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Research Papers: Contact Mechanics

An Approach for Modeling Material Grain Structure in Investigations of Hertzian Subsurface Stresses and Rolling Contact Fatigue

[+] Author and Article Information
Nick Weinzapfel

School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907weinzapf@purdue.edu

Farshid Sadeghi

School of Mechanical Engineering, Purdue University, West Lafayette, IN 47907sadeghi@ecn.purdue.edu

Vasilios Bakolas

Department of Bearing Fundamentals, Schaeffler Technologies GmbH & Co. KG, 91074 Herzogenaurach, Germanyvasilios.bakolas@schaeffler.com

J. Tribol 132(4), 041404 (Oct 08, 2010) (12 pages) doi:10.1115/1.4002521 History: Received January 06, 2010; Revised September 01, 2010; Published October 08, 2010; Online October 08, 2010

The continuum theory of elasticity and/or homogeneously discretized finite element models have been commonly used to investigate and analyze subsurface stresses in Hertzian contacts. These approaches, however, do not effectively capture the influence of the random microstructure topology on subsurface stress distributions in Hertzian contacts. In this paper, a finite element model for analyzing subsurface stresses in an elastic half-space subjected to a general Hertzian contact load with explicit consideration of the material microstructure topology is presented. The random internal geometry of polycrystalline microstructures is modeled using a 3D Voronoi tessellation, where each Voronoi cell represents a distinct material grain. The grains are then meshed using finite elements, and an algorithm was developed to eliminate poorly shaped elements resulting from “near degeneracy” in the Voronoi tessellations. Hertzian point and line contacts loads are applied as distributed surface loads, and the model’s response is evaluated with commercial finite element software ABAQUS . Internal stress results obtained from the current model compare well with analytical solutions from theory of elasticity. The influence of the internal microstructure topology on the subsurface stresses is demonstrated by analyzing the model’s response to an over rolling element using a critical plane approach.

Copyright © 2010 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Microscopy image of bearing steel (image courtesy of Schaeffler KG)

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Figure 2

Cross section of 3D Voronoi tessellation

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Figure 3

Hertzian pressure distribution geometry

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Figure 4

Copying points for periodic surfaces

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Figure 5

Algorithm for meshing the microstructure topology model

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Figure 6

Discretized Voronoi cell geometry: (a) meshed cell and (b) exploded view

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Figure 7

Voronoi cell short edge collapsing algorithm

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Figure 8

Microstructure topology models: (a) Hertzian point contact domain and (b) Hertzian line contact domain (for clarity, the hexahedral elements comprising the remainder of the elastic half-space are not shown)

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Figure 9

Applying kinematic constraints for multidirectional periodicity: (a) unit cell with complete set of boundary nodes, (b) constrained nodes for X-periodicity, (c) constrained nodes for Y-periodicity, (d) constrained nodes for XY-periodicity, (e) incompatible set of master nodes, and (f) compatible set of master nodes

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Figure 10

Elemental Tresca stresses in Hertzian point contacts (μ=0.0) and corresponding comparison of stresses under the central point of contact for various locations of the pressure center: (a) xc=0.0a and (b) xc=3.6a

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Figure 11

Elemental Tresca stresses in Hertzian line contacts (μ=0.0) and corresponding comparison of stresses under the central point of contact for various locations of the pressure center: (a) xc=0.0a and (b) xc=4.5a

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Figure 12

Comparison of subsurface stresses under the center of Hertzian point contact for various locations of the pressure center: (a) xc=0.0a and (b) xc=1.0a

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Figure 13

Comparison of subsurface stresses under the center of Hertzian line contact for various locations of the pressure center: (a) xc=0.0a and (b) xc=2.0a

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Figure 14

Stress transformation from Cartesian reference frame to local grain boundary coordinate system

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Figure 15

Resolved shear vector histories in plane of grain boundary and their critical shear stress ranges using the longest chord method

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