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Research Papers

Three-Dimensional Repeated Elasto-Plastic Point Contacts, Rolling, and Sliding

[+] Author and Article Information
W. Wayne Chen, Q. Jane Wang, Fan Wang, Leon M. Keer, Jian Cao

Department of Mechanical Engineering, Northwestern University, Evanston, IL 60208

J. Appl. Mech 75(2), 021021 (Feb 27, 2008) (12 pages) doi:10.1115/1.2755171 History: Received April 16, 2007; Revised June 11, 2007; Published February 27, 2008

Accumulative plastic deformation due to repeated loading is crucial to the lives of many mechanical components, such as gears, stamping dies, and rails in rail-wheel contacts. This paper presents a three-dimensional numerical model for simulating the repeated rolling or sliding contact of a rigid sphere over an elasto-plastic half-space. This model is a semi-analytical model based on the discrete convolution and fast Fourier transform algorithm. The half-space behaves either elastic-perfectly plastically or kinematic plastically. The analyses using this model result in histories of stress, strain, residual displacement, and plastic strain volume integral (PV) in the half-space. The model is examined through comparisons of the current results with those from the finite element method for a simple indentation test. The results of rolling contact obtained from four different hardening laws are presented when the load exceeds the theoretical shakedown limit. Shakedown and ratchetting behaviors are discussed in terms of the PV variation. The effect of friction coefficient on material responses to repeated sliding contacts is also investigated.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

Repeated rolling or sliding contacts of a rigid sphere on the surface of an elasto-plastic half-space

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Figure 2

Description of the mesh system: (a) the simulated domain with the mesh in a three-dimensional view and (b) the simulated contact surface with the mesh

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Figure 3

Strain hardening laws: (a) isotropic and (b) kinematic

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Figure 4

Evolutions of the plastic deformation region for 1≤ω∕ωc≤11: (a) from the current model and (b) from the FEM analysis in (26)

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Figure 5

Model verifications: (a) the dimensionless contact load versus the dimensionless interference and (b) the dimensionless contact area versus the dimensionless interference

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Figure 6

Simulation results obtained using the KP hardening law when the indenter passes the origin for the first three rolling contacts: (a) the effective plastic strain along the z-axis, (b) the dimensionless total von Mises stress along the z-axis, (c) the dimensionless residual von Mises stress along the z-axis, and (d) the residual surface normal displacement along the x-axis (positive for the inward displacement and negative for the outward displacement)

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Figure 7

Simulation results obtained using the KP hardening law when the indenter passes x=2aH for the first three rolling contacts: (a) the normal plastic strain εxxp along the x-axis at z=0.48aH, (b) the shear plastic strain εxzp along the x-axis at z=0.48aH, (c) the normal residual stress σxxr along the z-axis, and (d) the shear residual stress σxzr along the z-axis

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Figure 8

Comparisons of the results from different strain hardening laws for repeated rolling contacts: (a) variations of the effective plastic strain at z=0.48aH below the origin as a function of the number of passes, (b) the effective plastic strain along the z-axis after the third rolling pass, (c) the dimensionless total von Mises stress along the z-axis when the indenter passes the origin for the third time, (d) the residual surface normal displacement along the x-axis after the third rolling pass, (e) increments of the plastic strain volume integral as a function of the number of passes, and (f) curves of the shear strain component εxz versus the shear stress component σxz at z=0.48aH below the origin

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Figure 9

Shakedown and ratchetting behaviors: (a) the increment of the plastic strain volume integral versus the rolling pass number for different relative peak pressure values p0∕ks and (b) the PV increment versus the rolling pass number for different strain hardening laws (the numbers indicate the cycle number when shakedown occurs)

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Figure 10

Results of the repeated sliding contacts for different friction coefficients when the indenter passes the origin for the second time: (a) the dimensionless total von Mises stress along the z-axis, (b) the effective plastic strain along the z-axis, (c) the dimensionless residual von Mises stress along the z-axis, and (d) the residual surface displacement u3r along the x-axis

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Figure 11

Results of the repeated sliding contacts for different friction coefficients after the second passing: (a) the normal plastic strain εxxp along the x-axis at z=0.48aH, (b) the shear plastic strain εxzp along the x-axis at z=0.48aH, (c) the normal residual stress σxxr along the z-axis, and (d) the shear residual stress σxzr along the z-axis

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