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Elastic behavior of an edge dislocation inside the nanoscale coating layer

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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

  1. Hirth J.P., Lothe J.: Theory of Dislocations. McGraw-Hill, New York (1982)

    Google Scholar 

  2. Gryaznov V.G., Trusov L.I.: Size effects in micromechanics of nanocrystals. Progr. Mater. Sci. 37, 289–401 (1993)

    Article  Google Scholar 

  3. Nembach E.: Particle Strengthening of Metals and Alloys. Wiley, New York (1996)

    Google Scholar 

  4. Demkowicz M.J., Wang J., Hoagland R.G.: In: Hirth, J.P. (ed.) Dislocations in Solids, vol. 14, Elsevier North-Holland, Amsterdam (2008)

  5. Stagni L., Lizzio R.: Shape effects in the interaction between an edge dislocation and an elliptic inhomogeneity. Appl. Phys. A 30, 217–221 (1983)

    Article  Google Scholar 

  6. 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)

    Article  Google Scholar 

  7. 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)

    Article  Google Scholar 

  8. Gong S.X., Meguid S.A.: A screw dislocation interacting with an elastic elliptical inhomogeneity. Int. J. Eng. Sci. 32, 1221–1228 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  9. Jiang C.P.: Edge dislocation interacting with an interfacial crack along a circular inhomogeneity. Int. J. Solids Struct. 40, 5781–5797 (2003)

    Article  MATH  Google Scholar 

  10. 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)

    Google Scholar 

  11. 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)

    Article  Google Scholar 

  12. 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)

    Article  MATH  Google Scholar 

  13. Wang X., Sudak L.J.: Interaction of a screw dislocation with an arbitrary shaped elastic inhomogeneity. J. Appl. Mech. 73, 206–211 (2006)

    Article  MATH  Google Scholar 

  14. Zhou K., Nazarov A.A., Wu M.S.: Strengthening effect of disclinations in polycrystalline nanofilms. Philos. Mag. 88, 3181–3191 (2008)

    Article  Google Scholar 

  15. 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)

    Article  MATH  Google Scholar 

  16. 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)

    Article  MATH  Google Scholar 

  17. 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)

    Article  MATH  Google Scholar 

  18. Luo H.A., Chen Y.: An edge dislocation in a three-phase composite cylinder model. J. Appl. Mech. 58, 75–86 (1991)

    Article  MATH  Google Scholar 

  19. 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)

    Article  MATH  Google Scholar 

  20. 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)

    Article  MATH  Google Scholar 

  21. Xiao Z.M., Chen B.J.: A screw dislocation interacting with a coated fiber. Mech. Mater. 32, 485–494 (2000)

    Article  Google Scholar 

  22. 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)

    Article  MATH  Google Scholar 

  23. 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)

    Article  Google Scholar 

  24. 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)

    Article  MATH  Google Scholar 

  25. Shen M.H.: A magnetoelectric screw dislocation interaction with a circular layered inclusion. Eur. J. Mech. A/Solids 27, 429–442 (2008)

    Article  MATH  Google Scholar 

  26. Gurtin M.E., Murdoch A.I.: A continuum theory of elastic material surfaces. Arch. Rat. Mech. Anal. 57, 291–323 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  27. 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)

    Article  Google Scholar 

  28. 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)

    Article  MathSciNet  MATH  Google Scholar 

  29. 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)

    Article  Google Scholar 

  30. 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)

    Article  MATH  Google Scholar 

  31. 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)

    Google Scholar 

  32. 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)

    Article  Google Scholar 

  33. 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)

    Article  MATH  Google Scholar 

  34. 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)

    Article  Google Scholar 

  35. 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)

    Article  MATH  Google Scholar 

  36. Luo J., Wang X.: On the anti-plane shear of an elliptic nano inhomogeneity. Eur. J. Mech. A/Solids 28, 926–934 (2009)

    Article  MATH  Google Scholar 

  37. Zhang T.Y., Wang Z.J., Chan W.K.: Eigenstress model for surface stress of solids. Phys. Rev. B 81, 195427 (2010)

    Article  Google Scholar 

  38. 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)

    Article  Google Scholar 

  39. 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)

    Article  Google Scholar 

  40. 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)

    Article  Google Scholar 

  41. 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)

    Article  Google Scholar 

  42. Kolesnikovay A.L., Romanov A.E.: Misfit dislocation loops and critical parameters of quantum dots and wires. Philos. Mag. Lett. 84, 501–506 (2004)

    Article  Google Scholar 

  43. 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)

    Article  Google Scholar 

  44. 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)

    Article  Google Scholar 

  45. 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)

    Article  Google Scholar 

  46. 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)

    Article  Google Scholar 

  47. Zhu T., Li J.: Ultra-strength materials. Progr. Mater. Sci. 55, 710–757 (2010)

    Article  Google Scholar 

  48. 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)

    Article  Google Scholar 

  49. Muskhelishvili N.L.: Some Basic Problems of Mathematical Theory of Elasticity. P. Noordhoff, Groningen, The Netherlands (1975)

    MATH  Google Scholar 

  50. Povstenko Y.Z.: Theoretical investigation of phenomena caused by heterogeneous surface tension in solids. J. Mech. Phys. Solids 41, 1499–1514 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  51. England A.H.: Complex Variable Method in Elasticity. Wiley, New York (1971)

    Google Scholar 

  52. 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)

    Article  MathSciNet  MATH  Google Scholar 

  53. 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)

    Article  MATH  Google Scholar 

  54. 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)

    Article  Google Scholar 

  55. 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)

    Article  MATH  Google Scholar 

  56. Miller R.E., Shenoy V.B.: Size-dependent elastic properties of nanosize structural elements. Nanotechnology 11, 139–147 (2000)

    Article  Google Scholar 

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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

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