0
TECHNICAL PAPERS

Virtual Circular Dislocation-Disclination Loop Technique in Boundary Value Problems in the Theory of Defects

[+] Author and Article Information
A. I. Kolesnikova

Institute of Problems of Mechanical Engineering, Russian Academy of Sciences, Bolshoj 61, Vas. Ostrov, St. Petersburg 199178, Russia e-mail: ankolesnikova@yandex.ru

A. E. Romanov

Ioffe Physico-Technical Institute, Russian Academy of Sciences, Polytechnicheskaya 26, St. Petersburg, 194021, Russia e-mail: aer@mail.ioffe.ru

J. Appl. Mech 71(3), 409-417 (Jun 22, 2004) (9 pages) doi:10.1115/1.1757488 History: Received September 11, 2003; Revised December 30, 2003; Online June 22, 2004
Copyright © 2004 by ASME
Your Session has timed out. Please sign back in to continue.

References

Louat,  N., 1962, “Solution of Boundary Problems in Plane Strain,” Nature (London), 196(4859), pp. 1081–1082.
Marcinkowski, M. J., 1979, Unified Theory of the Mechanical Behavior of Matter, John Wiley and Sons, New York.
Romanov,  A. E., and Vladimirov,  V. I., 1981, “Straight Disclinations Near a Free Surface. I. Stress Fields,” Phys. Status Solidi A, 63(1), pp. 109–118.
Vladimirov,  V. I., Kolesnikova,  A. L., and Romanov,  A. E., 1985, “Wedge Disclinations in an Elastic Plate,” Phys. Met. Metall., 60(6), pp. 58–67 (translated from Russian).
Vladimirov, V. I., Romanov, A. E., and Kolesnikova, A. L., 1984, “Flux Line Near Surface of Superconductor,” Physics and Technology of the Treatment of Metal Surface, Physico-Technical Institute, Leningrad, Russia, pp. 33–38 (in Russian).
Jagannadham,  K., and Marcinkowski,  M. J., 1980, “Surface Dislocation Model of a Dislocation in a Two Phase Medium,” J. Mater. Sci., 15(2), pp. 709–726.
Gutkin,  M. Yu., and Romanov,  A. E., 1991, “Straight Edge Dislocation in a Thin Two-Phase Plate. I. Elastic Stress Fields,” Phys. Status Solidi A, 125(1), pp. 107–125.
Belov,  A. J., Chamrov,  V. A., Indenbom,  V. L., and Lothe,  J., 1983, “Elastic Fields of Dislocations Piercing the Interface of an Anisotropic Bicrystal,” Phys. Status Solidi B, 119(2), pp. 565–578.
Kolesnikova, A. L., and Romanov, A. E., 1986, “Circular Dislocation-Disclination Loops and Their Application to Boundary Problem Solution in the Theory of Defects,” preprint of Physico-Technical Institute, No. 1019, Leningrad, Russia (in Russian).
Kolesnikova,  A. L., and Romanov,  A. E., 1987, “Edge Dislocation Perpendicular to the Surface of a Plate,” Sov. Tech. Phys. Lett., 13(6), pp. 272–274 (translated from Russian).
Kolesnikova,  A. L., and Romanov,  A. E., 2003, “Dislocation and Disclination Loops in the Virtual-Defect Method,” Phys. Solid State, 45(9), pp. 1706–1728 (translated from Russian).
Louat,  N., and Sadananda,  K., 1991, “Some Consequences of the Elastic Interaction of Particles and Free Surfaces,” Philos. Mag. A, 64(1), pp. 213–221.
Salamon,  N. J., and Dundurs,  J., 1971, “Dislocation Loops in Inhomogeneous Materials,” J. Elast., 1(2), pp. 153–160.
Dundurs,  J., and Salamon,  N. J., 1972, “Circular Prismatic Dislocation Loop in Two-Phase Material,” Phys. Status Solidi B, 50(1), pp. 125–133.
Salamon,  N. J., and Comninou,  M., 1979, “The Circular Prismatic Dislocation Loop in an Interface,” Philos. Mag. A, 39(5), pp. 685–691.
Kuo,  H. H., and Mura,  T., 1972, “Circular Disclinations and Interface Effect,” J. Appl. Phys., 43(10), pp. 3936–3943.
Kuo,  H. H., Mura,  T., and Dundurs,  J., 1973, “Moving Circular Twist Disclination Loop in Inhomogeneous and Two-Phase Materials,” Int. J. Eng. Sci., 11(1), pp. 193–201.
Eason,  G., Noble,  B., and Sneddon,  I. N., 1955, “On Certan Integrals of Lipschitz-Hankel Type Involving Products of Bessel Functions,” Philos. Trans. R. Soc. London, Ser. A, 247(935), pp. 529–551.
Mura, T., 1987, Micromechanics of Defects in Solids, Martinus Nijhoff, Boston.
Ufliand, Ya. S., 1967, Integral Transformations in Problems of Theory of Elasticity, Nauka, Leningrad, Russia (in Russian).
Theodosiu, C., 1982, Elastic Models of Crystal Defects, Springer-Verlag, Berlin.
Seo,  K., and Mura,  T., 1979, “Elastic Field in a Half-Space due to Ellipsoidal Inclusions With Uniform Dilatation Eigenstrains,” ASME J. Appl. Mech., 46(3), pp. 568–572.

Figures

Grahic Jump Location
Dislocation-disclination loops being used as virtual defects in solutions of elastic boundary value problems. (a) Prismatic dislocation loop. (b) Twist disclination loop. (c) Radial disclination loop (Somigliana dislocation). The displacement jumps at the cut-surfaces are shown schematically.
Grahic Jump Location
Spherical inclusion in a plate. Distributions of virtual loop defects are shown on the plate surfaces.
Grahic Jump Location
Prismatic dislocation loop in a plate. Distributions of virtual loop defects are shown on the plate surfaces.
Grahic Jump Location
Twist disclination loop of radius a0 coaxial to a cylinder. Distribution of virtual twist disclination loops is shown on cylinder surface.

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In