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Research Papers: Contact Mechanics

# A Voronoi FE Fatigue Damage Model for Life Scatter in Rolling Contacts

[+] Author and Article Information

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

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

J. Tribol 132(2), 021404 (Mar 11, 2010) (14 pages) doi:10.1115/1.4001012 History: Received February 24, 2009; Revised January 04, 2010; Published March 11, 2010; Online March 11, 2010

## Abstract

It has been widely accepted that the microstructure of bearing materials can significantly affect their rolling contact fatigue (RCF) lives. Hence, microlevel topological features of materials will be of significant importance to RCF investigation. In order to estimate the fatigue lives of bearing elements and account for the effects of topological randomness of the bearing materials, in this work, damage mechanics modeling approach is incorporated into a Voronoi finite element method recently developed by the authors. Contrary to most of the life models existing in the literature for estimating the RCF lives, the current model considers microcrack initiation, coalescence, and propagation stages. The proposed model relates the fatigue life to a damage parameter $D$, which is a measure of the gradual material degradation under cyclic loading. In this investigation, 40 semi-infinite domains with different microstructural distributions are subjected to a moving Hertzian pressure. Using the fatigue damage model developed, the initiation and total lives of the 40 domains are obtained. Also, the effects of initial material flaws and inhomogeneous material properties (in the form of normal distribution of the elastic modulus) on the fatigue lives are investigated. It is observed that the fatigue lives calculated and their Weibull slopes are in good agreement with previous experimental and analytical results. It is noted that introducing inhomogeneous material properties and initial flaws within the domains decreases the fatigue lives and increases their scatters.

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## Figures

Figure 1

Subsurface cracks in the rolling contact fatigue (8)

Figure 2

Mechanism of surface initiated pitting (11)

Figure 3

(a) Discretizing a domain with the Voronoi elements; (b) dividing a Voronoi element to finer triangular elements

Figure 4

S-N curve reported by Styri (45) for AISI 52100 bearing steel under the completely reversed torsion

Figure 5

Jump-in-cycles method: damage evolution is assumed to be piecewise linear with respect to the number of cycles

Figure 6

Inserting two normal and tangential springs between the faces of the microcrack. These model the compressive and tangential stiffnesses between the faces of the microcrack.

Figure 7

Statistical distribution of elements in one of the generated domains: distribution of (a) the number of sides of the Voronoi elements in the domain and (b) of the elements’ area

Figure 8

(a) The comparison of the life curves obtained for the different proportionality constant values, (b) details of the life curve obtained for Cf=0.4, and (c) the effect of the tangential spring on the maximum range of the shear stress during the fatigue process

Figure 9

The nonlinear variation in the (a) damage and (b) elastic modulus of a randomly selected failed element in the domain with the number of cycles; (c) the experimental fatigue damage evolution of AISI 316 stainless steel (38)

Figure 10

The spalling mechanism (crack propagation) in the damaged zone under the contact surface. When increasing the number of loading cycles, (a) a microcrack is created close to the theoretical depth of the maximum range of shear stress, (b) more microcracks are created and some of them coalesce into longer cracks, and (c) the cracks move toward the contact surface and form an elliptical spall.

Figure 11

The comparison of (a) the values and (b) the depths of the Δτxy obtained using the 40 undamaged domains for cases of the same material properties, normal distribution of the elastic modulus, and the two initial flaws

Figure 12

The fatigue lives obtained for the 40 domains under Pmax=2 GPa

Figure 13

The comparison of the Weibull distributions of the (a) initiation and (b) total lives of the 40 domains for cases of the same material properties, normal distribution of the elastic modulus, and two initial flaws

Figure 14

The normal Gaussian distribution of the elastic modulus employed for the domain 1 with 10% variation in the average value of 200 GPa

Figure 15

A sample simulated RVE and the two initial flaws introduced in it

Figure 16

The comparison of Pmax versus L10 curve obtained by the current model and the existing experimental and theoretical results for AISI 52100 bearing steel

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