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TECHNICAL PAPERS

A Variational Boundary Integral Method for the Analysis of Three-Dimensional Cracks of Arbitrary Geometry in Anisotropic Elastic Solids

[+] Author and Article Information
G. Xu

Department of Mechanical Engineering, University of California, Riverside, CA 92521

J. Appl. Mech 67(2), 403-408 (Nov 26, 1999) (6 pages) doi:10.1115/1.1305276 History: Received October 22, 1999; Revised November 26, 1999
Copyright © 2000 by ASME
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References

Xu,  G., Argon,  A. S., and Ortiz,  M., 1997, “Critical Configurations for Dislocation From Crack Tips,” Philos. Mag. A, 75, p. 341.
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Gao,  H., and Rice,  J. R., 1989, “A First Order Perturbation Analysis on Crack-Trapping by Arrays of Obstacles,” ASME J. Appl. Mech., 56, p. 828.
Bower,  A. F., and Ortiz,  M., 1991, “A Three-Dimensional Analysis of Crack Trapping and Bridging by Tough Particles,” J. Mech. Phys. Solids, 39, No. 6, p. 815.
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Ben-Zion,  Y., and Rice,  J. R., 1995, “Slip Patterns and Earthquake Populations Along Different Classes of Faults in Elastic Solids,” J. Geophys. Res., 100, p. 12959.
Bui,  H. D., 1977, “An Integral Equation Method for Solving the Problem of a Plane Crack of Arbitrary Shape,” J. Mech. Phys. Solids, 25, p. 29.
Weaver,  J., 1977, “Three-Dimensional Crack Analysis,” Int. J. Solids Struct., 13, p. 321.
Cruse, T. A., 1988, Boundary Element Analysis in Computational Fracture Mechanics, Kluwer, Dordrecht, The Netherlands.
Sladek,  V., and Sladek,  J., 1983, “Three-Dimensional Curved Crack in an Elastic Body,” Int. J. Solids Struct., 19, No. 5, p. 425.
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Xu,  G., and Ortiz,  M., 1993, “A Variational Boundary Integral Method for the Analysis of 3-D Cracks of Arbitrary Geometry Modeled as Continuous Distributions of Dislocation Loops,” Int. J. Numer. Methods Eng., 36, p. 3675.
Lothe,  J., 1982, “Dislocations in Anisotropic Media: The Interaction Energy,” Philos. Mag. A, 46, p. 177.
Billy, B. A., and Eshelby, J. D., 1968, Fracture: An Advanced Treatise, Vol. 1, H. Liebowitz, ed., Academic Press, San Diego, CA.
Barnett,  D. M., and Asaro,  R. J., 1972, “The Fracture Mechanics of Slit-Like Cracks in Anisotropic Elastic Media,” J. Mech. Phys. Solids, 20, p. 353.
Xu,  G., Argon,  A. S., and Ortiz,  M., 1995, “Nucleation of Dislocations From Crack Tips Under Mixed Modes of Loading: Implications for Brittle Against Ductile Behaviour of Crystals,” Philos. Mag. A, 72, p. 415.
Kassir, M. K., and Sih, G. C., 1975, Mechanics of Fracture: Three-Dimensional Crack Problems, Noordhoff, Groningen.
Hirth, J. P., and Lothe, J., 1982, Theory of Dislocations, 2nd Ed., John Wiley and Sons, New York.

Figures

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Distributed dislocation loop representation of opening displacement field
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Two interacting dislocation loops
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An elliptical crack under mode I loading
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Example of mesh used in the analysis
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Opening displacements along x-axes of elliptical cracks in zinc
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Opening displacements along x-axes of elliptical cracks in barium titanate
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Local reference frame for the calculation of stress intensity factors in anisotropic materials
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Variation of KI along the elliptical crack in zinc
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Variation of KI along the elliptical crack in barium titanate

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