On Nix’s theorem for two skew dislocations in anisotropic elastic materials with a parabolic boundary. (English) Zbl 1475.30095
Summary: We make use of the Stroh sextic formalism to obtain explicit expressions for the net interaction force between two skewed line dislocations separated by a distance \(h\) in an anisotropic elastic material with a traction-free or rigid parabolic boundary. The net interaction force is found to be independent of the separation distance \(h\) and the orientation and shape of the parabola but dependent on the presence of the parabolic boundary.
MSC:
| 30E25 | Boundary value problems in the complex plane |
| 35Q74 | PDEs in connection with mechanics of deformable solids |
| 74B05 | Classical linear elasticity |
| 74E10 | Anisotropy in solid mechanics |
| 74M25 | Micromechanics of solids |
| 74S70 | Complex-variable methods applied to problems in solid mechanics |
References:
| [1] | Orlov, S. S.; Indenbom, V. L., The interaction of non-parallel dislocations in an anisotropic medium, Kristallografiya, 14, 780-783 (1969) |
| [2] | Nix, W.D.: Private communications with D.M. Barnett (1997) |
| [3] | Barnett, D. M., The net interaction force between two skew dislocations in an elastically anisotropic half-space, Scr. Mater., 39, 371-378 (1998) · doi:10.1016/S1359-6462(98)00211-5 |
| [4] | Barnett, D. M.; Ting, T. C.T.; Kirchner, H. O.K.; Taya, M.; Arsenault, R. J., The net interaction force between two skew dislocations in an anisotropic linear elastic bi-metallic medium, Materials Science and Engineering A, 18-24 (2000) |
| [5] | Ting, T. C.T.; Barnett, D. M., On Nix’s theorem for two skew dislocations in anisotropic elastic half-spaces and bimaterials, Math. Mech. Solids, 6, 3-27 (2001) · Zbl 1026.74006 · doi:10.1177/108128650100600101 |
| [6] | Ting, T. C.T., Independence of the presence of cracks or inclusions of the net interaction force acting on a dislocation by a skewed line singularity, J. Elast., 55, 61-72 (1999) · Zbl 0970.74006 · doi:10.1023/A:1007620704417 |
| [7] | Kirchner, H. O.K., Skew line defects in graded materials, Philos. Mag. Lett., 79, 209-216 (1999) · doi:10.1080/095008399177264 |
| [8] | Ting, T. C.T.; Hu, Y.; Kirchner, H. O.K., Anisotropic elastic materials with a parabolic or hyperbolic boundary: a classical problem revisited, ASME J. Appl. Mech., 68, 537-542 (2001) · Zbl 1110.74709 · doi:10.1115/1.1381393 |
| [9] | Ting, T. C.T., Anisotropic Elasticity-Theory and Applications (1996), New York: Oxford University Press, New York · Zbl 0883.73001 · doi:10.1093/oso/9780195074475.001.0001 |
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