Skip to main content
SpringerLink
Log in

A screw dislocation near a semi-infinite crack partially penetrating an elastic inhomogeneity of arbitrary shape

  • Original Paper
  • Published:
Acta Mechanica Aims and scope Submit manuscript

Abstract

A novel yet simple method is proposed to derive an analytical solution to the interaction problem of a screw dislocation inside an elastic inhomogeneity of arbitrary shape partially penetrated by a semi-infinite crack. The two analytic functions characterizing the elastic fields of stresses and displacement in the two-phase composite are readily obtained. Furthermore, we derive explicit expressions for the mode III stress intensity factor at the crack tip and the image force acting on the screw dislocation. Several specific examples are presented to demonstrate the obtained solution. An analytical solution to the case in which the screw dislocation is located in the cracked matrix is similarly derived.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

References

  1. Hutchinson, J.W.: Crack tip shielding by micro-cracking in brittle solids. Acta Metall. 35, 1605–1619 (1987)

    Article  Google Scholar 

  2. Erdogan, F., Gupta, G.D.: The inclusion problem with a crack crossing the boundary. Int. J. Fract. 11, 13–27 (1975)

    Article  Google Scholar 

  3. Steif, P.S.: A semi-infinite crack partially penetrating a circular inclusion. ASME J. Appl. Mech. 54, 87–92 (1987)

    Article  Google Scholar 

  4. Wu, C.H.: A semi-infinite crack penetrating an inclusion. ASME J. Appl. Mech. 55(3), 736–738 (1988)

    Article  Google Scholar 

  5. Li, Z., Chen, Q.: Crack–inclusion interaction for mode I crack analyzed by Eshelby equivalent inclusion method. Int. J. Fract. 118, 29–40 (2002)

    Article  Google Scholar 

  6. Yang, L.H., Chen, Q., Li, Z.H.: Crack–inclusion interaction for mode II crack analyzed by Eshelby equivalent inclusion method. Eng. Fract. Mech. 71, 1421–1433 (2004)

    Article  Google Scholar 

  7. Majumdar, B.S., Burns, S.J.: Crack tip shielding-an elastic theory of dislocations and dislocation arrays near a sharp crack. Acta Metall. 29, 579–588 (1981)

    Article  Google Scholar 

  8. Ohr, S.M., Chang, S.J., Thomson, R.: Elastic interaction of a wedge crack with a screw dislocation. J. Appl. Phys. 57, 1839–1843 (1985)

    Article  Google Scholar 

  9. Lin, I.H., Thomson, R.: Cleavage, dislocation emission and shielding for cracks under general loading. Acta Metall. 34, 187–206 (1986)

    Article  Google Scholar 

  10. Zhang, T.Y., Li, J.C.M.: Image forces and shielding effects of an edge dislocation near a finite length crack. Acta Metall. Mater. 39, 2739–2744 (1991)

    Article  Google Scholar 

  11. Lee, K.Y., Lee, W.G., Pak, Y.E.: Interaction between a semi-infinite crack and a screw dislocation in a piezoelectric material. ASME J. Appl. Mech. 67, 165–170 (2000)

    Article  Google Scholar 

  12. Huang, M.X., Li, Z.H.: Dislocation emission criterion from a blunt crack tip. J. Mech. Phys. Solids 52, 1991–2003 (2004)

    Article  Google Scholar 

  13. Bhandakkar, T.K., Chng, A.C., Curtin, W.A., Gao, H.: Dislocation shielding of a cohesive crack. J. Mech. Phy. Solids 58, 530–541 (2010)

    Article  MathSciNet  Google Scholar 

  14. Wang, X., Schiavone, P.: An edge dislocation interacting with two semi-infinite cracks. Eng. Fract. Mech. 232, 107044 (2020)

    Article  Google Scholar 

  15. Ting, T.C.T.: Anisotropic Elasticity-Theory and Applications. Oxford University Press, New York (1996)

    Book  Google Scholar 

  16. Dundurs, J.: Elastic interaction of dislocations with inhomogeneities. In: Mathematical Theory of Dislocations, pp. 70–115. American Society of Mechanical Engineers, New York (1969)

    Google Scholar 

  17. Lubarda, V.A.: Circular inclusion near a circular void: determination of elastic antiplane shear fields and configurational forces. Acta Mech. 226, 643–664 (2015)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant No. 11272121) and by a Discovery Grant from the Natural Sciences and Engineering Research Council of Canada (Grant No.: RGPIN–2017—03716115112).

Author information

Authors and Affiliations

  1. School of Mechanical and Power Engineering, East China University of Science and Technology, 130 Meilong Road, Shanghai, 200237, China

    Xu Wang

  2. Department of Mechanical Engineering, 10-203 Donadeo Innovation Centre for Engineering, University of Alberta, Edmonton, AB, T6G 1H9, Canada

    Peter Schiavone

Authors
  1. Xu Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Peter Schiavone
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Xu Wang or Peter Schiavone.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, X., Schiavone, P. A screw dislocation near a semi-infinite crack partially penetrating an elastic inhomogeneity of arbitrary shape. Acta Mech 232, 2919–2931 (2021). https://doi.org/10.1007/s00707-021-02989-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-021-02989-4

Search

Navigation