Skip to main content
SpringerLink
Log in

Elastic fields due to an edge dislocation in an isotropic film-substrate by the image method

  • Published:
Acta Mechanica Aims and scope Submit manuscript

Abstract

The stress and displacement fields due to an edge dislocation in a linearly elastic, isotropic film-substrate are derived using the method of image dislocations. The key features of the developed method are (1) a decomposition scheme in which the interfacial conditions are satisfied a priori, (2) all singular integrals are eliminated from the governing equations, (3) the elastic fields are obtained in the form of series, the terms of which can be exactly evaluated via integral transforms, and (4) the solutions converge satisfactorily with only three terms of the series. It is shown that the film thickness and dislocation position have a significant influence on the image force acting on the dislocation, and that the film thickness variation due to an accumulation of dislocations may degrade the performance of optical films.

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. Freund L.B., Suresh S.: Thin Film Materials. Cambridge University Press, Cambridge (2003)

    Google Scholar 

  2. Narayan J., Oktyabrsky S.: Formation of misfit dislocations in thin film heterostructures. J. Appl. Phys. 92, 7122–7127 (2002)

    Article  Google Scholar 

  3. Wang C.-M., Thevuthasan S., Gao F., McCready D.E., Chambers S.A.: The characteristics of interface misfit dislocations for epitaxial α − Fe2 O 3 on α − Al2 O 3(0001). Thin Sol. Films 414, 31–38 (2002)

    Article  Google Scholar 

  4. Groh S., Devincre B., Kubin L.P., Roos A., Feyel F., Chaboche J.-L.: Dislocations and elastic anisotropy in heteroepitaxial metallic thin films. Phil. Mag. Lett. 83, 303–313 (2003)

    Article  Google Scholar 

  5. Wang B., Woo C.H., Sun Q., Yu T.X.: Critical thickness for dislocation generation in epitaxial piezoelectric thin films. Phil. Mag. 1, 3753–3764 (2003)

    Google Scholar 

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

    Google Scholar 

  7. Chou Y.T.: Screw dislocations in and near lamellar inclusions. Phys. Stat. Sol. 17, 509–516 (1966)

    Article  Google Scholar 

  8. Koehler J.S.: Attempt to design a strong solid. Phys. Rev. B 2, 547–551 (1970)

    Article  Google Scholar 

  9. Kamat S.V., Hirth J.P.: Image forces on screw dislocations in multilayer structures. Scr. Metall. 21, 1587–1592 (1987)

    Article  Google Scholar 

  10. Dundurs J., Sendeckyj G.P.: Behavior of an edge dislocation near bimetallic interface. J. Appl. Phys. 36, 3353–3354 (1965)

    Article  Google Scholar 

  11. Lee M.S., Dundurs J.: Edge dislocation in a surface layer. Int. J. Eng. Sci. 11, 87–94 (1973)

    Article  MATH  Google Scholar 

  12. Suo Z., Hutchinson J.W.: Steady-state cracking in brittle substrate beneath adherent films. Int. J. Solids Struct. 25, 1337–1353 (1989)

    Article  Google Scholar 

  13. Fleck N.A., Hutchinson J.W., Suo Z.: Crack path selection in a brittle adhesive layer. Int. J. Solids Struct. 27, 1683–1703 (1991)

    Article  Google Scholar 

  14. Erdogan F., Wu B.: Interface crack problems in layered orthotropic materials. J. Mech. Phys. Solids 41, 889–917 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  15. Zhang T.Y.: Effect of elastic constants on the critical thickness of an epilayer. Phys. Stat. Sol. (a) 152, 415–429 (1995)

    Article  Google Scholar 

  16. Choi S.T., Earmme Y.Y.: Elastic study on singularities interacting with interfaces using alternating technique Part II. Isotropic trimaterial. Int. J. Solids Struct. 39, 1199–1211 (2002)

    Article  MATH  Google Scholar 

  17. Wu M.S., Kirchner H.O.K.: Line defects in the (110)-plane of a cubic crystal—an outstanding problem solved by the integral formalism. Proc. R. Soc. Lond. A 459, 2033–2047 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  18. Weertman J.: Dislocation Based Fracture Mechanics. World Scientific, Singapore (1996)

    Google Scholar 

  19. Wu M.S.: Exact solutions for a wedge disclination dipole in a transversely isotropic bimaterial. Int. J. Eng. Sci. 38, 1811–1835 (2000)

    Article  Google Scholar 

  20. Wu M.S., Huang H., Feng R.: Closed-form solutions for interfacial edge dislocations in anisotropic bicrystals by the image method. Mech. Mater. 35, 913–930 (2003)

    Article  Google Scholar 

  21. Zhou K., Wu M.S.: Exact solutions for periodic interfacial wedge disclination dipoles in a hexagonal bicrystal. Math. Mech. Solids 11, 337–360 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  22. Wang H.Y., Wu M.S., Fan H.: Image decomposition method for the analysis of a mixed dislocation in a general multilayer. Int. J. Solids Struct. 44, 1563–1581 (2007)

    Article  MATH  Google Scholar 

  23. Wen J., Wu M.S.: Analysis of a line defect in a multilayered smart structure by the image method. Mech. Mater. 39, 126–144 (2007)

    Article  Google Scholar 

  24. Hirth J.P., Lothe J.: Theory of Dislocations, Reprint Edition. Krieger, Malabar (1992)

    Google Scholar 

  25. Macleod H.A.: Thin-Film Optical Filters. Adam Hilger Ltd, Bristol (1986)

    Book  Google Scholar 

  26. Elsholz F., Schöll E., Rosenfeld A.: Control of surface roughness in amorphous thin-film growth. Appl. Phys. Lett. 84, 4167–4169 (2004)

    Article  Google Scholar 

  27. Lu H.L., Scarel G., Lamagna L., Fanciulli M., Ding S.-J., Zhang D.W.: Effect of rapid thermal annealing on optical and interfacial properties of atomic-layer-deposited Lu2O3 films on Si (100). Appl. Phys. Lett. 93, 152906-1–152906-3 (2008)

    Google Scholar 

  28. Hahn S.L.: Hilbert Transforms in Signal Processing. Artech House, Boston (1996)

    MATH  Google Scholar 

  29. Tricomi F.G.: Integral Equations. Dover Publications, New York (1985)

    Google Scholar 

Download references

Author information

Author notes

  1. Kun Zhou

    Present address: Department of Mechanical Engineering, Northwestern University, Evanston, IL, 60208, USA

Authors and Affiliations

  1. School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore, 639798, Singapore

    Kun Zhou & Mao S. Wu

Authors
  1. Kun Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mao S. Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mao S. Wu.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhou, K., Wu, M.S. Elastic fields due to an edge dislocation in an isotropic film-substrate by the image method. Acta Mech 211, 271–292 (2010). https://doi.org/10.1007/s00707-009-0226-8

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-009-0226-8

Keywords

Search

Navigation