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Boundary Behavior and Confinement of Screw Dislocations

Published online by Cambridge University Press:  30 May 2017

Marco Morandotti*
Affiliation:
Fakultät für Mathematik, Technische Universität München, Boltzmannstrasse, 3, 85748 Garching bei München, Germany.

Abstract

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In this note we discuss two aspects of screw dislocations dynamics: their behavior near the boundary and a way to confine them inside the material. In the former case, we obtain analytical results on the estimates of collision times (one dislocation with the boundary and two dislocations with opposite Burgers vectors with each other); numerical evidence is also provided. In the latter, we obtain analytical results stating that, under imposing a certain type of boundary conditions, it is energetically favorable for dislocations to remain confined inside the domain.

Type
Articles
Copyright
Copyright © Materials Research Society 2017 

References

REFERENCES

Blass, T. and Morandotti, M., J. Convex Anal., 24, 547560 (2017).Google Scholar
Caffarelli, L. A. and Friedman, A., Duke Math. J., 52, 431456 (1985).CrossRefGoogle Scholar
Cermelli, P. and Gurtin, M. E., Arch. Ration. Mech. Anal., 148, 352 (1999).CrossRefGoogle Scholar
Dal Maso, G., An introduction to Γ-convergence, Progress in Nonlinear Differential Equations and their Applications, 8, Birkhäuser Boston Inc., Boston, MA, 1993.CrossRefGoogle Scholar
Hirsch, P. B., Horne, R. W., and Whelan, M. J., Phil. Mag 1, 677684 (1956).CrossRefGoogle Scholar
Hirth, J.P. and Lothe, J.. Theory of Dislocations. Krieger Publishing Company, 1982.Google Scholar
Hudson, T. and Morandotti, M., Properties of screw dislocation dynamics: time estimates on boundary and interior collisions. arXiv:1703.02474. (2017) (submitted).Google Scholar
Lucardesi, I., Morandotti, M., Scala, R., and Zucco, D., Confinement of dislocations inside a crystal with a prescribed external strain. arXiv:1610.06852. (2016) (submitted).Google Scholar
Orowan, E., Zeitschrift für Physik, 89, 634659 (1934).CrossRefGoogle Scholar
Polanyi, M., Zeitschrift für Physik, 89, 660664 (1934).CrossRefGoogle Scholar
Taylor, G. I.. Proceedings of the Royal Society of London. Series A, 145, 362387 (1934).Google Scholar
Volterra, V., Annales scientifiques de l’École Normale Supérieure, 24, 401517 (1907).CrossRefGoogle Scholar