Abstract
The system of a wedge disclination dipole interacting with an internal crack was investigated. By using the complex variable method, the closed form solutions of complex potentials to this problem were presented. The analytic formulae of the physics variables, such as stress intensity factors at the tips of the crack produced by the wedge disclination dipole and the image force acting on disclination dipole center were obtained. The influence of the orientation, the dipole arm and the location of the disclination dipole on the stress intensity factors was discussed in detail. Furthermore, the equilibrium position of the wedge disclination dipole was also examined. It is shown that the shielding or antishielding effect of the wedge disclination to the stress intensity factors is significant when the disclination dipole moves to the crack tips.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Romanov A E. Screened disclinations in solids[J]. Materials Science & Engineering A, 1993, 164(1):58–68.
Romanov A E. Mechanics and physics of disclinations in solids[J]. European Journal of Mechanics, A/Solids, 2003, 22(5):727–741.
Li J C M. Disclination model of high angle grain boundaries[J]. Surface Science, 1972, 31(1):12–26.
Romanov A E. Straight disclinations near a free surface[J]. Physica Status Solidi, Ser A, 1981, 63(3):383–388.
Vladimirov V I, Romanov A E. The behaviors of wedge disclination systems near grain boundaries[J]. Physics of Metals, 1982, 4(6):1053–1062.
Romanov A E, Vladimirov V I. Disclinations in crystalline solids[M]. In: Nabarro F R N (ed). Dislocation in Solids. Vol 9, Elsevier, Amsterdam, 1992, 191–402.
Wu M S. Exact solutions for a wedge disclination dipole in a transversely isotropic biomaterial[J]. International Journal of Engineering Science, 2000, 38(16):1811–1835.
Sheinerman A G, Gutkin M Yu. Misfit disclinations and dislocation walls in a two-phase cylindrical composite[J]. Physica Status Solidi, Ser A, 2001, 184(2):485–505.
Ballarini R, Denda M. Interaction between a crack and a dislocation dipole[J]. International Journal of Fracture, 1988, 37(1):61–71.
Wang S D, Lee S B. Mechanical equilibrium of an edge dislocation dipole near a semi-infinite crack tip[J]. International Journal of Fracture, 1992, 57(4):317–324.
Lin K M, Hu C T, Lee S B. Screw dislocation dipoles near an internal crack[J]. Engineering Fracture Mechanics, 1993, 45(3):321–331.
Yang Y S, Lee S L, Lan B T. Elastic behavior of dislocation dipole near a blunt crack[J]. Engineering Fracture Mechanics, 1995, 52(1):83–93.
Muskhelishvili N L. Some Basic Problems of Mathematical Theory of Elasticity[M]. Noordhoff, Leyden, 1975, 331–340.
Fan Dajun. Mathematical Theory of Elasticity[M]. New Times Press, Beijing, 1983, 377–379 (in Chinese).
Zhang T Y, Li J C M. Interaction of an edge dislocation with an interfacial crack[J]. Journal of Applied Physics, 72(6):2215–2226.
Fang Qihong, Liu Youwen, Jiang Chiping. Edge dislocation interacting with an interfacial crack along a circular inhomogeneity[J]. International Journal of Solids and Structures, 2003, 40(21):5781–5797.
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by FAN Da-jun, Original Member of Editorial Committee, AMM
Project supported by the National Natural Science Foundation of China (No.10472030)
Rights and permissions
About this article
Cite this article
Fang, Qh., Liu, Yw. Elastic interaction between wedge disclination dipole and internal crack. Appl Math Mech 27, 1239–1247 (2006). https://doi.org/10.1007/s10483-006-0911-z
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/s10483-006-0911-z