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Research Papers: Contact Mechanics

Contact Pressure and Residual Strain in 3D Elasto-Plastic Rolling Contact for a Circular or Elliptical Point Contact

[+] Author and Article Information
Thibaut Chaise, Daniel Nélias

 Université de Lyon, CNRS, INSA-Lyon, LaMCoS UMR5259, F69621, France

J. Tribol. 133(4), 041402 (Oct 06, 2011) (9 pages) doi:10.1115/1.4004878 History: Received September 03, 2010; Revised July 20, 2011; Published October 06, 2011; Online October 06, 2011

What is often referred to as a Hertzian contact can undergo plasticity either at the macroscale, due to an accidental overload, or at an asperity scale, due to the presence of surface defects and/or roughness. An elastic solution does not explicitly consider the surface velocity or loading history, but it is also apparent that a moving (rolling) load will not yield the same residual stress and strain distribution as a purely vertical loading/unloading. Three-dimensional (3D) analysis is also more complex than the two-dimensional (2D) problem because it implies a change in the surface conformity. This paper presents the results of a numerical investigation of frictionless elastic-plastic elliptical point contacts with a moving load, as compared to a purely vertical (indentation) load. In the present analysis, both bodies may behave in an elastic-plastic mode. Both kinematic and isotropic hardening are considered to account for repeated rolling contacts. The contact pressure and the plastic strain are found to be reduced when the two bodies are elastic-plastic, as compared to the case in which one of the bodies remains elastic. Numerical results also indicate that at a given load intensity, the maximum contact pressure and equivalent plastic strain are affected by the contact geometry (circular and elliptical point contacts) and differ significantly when the load is moving as compared to purely vertical indentation. Although the maximum elastic contact pressure (Hertz solution) is often used as a control parameter for rolling contact fatigue analysis, whatever the geometry of the contact (point, elliptical, or line contact), the results presented here show that the effective contact pressure and subsequent residual strains are strongly dependent on the contact geometry in the elastic-plastic regime.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

Flow chart of the numerical algorithm

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Figure 2

Hardening curves for the isotropic Swift hardening law and the kinematic Armstrong–Frederick law

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Figure 3

Pressure profile under maximum load for vertical indentation of an elastic ball on an EP flat surface with either isotropic or kinematic hardening (k = 1, PHertz  = 5.7 GPa)

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Figure 4

Equivalent plastic strain profile in depth at the center of the contact for vertical indentation of an elastic ball on an EP flat surface with either isotropic or kinematic hardening (k = 1, PHertz  = 5.7 GPa)

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Figure 5

Longitudinal profile for vertical indentation of an elastic ball on an EP flat surface with either isotropic or kinematic hardening (k = 1, PHertz  = 5.7 GPa)

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Figure 6

Pressure profiles generated by an elastic ball on an elastic-plastic flat during indentation and rolling. The dissymmetry of the pressure profile during rolling leads to a swift of the reaction force from the Oz axis.

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Figure 7

Kinematics of a ball rolling on a flat. A normal load P0 is applied to the ball. The dissymmetry of the contact pressure distribution leads to a swift of the reaction force Fc , which generates a moment compensated by the rolling moment MR .

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Figure 8

Longitudinal profile comparison of vertical loading/unloading with and without rolling (k = 1, PHertz  = 5.7 GPa, elastic ball on an EP flat surface with isotropic hardening; after one, two, and three cycles, with a rolling distance of 6.6a). Loading, rolling, and unloading are represented by the heavy arrows.

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Figure 9

Longitudinal profile comparison of vertical loading/unloading with and without rolling (k = 1, PHertz  = 5.7 GPa, elastic ball on an EP flat surface with kinematic hardening; after the five first cycles, with a rolling distance of 6.6a). Loading, rolling, and unloading are represented by the heavy arrows.

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Figure 10

Profiles in the plane (y = 0) of normalized stresses σxz generated by the normalized contact pressure at t and t − Δt separated by a rolling distance of 1.75a. First rolling cycle of an elastic sphere over an elastic plastic plane with kinematic hardening. Both represented states correspond to steady-state during the rolling load.

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Figure 11

Maximum contact pressure Pmax , normalized by the elastic solution PHertz (Hertz pressure); and equivalent plastic strain, ep (%), versus the load intensity, PHertz /σY , for two EP bodies pressed against each other, first cycle (same solution for the second cycle). E and EP refer to elastic and elastic-plastic, respectively. The elastic solution (E_E) is the Hertz solution.

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Figure 12

Maximum contact pressure Pmax normalized by the elastic solution PHertz (Hertz pressure), and the equivalent plastic strain ep (%) versus the load intensity PHertz /σY for the three first frictionless rolling cycles; circular point contact (k = 1)

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Figure 13

Maximum contact pressure Pmax normalized by the elastic solution, PHertz (Hertz pressure), and the equivalent plastic strain ep (%) versus the load intensity PHertz /σY for frictionless vertical loading for the first cycle cycle (same results for the second cycle); elliptical point contact (k = 8)

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Figure 14

Maximum contact pressure Pmax normalized by the elastic solution, PHertz (Hertz pressure), and the equivalent plastic strain ep (%) versus the load intensity PHertz /σY for the first three frictionless rolling cycles; elliptical point contact (k = 8)

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