Abstract
The interaction between a screw dislocation and a circular inhomogeneity in gradient elasticity is investigated. The screw dislocation is located inside either the inhomogeneity or the matrix. By using the Fourier transform method, closed analytical solutions are obtained when the inhomogeneity and the matrix have the same gradient coefficient. The explicit expressions of image forces exerted on screw dislocations are derived. The motion of the appointed screw dislocation and its equilibrium positions are discussed. The results show that the classical singularity is eliminated. Especially, for the case of a tiny inhomogeneity, the relation of dislocations and inhomogeneities become quite different. The screw dislocation may be attracted by the stiff inhomogeneity and repelled by the soft inhomogeneity when it tends to the interface. So there is an unstable equilibrium position when a dislocation tends to a tiny stiff inhomogeneity and there is a stable equilibrium position when a dislocation tends to a tiny soft inhomogeneity.
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References
Smith E (1968) The interaction between dislocations and inhomogeneities-I. Int J Eng Sci 6:129–143
Gong SX, Meguid SA (1994) A screw dislocation interaction with an elastic elliptical inhomogeneity. Int J Eng Sci 32:1221–1228
Zhang TY, Qian CF (1996) Interaction of a screw dislocation with a thin-film-covered mode III crack. Acta Metall Mater 39:2739–2744
Gutkin MYu, Aifantis EC (1996) Screw dislocation in gradient elasticity. Scr Mater 35:1353–1358
Gutkin MYu, Aifantis EC (1997) Edge dislocation in gradient elasticity. Scr Mater 36:129–135
Gutkin MYu, Aifantis EC (1999) Dislocation in the theory of gradient elasticity. Scr Mater 40:559–566
Gutkin MYu, Aifantis EC (1999) Dislocations and disclinations in gradient elasticity. Phys Status Solidi 214:245–284
Gutkin MYu, Aifantis EC (1999) Dislocations and disclinations in the gradient theory of elasticity. Phys Solid State 41:1980–1988
Ru CQ, Aifantis EC (1993) Some studies on boundary value problems in gradient elasticity. MTU Report, Houghton, MI (Preprint)
Ru CQ, Aifantis EC (1993) A simple approach to solve boundary-value problems in gradient elasticity. Acta Mech 101:59–68
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Song, H.P., Fang, Q.H. & Liu, Y.W. The interaction between a screw dislocation and a circular inhomogeneity in gradient elasticity. Meccanica 44, 499–506 (2009). https://doi.org/10.1007/s11012-008-9185-8
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DOI: https://doi.org/10.1007/s11012-008-9185-8