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Research Papers: Other (Seals, Manufacturing)

A 3D Finite Element Study of Fatigue Life Dispersion in Rolling Line Contacts

[+] 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

School of Mechanical Engineering,  Purdue University, West Lafayette, IN 47907vasilios.bakolas@schaeffler.com

Alexander Liebel

Schaeffler Technologies GmbH & Co. KG, 91074 Herzogenaurach, D-91074, Germanyliebeaex@schaeffler.com

J. Tribol 133(4), 042202 (Oct 06, 2011) (10 pages) doi:10.1115/1.4005000 History: Received May 09, 2011; Revised September 02, 2011; Published October 06, 2011; Online October 06, 2011

Rolling contact fatigue of rolling element bearings is a statistical phenomenon that is strongly affected by the heterogeneous nature of the material microstructure. Heterogeneity in the microstructure is accompanied by randomly distributed weak points in the material that lead to scatter in the fatigue lives of an otherwise identical lot of rolling element bearings. Many life models for rolling contact fatigue are empirical and rely upon correlation with fatigue test data to characterize the dispersion of fatigue lives. Recently developed computational models of rolling contact fatigue bypass this requirement by explicitly considering the microstructure as a source of the variability. This work utilizes a similar approach but extends the analysis into a 3D framework. The bearing steel microstructure is modeled as randomly generated Voronoi tessellations wherein each cell represents a material grain and the boundaries between them constitute the weak planes in the material. Fatigue cracks initiate on the weak planes where oscillating shear stresses are the strongest. Finite element analysis is performed to determine the magnitude of the critical shear stress range and the depth where it occurs. These quantities exhibit random variation due to the microstructure topology which in turn results in scatter in the predicted fatigue lives. The model is used to assess the influence of (1) topological randomness in the microstructure, (2) heterogeneity in the distribution of material properties, and (3) the presence of inherent material flaws on relative fatigue lives. Neither topological randomness nor heterogeneous material properties alone account for the dispersion seen in actual bearing fatigue tests. However, a combination of both or the consideration of material flaws brings the model’s predictions within empirically observed bounds. Examination of the critical shear stress ranges with respect to the grain boundaries where they occur reveals the orientation of weak planes most prone to failure in a three-dimensional sense that was not possible with previous models.

Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 3

Histograms of grain geometric features (a) volume, (b) vertices, (c) edges, and (d) faces

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Figure 12

Critical shear stress reversals experienced by elements according to the orientation of the grain boundary on which they occur: (a) single RVE, (b) composite results of several RVEs, and (c) bounding contours by percentage of the largest critical shear stress reversal

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Figure 13

Representative Gaussian distribution of elastic modulus applied to grains of the microstructure model

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Figure 14

Weibull probability plots of relative lives for six selected domains from Fig. 9 with 100 Gaussian distributions of E each

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Figure 15

Weibull probability plot of relative fatigue lives for 98 homogeneous and heterogeneous MMs

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Figure 16

Flaw insertion procedure

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Figure 17

Comparison of Weibull slopes for material flaws study

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Figure 18

Trend in Weibull slope versus flaws with analytical and empirical benchmarks

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Figure 1

Microscopy image of bearing steel with some grain boundaries identified (microscopy image courtesy of Schaeffler Technologies)

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Figure 2

Voronoi microstructure model construction process: (a) bounding volume and regular arrangement of generating points along surfaces to be connected to elastic foundation model, (b) oversaturation of generating points, (c) remaining generating points after cropping, and (d) final Voronoi tessellation

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Figure 4

(a) Discretized Voronoi cell and (b) exploded view

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Figure 5

Microstructure model for Hertzian line contact analysis with representative volume element (RVE), constant strain tetrahedra (CST), and linear strain tetrahedra (LST) regions delineated

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Figure 6

Finite element model for simulating a rolling contact cycle

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Figure 7

Example histories of the resolved shear traction vector as measured on the grain boundary for different elements in the same grain during a rolling contact pass

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Figure 8

XY locations of the largest critical shear stress ranges experienced within the RVEs of 100 microstructure models with homogeneous material properties (E = 200 GPa, ν = 0.3, pmax  = 2.0 GPa)

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Figure 9

XZ locations of the largest critical shear stress ranges experienced within the RVEs of 100 microstructure models with homogeneous material properties (E = 200 GPa, ν = 0.3, pmax  = 2.0 GPa)

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Figure 10

Magnitudes of the largest critical shear stress ranges experienced within the RVEs of 100 microstructure models with homogeneous material properties (E = 200 GPa, ν = 0.3, pmax  = 2.0 GPa)

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Figure 11

Weibull probability plot of relative lives for 98 microstructure models with homogeneous material properties (E = 200 GPa, ν = 0.3, pmax  = 2.0 GPa)

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