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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Xu,  G., Argon,  A. S., and Ortiz,  M., 1997, “Critical Configurations for Dislocation From Crack Tips,” Philos. Mag. A, 75, p. 341.
Fares,  N., 1989, “Crack Fronts Trapped by Arrays of Obstacles: Numerical Solutions Based on Surface Integral Representation,” ASME J. Appl. Mech., 56, p. 837.
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.
Clifton, R. J., 1989, “Three-Dimensional Fracture-Propagation Models,” J. L. Gidley, ed., Hydraulic Fracturing, SPE Monograph.
Rice,  J. R., 1993, “Spatio-Temporal Complexity of Slip on a Fault,” J. Geophys. Res., 98, pp. 9885–9907.
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.
Murakami,  Y., and Nemat-Nasser,  S., 1983, “Growth and Stability of Interacting Surface Flaws of Arbitrary Shape,” Eng. Fract. Mech., 17, No. 3, p. 193.
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.


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



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