Abstract
The problem of an edge dislocation inside the nanoscale coating layer accounting for the interface effects is addressed. By combining the sectionally holomorphic function, Laurent series expansion techniques and the complex variable function method, the stress fields in the coating layer and the image force acting on the edge dislocation are derived analytically. The results indicate that an additional repulsive force or attractive force will act on the edge dislocation for considering the interface effects, and there exists more than one stable (unstable) dislocation equilibrium point. The material elastic dissimilarity, the coating thickness, the interface stress as well as the relative position of the dislocation have great influence on the force acting on the edge dislocation in the coating layer. The present solutions contain previously several known results, which can be shown to be special cases.
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References
Hirth J.P., Lothe J.: Theory of Dislocations. McGraw-Hill, New York (1982)
Gryaznov V.G., Trusov L.I.: Size effects in micromechanics of nanocrystals. Progr. Mater. Sci. 37, 289–401 (1993)
Nembach E.: Particle Strengthening of Metals and Alloys. Wiley, New York (1996)
Demkowicz M.J., Wang J., Hoagland R.G.: In: Hirth, J.P. (ed.) Dislocations in Solids, vol. 14, Elsevier North-Holland, Amsterdam (2008)
Stagni L., Lizzio R.: Shape effects in the interaction between an edge dislocation and an elliptic inhomogeneity. Appl. Phys. A 30, 217–221 (1983)
Tsuchida E., Ohno M., Kouris D.A.: Effects of an inhomogeneous elliptical insert on the elastic field of an edge dislocation. Appl. Phys. A 53, 285–291 (1991)
Stagni L.: Edge dislocation near an elliptic inhomogeneity with either an adhering or a slipping interface: a comparative study. Philos. Mag. A 68, 49–57 (1993)
Gong S.X., Meguid S.A.: A screw dislocation interacting with an elastic elliptical inhomogeneity. Int. J. Eng. Sci. 32, 1221–1228 (1994)
Jiang C.P.: Edge dislocation interacting with an interfacial crack along a circular inhomogeneity. Int. J. Solids Struct. 40, 5781–5797 (2003)
Ma C.C., Lu H.T.: Theoretical analysis of screw dislocations and image forces in anisotropic multilayered media. Phys. Rev. B 73, 144102-1–144102-12 (2006)
Liu Y.W., Fang Q.H.: Analysis of a screw dislocation inside an inhomogeneity with interface stress. Mater. Sci. Eng. A 464, 117–123 (2007)
Wang T., Luo J., Xiao Z.M., Chen J.Q.: On the nucleation of a Zener crack from a wedge disclination dipole in the presence of a circular inhomogeneity. Eur. J. Mech. A/Solids 28, 688–696 (2009)
Wang X., Sudak L.J.: Interaction of a screw dislocation with an arbitrary shaped elastic inhomogeneity. J. Appl. Mech. 73, 206–211 (2006)
Zhou K., Nazarov A.A., Wu M.S.: Strengthening effect of disclinations in polycrystalline nanofilms. Philos. Mag. 88, 3181–3191 (2008)
Zhou K., Chen W.W., Keer L.M., Wang Q.J.: A fast method for solving three-dimensional arbitrarily-shaped inclusions in a half space. Comput. Meth. Appl. Mech. Eng. 198, 885–892 (2009)
Zhou K., Wu M.S.: Stresses and displacements of an edge dislocation in an isotropic film-substrate by the image method. Acta Mech. 211, 271–292 (2010)
Christensen R.M., Lo K.H.: Solution for effective shear properties in three phase sphere and cylinder models. J. Mech. Phys. Solids 27, 315–330 (1979)
Luo H.A., Chen Y.: An edge dislocation in a three-phase composite cylinder model. J. Appl. Mech. 58, 75–86 (1991)
Qaissaunee M.T., Santare M.H.: Edge dislocation interacting with an elliptical inclusion surrounded by an interfacial zone. Q. J. Mech. Appl. Math. 48, 465–482 (1995)
Chen F.M., Chao C.K., Chen C.K.: Interaction of an edge dislocation with a coated elliptic inclusion. Int. J. Solids Struct. 48, 1451–1465 (2011)
Xiao Z.M., Chen B.J.: A screw dislocation interacting with a coated fiber. Mech. Mater. 32, 485–494 (2000)
Xiao Z.M., Chen B.J.: On the interaction between an edge dislocation and a coated inclusion. Int. J. Solids Struct. 38, 2533–2548 (2001)
Liu Y.W., Jiang C.P., Chueng Y.K.: A screw dislocation interacting with an interphase layer between a circular inhomogeneity and the matrix. Int. J. Eng. Sci. 41, 1883–1898 (2003)
Liu Y.W., Fang Q.H., Jiang C.P.: A piezoelectric screw dislocation interacting with an interphase layer between a circular inclusion and the matrix. Int. J. Solids Struct. 41, 3255–3274 (2004)
Shen M.H.: A magnetoelectric screw dislocation interaction with a circular layered inclusion. Eur. J. Mech. A/Solids 27, 429–442 (2008)
Gurtin M.E., Murdoch A.I.: A continuum theory of elastic material surfaces. Arch. Rat. Mech. Anal. 57, 291–323 (1975)
Cammarata R.C., Sieradzki K., Spaepen F.: Simple model for interface stresses with application to misfit dislocation generation in epitaxial thin films. J. Appl. Phys. 87, 1227–1234 (2000)
