Skip to main content
SpringerLink
Log in

Interaction between a screw dislocation and an elastic elliptical inhomogeneity with interfacial cracks

  • Published:
Acta Mechanica Sinica Aims and scope Submit manuscript

Abstract.

The elastic interaction between a screw dislocation and an elliptical inhomogeneity with interfacial cracks is studied. The screw dislocation may be located outside or inside the inhomogeneity. An efficient complex variable method for the complex multiply connected region is developed, and the general solutions to the problem are derived. As illustrative examples, solutions in explicit series form for complex potentials are presented in the case of one or two interfacial cracks. Image forces on the dislocation are calculated by using the Peach-Koehler formula. The influence of crack geometries and material properties on the image forces is evaluated and discussed. It is shown that the interfacial crack has a significant effect on the equilibrium position of the dislocation near an elliptical-arc interface. The main results indicate, when the length of the crack goes up to a critical value, the presence of the interfacial crack can change the interaction mechanism between a screw dislocation and an elliptical inclusion. The present solutions can include a number of previously known results as special cases.

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. Dundurs, J.: Mathematical Theory of Dislocations. Edited by Mura T, ASME, 1969

  2. Smith, E.: The interaction between dislocation and inhomogeneities-1. I. J. Eng. Sci., 6: 129–143 (1968)

    Google Scholar 

  3. Gong, S.X., Meguid, S.A.: A screw dislocation interaction with an elastic elliptical inhomogenety. I. J. Eng. Sci., 32: 1221–1228 (1994)

    Google Scholar 

  4. Santare, M.H., Keer, L.M.: Interaction between an edge dislocation and a rigid elliptical inclusion. J. Appl Mech, 53: 382–385 (1986)

    Google Scholar 

  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)

    Google Scholar 

  6. Warren, W.E.: The edge dislocation inside an elliptical inclusion. Mechanics of Materials, 2: 319–330 (1983)

    Google Scholar 

  7. Qaissaunee, M.T., Santare, M.H.: Edge dislocation interaction with an elliptical inclusion surrounding by an interfacial zone. The Quart. J. Mech. Appl. Math., 48: 465–482 (1995)

    Google Scholar 

  8. Liu, Y.W., Jiang, C.P.: On the interaction between a screw dislocation and an elastic elliptical inhomogentey with an interphase laye. In: Mechanics and Material Engineering for Science and Experiments, New York Ltd., 98–102 (2001)

  9. Stagni, L.: Edge dislocation near an elliptic inhomogeneity with either an adhering or a slipping interface: A comparative study. Philosophical Magazine A, 68: 49–57 (1993)

    Google Scholar 

  10. Stagni, L.: The effect of the interface on the interaction of an interior edge dislocation with an elliptical inhomogeneity. J. Appl. Math. Phys. (ZAMP), 50: 327–337 (1999)

    Google Scholar 

  11. 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)

    Google Scholar 

  12. Wang, X., Shen, Y.P.: An edge dislocation in a three-phase composite cylinder model with a sliding interface. ASME J. Appl. Mech., 69: 527–538 (2002)

    Google Scholar 

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

    Google Scholar 

  14. Fang, Q.H., Liu, Y.W., Jiang, C.P.: Edge dislocation interacting with an interfacial crack along a circular inhomogeneity. I. J. Solids Struct., 40(22): 5781–5797 (2003)

    Google Scholar 

  15. Muskhelishvili, N.L.: Some Basic Problems of Mathematical Theory of Elasticity. Leyden: Noordhoff, 1975

  16. Gradshteyn, I.S., Ryzhik, I.M.: Table of integrals, Series, and Products. New York: Academic Press, 1980

  17. Hirth, J.P., Lothe, J.: Theory of Dislocations 2nd edn. New York: John-wiley, 1982

  18. Lung, C.W., Wang, L.: The image force on the dislocation near a finite length crack tip. Philosophical Magazine A, 50(5): L19–L22 (1984)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Engineering Mechanics, Hunan University, Changsha, 410082, China

    Qihong Fang & Youwen Liu

  2. Solid Mechanics Research Center, Beijing University of Aeronautics and Astronautics, Beijing, 100083, China

    Chiping Jiang

Authors
  1. Qihong Fang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Youwen Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Chiping Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Youwen Liu.

Additional information

The project supported by the National Natural Science Foundation of China(10272009 and 10472030) and the Natural Science Foundation of Hunan Province(02JJY2014)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fang, Q., Liu, Y. & Jiang, C. Interaction between a screw dislocation and an elastic elliptical inhomogeneity with interfacial cracks. ACTA MECH SINICA 21, 151–159 (2005). https://doi.org/10.1007/s10409-005-0022-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10409-005-0022-1

Keywords

Search

Navigation