b) the RF case.

Figure 5

Variations of A∕Aec with δ∕δec. They are evaluated by five types of meshing schemes and compared with the theoretical solutions of the RF case in the elastic regime.

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