Duan H.L., Wang J., Huang Z.P., Karihaloo B.L.: Size-dependent effective elastic constants of solids containing nano-inhomogeneities with interface stress. J. Mech. Phys. Solids 53, 1574–1596 (2005)
Fang Q.H., Liu Y.W.: Size-dependent elastic interaction between a screw dislocation and a circular nano-inhomogeneity incorporating interface stress. Scripta Mater. 55, 99–102 (2006)
Chen T., Dvorak G.J., Yu C.C.: Solids containing spherical nano-inclusions with interface stresses: effective properties and thermal–mechanical connections. Int. J. Solids Struct. 44, 941–955 (2007)
Wang G.F.: Diffraction of plane compressional wave by a nanosized spherical cavity with surface effects. Appl. Phys. Lett. 90, 211907-1– 211907-3 (2007)
Zhang T.Y., Luo M., Chan W.K.: Size-dependent surface stress, surface stiffness, and Young’s modulus of hexagonal prism [111] β-SiC nanowires. J. Appl. Phys. 103, 104308 (2008)
Fang Q.H., Liu Y.W., Jin B., Wen P.H.: Effect of interface stresses on the image force and stability of an edge dislocation inside a nanoscale cylindrical inclusion. Int. J. Solids Struct. 46, 1413–1422 (2009)
Fang Q.H., Liu Y.W., Wen P.H.: Screw dislocations in a three-phase composite cylinder model with interface stress. J. Appl. Mech. 75, 041019-1–041019-8 (2008)
Fang Q.H., Liu Y.W., Jin B., Wen P.H.: Interaction between a dislocation and a core-shell nanowire with interface effects. Int. J. Solids Struct. 46, 1539–1546 (2009)
Luo J., Wang X.: On the anti-plane shear of an elliptic nano inhomogeneity. Eur. J. Mech. A/Solids 28, 926–934 (2009)
Zhang T.Y., Wang Z.J., Chan W.K.: Eigenstress model for surface stress of solids. Phys. Rev. B 81, 195427 (2010)
Luo J., Liu F.: Stress analysis of a wedge disclination dipole interacting with a circular nano inhomogeneity. Eur. J. Mech. A/Solids 30, 22–32 (2011)
Ou Z.Y., Pang S.D.: A screw dislocation interacting with a coated nano-inhomogeneity incorporating interface stress. Mater. Sci. Eng. A 528, 2762–2775 (2011)
Moeini-Ardakani S.S., Gutkinb M.Y., Shodja H.M.: Elastic behavior of an edge dislocation inside the wall of a nanotube. Scripta Mater. 64, 709–712 (2011)
Chen X.B., Lou Y.B., Samia A.C., Burda C.: Coherency strain effects on the optical response of core/shell heteronanostructures. Nano Lett. 3, 799–803 (2003)
Kolesnikovay A.L., Romanov A.E.: Misfit dislocation loops and critical parameters of quantum dots and wires. Philos. Mag. Lett. 84, 501–506 (2004)
Duan H.L., Karihaloo B.L., Wang J., Yi X.: Compatible composition profiles and critical sizes of alloyed quantum dots. Phys. Rev. B 74, 195328 (2006)
Sakasegawa H., Chaffron L., Legendre F. et al.: Evaluation of threshold stress of the MA957 ODS ferritic alloy. J. Nucl. Mater. 386, 511–514 (2009)
Li N., Wang J., Huang J.Y. et al.: In situ TEM observations of room temperature dislocation climb at interfaces in nanolayered Al/Nb composites. Scripta Mater. 63, 363–366 (2010)
Byun T.S., Kim J.H., Yoon J.H. et al.: High temperature fracture characteristics of a nanostructured ferritic alloy (NFA). J. Nucl. Mater. 407, 78–82 (2010)
Zhu T., Li J.: Ultra-strength materials. Progr. Mater. Sci. 55, 710–757 (2010)
Sharma P., Ganti S., Bhate N.: Effect of surfaces on the size-dependent elastic state of nano-inhomogeneities. Appl. Phys. Lett. 82, 535–537 (2003)
Muskhelishvili N.L.: Some Basic Problems of Mathematical Theory of Elasticity. P. Noordhoff, Groningen, The Netherlands (1975)
Povstenko Y.Z.: Theoretical investigation of phenomena caused by heterogeneous surface tension in solids. J. Mech. Phys. Solids 41, 1499–1514 (1993)
England A.H.: Complex Variable Method in Elasticity. Wiley, New York (1971)
Worden R.E., Keer L.M.: Green’s functions for a point load and dislocation in an annular region. J. Appl. Mech. 58, 954–959 (1991)
Chao C.K., Tan C.J.: On the general solution for annular problems with a point heat source. J. Appl. Mech. 67, 511–518 (2000)
Fang Q.H., Liu Y.W.: Size-dependent interaction between an edge dislocation and a nanoscale inhomogeneity with interface effects. Acta Mater. 54, 4213–4220 (2006)
Zhang T.Y., Qian C.F., Wang T.H., Tong P.: Interaction of an edge dislocation with a thin-film-covered crack. Int. J. Solids Struct. 37, 5465–5492 (2000)
Miller R.E., Shenoy V.B.: Size-dependent elastic properties of nanosize structural elements. Nanotechnology 11, 139–147 (2000)
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Liu, Y.W., Zhao, Y.X., Wen, P.H. et al. Elastic behavior of an edge dislocation inside the nanoscale coating layer. Acta Mech 223, 1917–1935 (2012). https://doi.org/10.1007/s00707-012-0689-x
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DOI: https://doi.org/10.1007/s00707-012-0689-x