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An edge dislocation interacting with a completely coated semi-infinite crack

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Abstract

We derive an analytic solution to the plane problem associated with an edge dislocation interacting with a completely coated semi-infinite crack in the presence of remote in-plane loading. The semi-infinite crack and the parabolic coating–matrix interface are confocal, and the coating and the matrix have the same shear modulus but distinct Poisson’s ratios. Through the introduction of a conformal mapping function and the application of analytic continuation, a closed-form representation of a particular auxiliary function can be obtained leading to analytic expressions of the two pairs of analytic functions in the image plane characterizing the elastic fields in the two-phase composite. The local mode I and mode II stress intensity factors at the crack tip and the image force acting on the edge dislocation are then derived.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant No. 11272121) and through 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, Alberta, 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. An edge dislocation interacting with a completely coated semi-infinite crack. Z. Angew. Math. Phys. 71, 176 (2020). https://doi.org/10.1007/s00033-020-01403-8

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  • DOI: https://doi.org/10.1007/s00033-020-01403-8

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