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TECHNICAL PAPERS

# Fatigue Modeling for Elastic Materials With Statistically Distributed Defects

[+] Author and Article Information
Ilya I. Kudish

Science & Mathematics Department,  Kettering University, 1700 W. Third Avenue, Flint, MI 48504ikudish@kettering.edu

J. Appl. Mech 74(6), 1125-1133 (Jan 04, 2007) (9 pages) doi:10.1115/1.2722771 History: Received June 30, 2006; Revised January 04, 2007

## Abstract

The paper is devoted to formulation and analysis of a new model of structural fatigue that is a direct extension of the model of contact fatigue developed by Kudish (2000, STLE Tribol. Trans., 43, pp. 711–721). The model is different from other published models of structural fatigue (Collins, J. A., 1993, Failure of Materials and Mechanical Design: Analysis, Prediction, Prevention, 2nd ed., Wiley, New York) in a number of aspects such as statistical approach to material defects, stress analysis, etc. The model is based on fracture mechanics and fatigue crack propagation. The model takes into account local stress distribution, initial statistical distribution of defects versus their size, crack location, and orientation, and material fatigue resistance parameters. The assumptions used for the new model derivation are stated clearly and their validity is discussed. The model considers the kinetics of crack distribution by taking into account the fact that the crack distribution varies with the number of applied loading cycles due to crack growth. A qualitative and quantitative parametric analysis of the model is performed. Some analytical formulas for fatigue life as a function of the initial defect distribution, material fatigue resistance, and stress state are obtained. Examples of application of the model to predicting fatigue of beam bending and torsion and contact fatigue for tapered bearings is presented.

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## Figures

Figure 3

Illustration of nonuniform over material volume growth of the stress intensity factor k1 caused by crack growth under cycling loading for the number of loading cycles N1=0, N2, N3; 0<N2<N3. The data are obtained for the power n=9.

Figure 1

Schematic graph of crack propagation rate dl∕dN versus crack radius∕size l

Figure 2

Schematic view of a crack distribution evolution with number of loading cycles, N1<N2

Figure 4

Graphs of pitting probability 1−P(N) calculated for the basic set of parameters with μ=49.41μm, σ=7.61μm (μln=3.888+ln(μm), σln=0.1531), for the same set of parameters with changed initial value of crack mean half lengths μ=74.12μm (μln=4.300+ln(μm), σln=0.1024), and for the same set of parameters with changed initial value of crack standard deviation σ=11.423μm (μln=3.874+ln(μm), σln=0.2282)

Figure 5

Graphs of pitting probability 1−P(N) calculated for the basic set of parameters with λ=0.002 and for the same set of parameters with changed friction coefficient λ=0.004

Figure 6

Graphs of pitting probability 1−P(N) calculated for the basic set of parameters and for the same set of parameters with changed profile of residual stress q0 in such a way that at points where q0 is compressive, its magnitude is unchanged and at points where q0 is tensile, its magnitude is doubled

Figure 7

Bearing life-inclusion versus cumulative length correlation (Fig. 19 from (30) is reprinted with permission of the Iron and Steel Society)

## Errata

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