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The effect of cracks on the superconducting transport current in thin films: The analogy with two-dimensional elasticity and plasticity

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Abstract

Simulations of arrays of resistively shunted Josephson junctions containing a crack of uncoupled junctions indicate that the crack can distort the supercurrent flow and provide a nucleation site at the crack tip for the formation of superconducting vortices at applied currents below the critical current of the homogeneous material. An analogy is established between the supercurrent distribution in two dimensions and the stress field distribution around the crack for antiplane mechanical loading. The analogy is used to show that the supercurrent distribution can be described analytically in terms of a Westergaard function used in elasticity theory. In addition, using a correspondence between the forces acting on a vortex and a crystal dislocation, models for screw dislocation emission from a crack tip are transposed to describe vortex emission from a crack tip. These lead to predictions for the pinning force required to prevent dissipation by vortex emission from the crack tip, as well as for the size of a vortex zone ahead of the crack for different values of the ratio of the applied current to the pinning force.

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References

  1. E. Olsson, A. Gupla, M.D. Thouless, and D.R. Clarke, Appl. Phys. Lett. 58, 1682 (1991).

    Article  CAS  Google Scholar 

  2. U.S. Hellman, E. H. Hartford, and K. M. Gyorgy, Appl. Phys. Lett. 58, 1335 (1991).

    Article  CAS  Google Scholar 

  3. T. M. Shaw, S. L. Shindc, D. Dimos. R. F. Cook. P. R. Duncombc, and C. Kroll. J. Mater. Res. 4, 248 (1989).

    Article  CAS  Google Scholar 

  4. D. R. Clarke. T. M. Shaw, and D. Dimes, J. Am. Ceram. Soc. 72, 1103 (1989).

    Article  CAS  Google Scholar 

  5. A.G. Kvans, Acta Metall. 26, 1845 (1978).

    Article  CAS  Google Scholar 

  6. D.R. Clarke, Acta Metall. 28, 913 (1980).

    Article  CAS  Google Scholar 

  7. S.G. Kim and P.M. Duxbury. J. Appl. Phys. 70, 3164 (1991).

    Article  Google Scholar 

  8. W. Xia and P. L. Leath, Phys. Rev. Lett. 63, 1428 (1989).

    Article  CAS  Google Scholar 

  9. P. Haasen, Contemporary Physics 18, 373 (1977).

    Article  CAS  Google Scholar 

  10. H.R. Hilzinger. Philos. Mag. 36, 225 (1977).

    Article  CAS  Google Scholar 

  11. J. R. Clem, Physica C 153–155, 56 (1988).

    Google Scholar 

  12. D. Dimos, J. Mannhart. and P. Chaudhari, Phys. Rev. B 41, 4038 (1990).

    Article  CAS  Google Scholar 

  13. C.S. Nichols and D.R. Clarke, Acta Metall. 39, 995 (1991).

    Article  CAS  Google Scholar 

  14. D.E. McCumber, J. Appl. Phys. 39, 3113 (1968).

    Article  Google Scholar 

  15. W.C. Stewart, Appl. Phys. Lett. 12, 277 (1968).

    Article  Google Scholar 

  16. M. Tinkham. Introduction to Superconductivity (R. E. Krieger, New York, 1980).

    Google Scholar 

  17. T. Van Duzer and C. W. Turner, Principles of Superconductive Devices and Circuits (Elsevier, New York, 1981).

    Google Scholar 

  18. H.M. Westergaard. J. Appl. Mech. 6, 49–53 (1939).

    Google Scholar 

  19. H. Tada, P. C. Paris, and G. R. Irwin, The Stress Analysts of Cracks Handbook (Del Research, 1978).

    Google Scholar 

  20. G.C. Sih, Handbook of Stress Intensity Factors (Institute of Fracture and Solid Mechanics, Lehigh University, Bethlehem, PA).

  21. J. R. Rice. J. Appl. Mech. 35, 379 (1968).

    Article  Google Scholar 

  22. J. R. Rice and R. M. Thomson, Philos. Mag. 29, 73 (1974).

    Article  CAS  Google Scholar 

  23. P.G. de (iennes, Superconductivity of Metals and Alloys (W. A. Benjamin. New York, 1966).

    Google Scholar 

  24. J. P. Hirth and J. Lothe, Theory of Dislocations (McGraw-Hill. New York. 1968).

    Google Scholar 

  25. M.O. Peach and J.S. Kochler, Phys. Rev. 80, 436 (1950).

    Article  Google Scholar 

  26. R.M. Thomson, Solid State Phys. 39, 1 (1986).

    Article  Google Scholar 

  27. Y-H. Chiao and D.R. Clarke, Acta Metall. 37, 203 (1989).

    Article  CAS  Google Scholar 

  28. M. Tinkham and C.J. Lobb, Solid State Phys. 42, 91 (1989).

    Article  CAS  Google Scholar 

  29. B.A. Bilby, A. H. Cottrell, and K. H. Swindcn, Proc. R. Soc. A 272, 304 (1963).

    Google Scholar 

  30. B. A. Bilby and J. D. F.shelby, in Fracture, edited by H. Leibowitz, 1, 99.

  31. J.D. Livingston, Phys. Status Solidi 44, 295 (1977).

    Article  CAS  Google Scholar 

  32. P.J. Lce and D.C. I.arbalcstier, Acta Mctall. 35, 2523 (1987).

    Article  CAS  Google Scholar 

  33. A.M. Campbell and J. E. Evetts, Adv. Phys. 21, 199 (1972).

    Article  CAS  Google Scholar 

  34. R. Labusch, Crystal Lattice Defects 1, 1 (1969).

    Google Scholar 

  35. E.J. Kramer, J. Appl. Phys. 41, 621 (1971).

    Article  Google Scholar 

  36. E.J. Kramer, J. Appl. Phys. 44, 1360 (1973).

    Article  CAS  Google Scholar 

  37. H. Trauble and U. Essmann. J. Appl. Phys. 39, 4052 (1968).

  38. U. Essmann and H. Trauble. Phys. Status Solidi 32, 337 (1969).

    Article  CAS  Google Scholar 

  39. C. Herring, Phys. Lett. A 47, 105 (1974).

    Article  CAS  Google Scholar 

  40. G.J. Dolan, G. V. Chandrashekhar, T. R. Dinger, C. Leild. and F. Hollzberg, Phys. Rev. Lett. 62, 827 (1989).

    Article  CAS  Google Scholar 

  41. N.V. Sarma. Phys. Lett. A 25, 315 (1967).

    Article  CAS  Google Scholar 

  42. U. Krageloh, Phys. Status Solidi 42, 559 (1970).

    Article  Google Scholar 

  43. M.R. Beasley, R. Labusch, and W.W. Webb. Phys. Rev. 181, 682 (1969).

    Article  Google Scholar 

  44. J.R. Rice, J. Mech. and Phys. Solids 40, 239 (1992).

    Article  CAS  Google Scholar 

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Authors and Affiliations

  1. Materials Department, University of California, California, 93106, Santa Barbara, USA

    David R. Clarke & Marc DeGraef

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  1. David R. Clarke
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  2. Marc DeGraef
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Clarke, D.R., DeGraef, M. The effect of cracks on the superconducting transport current in thin films: The analogy with two-dimensional elasticity and plasticity. Journal of Materials Research 8, 1515–1532 (1993). https://doi.org/10.1557/JMR.1993.1515

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  • DOI: https://doi.org/10.1557/JMR.1993.1515

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