Skip to main content
SpringerLink
Log in

The interaction of a screw dislocation with a circular inhomogeneity near the free surface

  • Original
  • Published:
Archive of Applied Mechanics Aims and scope Submit manuscript

Abstract

The interaction of a screw dislocation with a circular inhomogeneity near the free surface is discussed in this paper. By using the complex potential and conformal mapping technique, an explicit series solution is obtained. Then, the solution is cast into a new expression to separate the interaction effects between the dislocation, inhomogeneity, and free surface. The new expression is not only convenient to reveal the coupling interaction effects, but also helpful to improve the convergence of the solution. As an application of the new expression, a simple approximate formula is presented with high accuracy. Finally, the full-field interaction energy and image force are evaluated and studied graphically. It is found that when the screw dislocation, inhomogeneity, and free surface are close to each other, their interaction effects strongly and intricately couple in the near field. In the case of a soft inhomogeneity or a hole, there is an unstable equilibrium point of the screw dislocation between the inhomogeneity and free surface, whereas in the case of a hard or rigid inhomogeneity, there is an unstable equilibrium point on the opposite side of the inhomogeneity.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Head A.K.: The interaction of dislocations and boundaries. Philos. Mag. 44, 92–94 (1953)

    Google Scholar 

  2. Smith E.: The interaction between dislocations and inhomogeneities-I. Int. J. Eng. Sci. 6, 129–143 (1968)

    Article  Google Scholar 

  3. Li Z.H., Shi J.Y.: The interaction of a screw dislocation with inclusion analyzed by Eshelby equivalent inclusion method. Scripta Mater. 47, 371–375 (2002)

    Article  Google Scholar 

  4. Shen M.H., Chen S.N., Lin C.P.: The interaction between a screw dislocation and a piezoelectric fiber composite with a wedge crack. Arch. Appl. Mech. 82, 215–227 (2012)

    Article  Google Scholar 

  5. Zeng X., Fang Q.H., Liu Y.W.: Exact solutions for piezoelectric screw dislocations near two asymmetrical edge cracks emanating from an elliptical hole. Arch. Appl. Mech. 83, 1097–1107 (2013)

    Article  Google Scholar 

  6. Zhang J., Qu Z., Huang Q.Q., Xie L.C., Xiong C.B.: Interaction between cracks and a circular inclusion in a finite plate with the distributed dislocation method. Arch. Appl. Mech. 83, 861–873 (2013)

    Article  Google Scholar 

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

    Article  Google Scholar 

  8. Jiang C.P., Xu Y.L., Liu Y.W.: Interaction of a screw dislocation in the interphase layer with the inclusion and matrix. Appl. Math. Mech. 24, 979–988 (2003)

    Article  MATH  Google Scholar 

  9. Honein E., Rai H., Najjar M.I.: The material force acting on a screw dislocation in the presence of a multi-layered circular inclusion. Int. J. Solids Struct. 43, 2422–2440 (2006)

    Article  MATH  Google Scholar 

  10. Sudak L.J.: On the interaction between a dislocation and a circular inhomogeneity with imperfect interface in antiplane shear. Mech. Res. Commun. 30, 53–59 (2003)

    Article  MATH  Google Scholar 

  11. Fang Q.H., Liu Y.W.: Size-dependent elastic interaction of a screw dislocation with a circular nano-inhomogeneity incorporating interface stress. Scripta Mater. 55, 99–102 (2006)

    Article  Google Scholar 

  12. Luo J., Xiao Z.M.: Analysis of a screw dislocation interacting with an elliptical nano inhomogeneity. Int. J. Eng. Sci. 47, 883–892 (2009)

    Article  MathSciNet  Google Scholar 

  13. Ahmadzadeh-Bakhshayesh H., Gutkin M.Yu., Shodja H.M.: Surface/interface effects on elastic behavior of a screw dislocation in an eccentric core-shell nanowire. Int. J. Solids Struct. 49, 2422–2440 (2012)

    Article  Google Scholar 

  14. Gilman J.J., Johnston W.G.: Observations of dislocation glide and climb in lithium fluoride crystals. J. Appl. Phys. 27, 1018–1022 (1956)

    Article  Google Scholar 

  15. D’Aragona F.S.: Dislocation etch for (100) planes in silicon. J. Electrochem. Soc. 119, 948–951 (1972)

    Article  Google Scholar 

  16. Osakabe N., Endo J., Matsuda T., Tonomura A., Fukuhara A.: Observation of surface undulation due to single-atomic shear of a dislocation by reflection-electron holography. Phys. Rev. Lett. 62, 2969–2972 (1989)

    Article  Google Scholar 

  17. Fuente O.R., Zimmerman J.A., González M.A., Figuera J., Hamilton J.C., Pai W.W., Rojo J.M.: Dislocation emission around nanoindentations on a (001) fcc metal surface studied by scanning tunneling microscopy and atomistic simulations. Phys. Rev. Lett. 88, 036101 (2002)

    Article  Google Scholar 

  18. Muskhelishvili N.I.: Some Basic Problems of the Mathematical Theory of Elasticity. Noorhoff, Groningen, Holland (1953)

    MATH  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  20. Shi J., Li Z.: An approximate solution of the interaction between an edge dislocation and an inclusion of arbitrary shape. Mech. Res. Commun. 33, 804–810 (2006)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Aeronautic Science and Engineering, Beihang University, Beijing, 100191, China

    Chiping Jiang, Hui Chai & Peng Yan

  2. State Key Laboratory of Nonlinear Mechanics (LNM), Institute of Mechanics, Chinese Academy of Sciences, Beijing, 100190, China

    Chiping Jiang & Fan Song

Authors
  1. Chiping Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hui Chai
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Peng Yan
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Fan Song
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chiping Jiang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jiang, C., Chai, H., Yan, P. et al. The interaction of a screw dislocation with a circular inhomogeneity near the free surface. Arch Appl Mech 84, 343–353 (2014). https://doi.org/10.1007/s00419-013-0803-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00419-013-0803-0

Keywords

Search

Navigation