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Research Papers: Contact Mechanics

Numerical Modeling of Distributed Inhomogeneities and Their Effect on Rolling-Contact Fatigue Life

[+] Author and Article Information
Qinghua Zhou

State Key Laboratory
of Mechanical Transmission,
Chongqing University,
Chongqing 400030, China;
School of Aeronautics and Astronautics,
Sichuan University,
Chengdu 610065, China;
Department of Mechanical Engineering,
Northwestern University,
Evanston, IL 60208

Lechun Xie

Department of Mechanical Engineering,
Northwestern University,
Evanston, IL 60208;
State Key Laboratory
of Metal Matrix Composites,
Shanghai Jiao Tong University,
Shanghai 200240, China

Xiaoqing Jin

State Key Laboratory
of Mechanical Transmission,
Chongqing University,
Chongqing 400030, China
e-mail: jinxq@cqu.edu.cn

Zhanjiang Wang

State Key Laboratory
of Mechanical Transmission,
Chongqing University,
Chongqing 400030, China

Jiaxu Wang

State Key Laboratory
of Mechanical Transmission,
Chongqing University,
Chongqing 400030, China;
School of Aeronautics and Astronautics,
Sichuan University,
Chengdu 610065, China

Leon M. Keer

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

Qian Wang

Department of Mechanical Engineering,
Northwestern University,
Evanston, IL 60208;
State Key Laboratory
of Mechanical Transmission,
Chongqing University,
Chongqing 400030, China
e-mail: qwang@northwestern.edu

1Corresponding authors.

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received April 1, 2014; final manuscript received August 19, 2014; published online September 24, 2014. Assoc. Editor: Xiaolan Ai.

J. Tribol 137(1), 011402 (Sep 24, 2014) (11 pages) Paper No: TRIB-14-1072; doi: 10.1115/1.4028406 History: Received April 01, 2014; Revised August 19, 2014

The present work proposes a new efficient numerical solution method based on Eshelby's equivalent inclusion method (EIM) to study the influence of distributed inhomogeneities on the contact of inhomogeneous materials. Benchmark comparisons with the results obtained with an existing numerical method and the finite element method (FEM) demonstrate the accuracy and efficiency of the proposed solution method. An effective influence radius is defined to quantify the scope of influence for inhomogeneities, and the biconjugate gradient stabilized method (Bi-CGSTAB) is introduced to determine the eigenstrains of a large number of inclusions efficiently. Integrated with a rolling-contact fatigue (RCF) life prediction model, the proposed numerical solution is applied to investigate the RCF life of (TiB + TiC)/Ti-6Al-4V composites, and the results are compared with those of a group of RCF tests, revealing that the presence of the reinforcements causes reduction in the RCF lives of the composites. The comparison illustrates the capability of the proposed solution method on RCF life prediction for inhomogeneous materials.

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Figures

Grahic Jump Location
Fig. 1

Basic material configuration and problem description. (a) Parametric model for the inhomogeneity i in a homogeneous half-space subjected to a Hertz contact load (contact radius r and maximum pressure p0). Parameters xi, yi, zi and ai, bi, ci are introduced to determine the location and size of the inhomogeneity. (b) Euler angles, θi, ξi, and ηi, for characterizing the orientations of the inhomogeneity.

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Fig. 2

Schematic of the half-space inclusion solution composed of two portions: the inclusion solution in the full space and the homogeneous solution in the half-space with surface traction cancellation

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Fig. 3

Average deviation between the equivalent eigenstrains of the double-inhomogeneity and single-inhomogeneity cases as a function of inhomogeneity distance, d. The double inhomogeneities have identical size and material properties.

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Fig. 4

Variation of the average eigenstrain deviation for distributed equivalent inclusions with respect to candidate influence radius. The distributed inhomogeneities are of spherical shapes having identical size and material properties.

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Fig. 5

Determination of the effective influence radius for arbitrarily distributed inhomogeneities with different volume fractions. A wide range of material combinations is considered. Two groups of inhomogeneities of different aspect ratios are employed for the computations.

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Fig. 6

Performance of the Bi-CGSTAB. The computational domain is 3r × 3r × 3r and the radius of the inhomogeneities is 0.02r. (a) Comparisons of time consumption between lower upper (LU) decomposition and Bi-CGSTAB for quasi-sparse linear systems. Influence matrix A has different fractions of nonzero elements. (b) Variations of time and memory usages with respect to the fraction of nonzero elements in influence matrix A for the Bi-CGSTAB.

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Fig. 7

SEM images for the titanium matrix composites. (a) Radial direction and (b) axial direction.

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Fig. 8

Probability density distributions for the distributed reinforcements. (a) Depth, z, of the TiB reinforcements; (b) major semi-axis, a, of the TiB reinforcements; (c) minor semi-axis, b, of the TiB reinforcements; (d) minor semi-axis, c, of the TiB reinforcements; (e) major semi-axis, a, of the TiC reinforcements; and (f) minor semi-axis, b, of the TiC reinforcements.

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Fig. 9

Regenerated distributions of the two types of reinforcements. (a) Radial direction and (b) axial direction.

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Fig. 10

Experiment setup and sample. (a) Schematic of the RCF life tester, the front view; (b) top view; and (c) rod samples before and after a RCF test and balls.

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Fig. 11

Variations of the relative RCF lives of the composite materials as functions of reinforcement distribution parameters. (a) Volume ratio; (b) reinforcement constituents at a given volume ratio; and (c) reinforcement size at a given volume ratio, 2% is used.

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Fig. 12

The ziggurat method with rectangles and a bottom base strip [42]

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