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A screw dislocation interacting with a cycloid rough surface

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Abstract

We study the interaction between a screw dislocation and a traction-free periodic cycloid wavy surface under uniform remote anti-plane stress. A closed-form solution to the interaction problem is derived using conformal mapping and the image method. The image force acting on the screw dislocation is obtained by applying the Peach–Koehler formula. In the case of a cusped cycloid surface, we determine the mode III stress intensity factors at the cusp tips. Criteria for the emission of the screw dislocation from sharp and blunt cusp tips are established.

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References

  1. Gao, H., Nix, W.D.: Surface roughening of heteroepitaxial thin films. Annu. Rev. Mater. Sci. 29, 173–209 (1999)

    Article  Google Scholar 

  2. Jesson, D.E., Chen, K.M., Pennycook, S.J., Thundat, T., Warmack, R.J.: Crack-like sources of dislocation nucleation and multiplication in thin films. Science 268(5214), 1161–1163 (1995)

    Article  Google Scholar 

  3. Chiu, C.H., Gao, H.: Stress singularities along a cycloid rough surface. Int. J. Solids Struct. 30, 2983–3012 (1993)

    Article  Google Scholar 

  4. Fan, H., Xiao, Z.M.: Dislocation interacting with a slightly wavy interface. Mech. Mater. 40(1), 2137–2161 (1996)

    MathSciNet  MATH  Google Scholar 

  5. Xiao, Z.M., Chen, B.J., Steele, C.R.: An edge dislocation interacting with a slightly wavy interface. Int. J. Eng. Sci. 40, 2137–2161 (2002)

    Article  MathSciNet  Google Scholar 

  6. Lubarda, V.A.: Dislocation Burgers vector and the Peach–Koehler force: a review. J. Mater. Res. Tech. 8, 1550–1565 (2018)

    Article  Google Scholar 

  7. Dundurs, J.: Elastic interaction of dislocations with inhomogeneities. In: Mura, T. (ed.) Mathematical theory of dislocations, pp. 70–115. American Society of Mechanical Engineers, New York (1969)

    Google Scholar 

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

    Article  Google Scholar 

  9. Rice, J.R., Thomson, R.: Ductile versus brittle behaviour of crystals. Philos. Mag. 29, 73–97 (1974)

    Article  Google Scholar 

  10. 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 

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

    Book  Google Scholar 

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Acknowledgements

This work is supported by a Discovery Grant from the Natural Sciences and Engineering Research Council of Canada (Grant No: RGPIN – 2017 - 03716115112).

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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

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  1. Xu Wang
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  2. Peter Schiavone
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Correspondence to Xu Wang or Peter Schiavone.

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Wang, X., Schiavone, P. A screw dislocation interacting with a cycloid rough surface. Acta Mech 232, 2417–2423 (2021). https://doi.org/10.1007/s00707-021-02961-2

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  • DOI: https://doi.org/10.1007/s00707-021-02961-2

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