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TECHNICAL PAPERS

An Analysis of a Near-Surface Crack Branching Under a Rigid Indenter

[+] Author and Article Information
David J. Mukai

Louisiana State University, Department of Civil and Environmental Engineering, Baton Rouge, LA 70803-6405 e-mail: dmukai@lsu.edu

J. Tribol 122(1), 23-29 (Mar 29, 1999) (7 pages) doi:10.1115/1.555325 History: Received June 25, 1998; Revised March 29, 1999
Copyright © 2000 by ASME
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References

Zaretsky,  E. V., Parker,  R. J., and Anderson,  W. J., 1982, “Rolling Contact Fatigue Testing of Bearing Steels,” American Society for Testing Materials, ASTM Spec. Tech. Publ., 771, pp. 1–45.
Chiu,  Y. P., Tallian,  T. E., McCool,  J. I., and Martin,  J. A., 1969, “A Mathematical Model of Spalling Fatigue Failure,” ASLE Trans., 12, pp. 106–116.
Sih, G. C., 1973, Methods of Analysis and Solutions of Crack Problems 1, G. C. Sih, ed., Noordhoff International Publishing, Lyden, pp. 21–45.
Swedlow,  J. L., 1976, ASTM Spec. Tech. Publ., 601, pp. 506–521.
Theocaris,  P. S., and Andrianopoulos,  N. P., 1982, “The Mises Elastic-Plastic Boundary as the Core Region in Fracture Criteria,” Eng. Fract. Mech., 16, pp. 425–432.
Streit,  R., and Finnie,  Il., 1980, “An Experimental Investigation of Crack-Path Directional Stability,” Exp. Mech., 20, pp. 17–23.
Ramulu,  M., and Kobayashi,  A. S., 1985, “Mechanics of Crack Curving and Branching—a Dynamic Fracture Analysis,” Int. J. Fract. Mech., 27, pp. 187–201.
Lo,  K. K., 1978, “Analysis of Branched Cracks,” ASME J. Appl. Mech., 45, pp. 797–802.
Miller,  G. R., 1988, “A Preliminary Analysis of Subsurface Crack Branching Under a Surface Compressive Load,” ASME J. Tribol., 110, pp. 292–297.
Sheppard,  S., Barber,  J. R., and Comninou,  M., 1985, “Short Subsurface Cracks Under Conditions of Slip and Stick Caused by a Moving Compressive Load,” ASME J. Appl. Mech., 52, p. 811.
Bryant,  M. D., Miller,  G. R., and Keer,  L. M., 1984, “Line Contact Between a Rigid Indenter and a Damaged Elastic Body,” Q. J. Mech. Appl. Math., 37, pp. 467–478.
Gerasoulis,  A., 1982, “The Use of Piecewise Quadratic Polynomials for the Solution of Singular Integral Equations of Cauchy Type,” Comput. Math. Appl., 8, pp. 15–22.
He,  M. Y., and Hutchinson,  J. W., 1989, “Kinking of a Crack Out of an Interface,” ASME J. Appl. Mech., 56, pp. 270–278.
Muskhelishvili, N. I., 1953, Singular Integral Equations, Noordhoff, Groningen.
Mukai,  D. J., Ballarini,  R., and Miller,  G. R., 1990, “Analysis of Branched Interface Cracks,” ASME J. Appl. Mech., 57, pp. 887–893.

Figures

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Subsurface crack problem configuration
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An element and its sub-sections
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Typical dislocation density distribution for a short branch crack
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Comparison with Sheppard; mode I SIF versus distance from crack tip
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Comparison with Miller; SIF range versus extension angle
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Nondimensional mode I and mode II SIFs, KIR/P and KIIR/P, versus nondimensional contact location, xc/R, for θ=20 deg and d/a=0.7
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Nondimensional mode I SIF range, ΔKIR/P versus extension angle, θ, for d/a=0.7
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Hypothetical ΔKI-ΔKII two-space description of a specimen
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Hypothetical ΔKI-ΔKII two-space parameter study
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ΔKII-ΔKI two-space for increasing crack length; indenter footprint c=0.1R, contact friction f=0, and crack face friction cff=0.5
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ΔKII-ΔKI two-space for increasing crack length; indenter footprint c=0.5R, contact friction f=0, and crack face friction cff=0.5
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ΔKII-ΔKI two-space for decreasing crack depth for indenter footprint c=0.1R. Respective points on the three curves correspond to the same d/R values. 0.25<d/R<2.
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ΔKII-ΔKI two-space for decreasing crack depth for indenter footprint c=1R. Respective points on the three curves correspond to the same d/R values. 0.25<d/R<2.
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τyx−cffσyy contours under an indenter with footprint c=R

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