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TECHNICAL PAPERS

Micromechanics of Hysteresis Loops of Fatigue in a Single Crystal

[+] Author and Article Information
T. H. Lin, K. K. F. Wong

Department of Civil and Environmental Engineering, University of California, Los Angeles, CA 90095-1593

N. J. Teng

Universal Analytics, Inc., Torrance, CA 90503

J. Appl. Mech 67(2), 338-343 (Oct 01, 1999) (6 pages) doi:10.1115/1.1304917 History: Received February 17, 1998; Revised October 01, 1999
Copyright © 2000 by ASME
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References

Walker, K. P., and Jordan, E. M., 1989, “Biaxial Constitutive Modeling and Testing of a Single Crystal Superalloy at Elevated Temperatures,” Biaxial and Multiaxial Fatigue, EGF3,” M. W. Brown and K. J. Miller, eds., Mechanical Engineering Publication, London, pp. 145–170.
Lin,  T. H., 1992, “Micromechanics of Crack Initiation in High-Cyclic Fatigue,” Adv. Appl. Mech., 29, pp. 1–62.
Forsyth,  P. J. E., and Stubbington,  C. A., 1955, “The Slip Band Extrusion Effect Observed in Some Aluminum Alloys Subjected to Cyclic Stresses,” J. Inst. Met., 83, p. 395.
Essmann,  V., Gossel,  V., and Mughrabi,  H., 1981, “A Model of Extrusions and Intrusions in Fatigued Metals I—Point Defect Production and the Growth of Extrusions,” Philos. Mag. A, 44, pp. 405–426.
Mughrabi, H., Wang, R., Differt, K., and Essmann, V., 1983, “Fatigue Crack Initiation by Cyclic Slip Irreversibilities in High-Cycle Fatigue,” Fatigue Mechanism, STM-STP-811, pp. 5–45.
Lin,  T. H., Lin,  S. R., and Wu,  X. Q., 1989, “Micromechanics of an Extrusion in High-Cyclic Fatigue,” Philos. Mag. A, 59, pp. 1263–1276.
Zhai,  T., Briggs,  G. A. D., and Matin,  J. W., 1996, “Fatigue Damage at Room Temperature in Aluminum Single Crystals IV: Secondary Slip,” Acta Mater., 44, pp. 3489–3496.
Wood,  W. A., and Bendler,  A. M., 1962, “The Fatigue Process in Copper as Studies by Electron Metallography,” Trans. Metall. Soc. AIME, 244, pp. 180–186.
Wood, W. A., 1956, “Mechanisms of Fatigue,” Fatigue in Aircraft Structure, A. M. Freudenthal, ed., Academic Press, New York, pp. 1–19.
Lin, T. H., 1968, Theory of Inelastic Structures, John Wiley and Sons, New York.
Mecke,  K., and Blockwitz,  C., 1980, “Internal Displacement of Persistent Slip Bands in Cyclically Deformed Nickle Single Crystals,” Phys. Status Solidi A, 64, pp. K5–K7.
Basinski,  Z. S., Pascual,  R., and Bainski,  S. J., 1983, “Low Amplitude Fatigue of Copper Single Crystals I—The Role of the Surface in Fatigue Failure,” Acta Metall., 31, pp. 591–602.
Basinski,  Z. S., and Bainski,  S. J., 1985, “Low Amplitude Fatigue of Copper Single Crystals II—PSB Sections,” Acta Metall., 33, pp. 1319–1327.
Zhai,  T., Lin,  S., and Xiao,  J. M., 1990, “Influence on Non-Geometric Effect of PSB on Crack Initiation in Aluminum Single Crystal,” Acta Metall. Mater., 38, pp. 1687–1692.
Zhai,  T., Matin,  J. W., and Briggs,  G. A. D., 1995, “Fatigue Damage at Room Temperature in Aluminum Single Crystals I: On the Surface Containing the Slip Burger’s Vector,” Acta Metall. Mater., 43, pp. 3813–3825.
Thompson,  N., and Wadsworth,  N. J., 1958, “Metal Fatigue,” Adv. Phys., 7, pp. 72–170.
Kennedy, A. J., 1963, Process of Creep and Fatigue of Metals, John Wiley and Sons, New York.
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Figures

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Slip lines in polycrystalline nickel during two stages of cyclic loading (17)
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Instrusions and extrusions in copper during fatigue (17)
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Typical plastic strain distribution under cyclic loadings of aluminum
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Initially straight scratches a, b, c are displaced unidirectionally by static slip band AB. (Reproduced from Trans. Metal Soc. AIME, 1962, courtesy of AIME.)
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Cyclic slip band CD produces no overall displacement of scratches d, e, f. Within the slip band; the scratches are displaced equally backward and forward. (The same as Fig. 6, courtesy of AIME.)
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X-ray reflection patterns: (a) Sharp X-ray annealed α-brass. (b) From same specimen as (a) after a unidirectional strain 150×50 deg twist. (c) From same specimen as (a) after 1500 reversals of plastic strain 1.5-deg twist and showing same reflections as (a). (Reproduced from the book Fracture, 1959, courtesy of Technological Press, MIT.)
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Procedure for decoupling the single crystal problem
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Removal of boundary tractions for a single crystal
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Extrusions observed in single crystal 11
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Plastic strain distribution with initial strain at center. P & Q′ and Q & P′ are symmetrically located. Extrusions protruding out on both faces.
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Hysteresis loops of an aluminum single crystal
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Experimental observation of hysteresis loops in aluminum single crystal (18)

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