Hostname: page-component-586b7cd67f-t7czq Total loading time: 0 Render date: 2024-11-25T15:49:27.399Z Has data issue: false hasContentIssue false
  • English
  • Français

Comparison of closure approximations for continuous dislocation dynamics

Published online by Cambridge University Press:  17 January 2014

Mehran Monavari ,
Michael Zaiser  and
Stefan Sandfeld
Mehran Monavari
Affiliation:
Institute for Materials Simulation (WW8), Friedrich-Alexander-University Erlangen-Nürnberg, Dr.-Mack-Str. 77, 90762 Fürth, Germany
Michael Zaiser
Affiliation:
Institute for Materials Simulation (WW8), Friedrich-Alexander-University Erlangen-Nürnberg, Dr.-Mack-Str. 77, 90762 Fürth, Germany
Stefan Sandfeld
Affiliation:
Institute for Materials Simulation (WW8), Friedrich-Alexander-University Erlangen-Nürnberg, Dr.-Mack-Str. 77, 90762 Fürth, Germany
Get access

Abstract

We discuss methods to describe the evolution of dislocation systems in terms of a limited number of continuous field variables while correctly representing the kinematics of systems of flexible and connected lines. We show that a satisfactory continuum representation may be obtained in terms of only four variables. We discuss the consequences of different approximations needed to formulate a closed set of equations for these variables and propose a benchmark problem to assess the performance of the resulting models. We demonstrate that best results are obtained by using the maximum entropy formalism to arrive at an optimal estimate for the dislocation orientation distribution based on its lowest-order angular moments.

Keywords

dislocationsmicrostructuresimulation
Type
Articles
Information
MRS Online Proceedings Library (OPL) , Volume 1651: Symposium KK – Dislocation Plasticity , 2014 , mrsf13-1651-kk03-02
Copyright
Copyright © Materials Research Society 2014 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Nye, J.F., Acta Metall. 1, 153 (1953).CrossRefGoogle Scholar
Kröner, E., Kontinuumstheorie der Versetzungen und Eigenspannungen (Springer, 1958).CrossRefGoogle Scholar
Johnston, W.G. and Gilman, J.J., J. Appl. Phys. 30, 189 (1959).Google Scholar
Kocks, U.F., Kocks, UF, J. Engng Mater. Technol. (ASME series H) 98, 76 (1976).CrossRefGoogle Scholar
Groma, I., Phys. Rev. B 56, 5807 (1997).CrossRefGoogle Scholar
El-Azab, A., Phys. Rev. B 61, 11956 (2000).CrossRefGoogle Scholar
Sedláček, R., Kratochvíl, J. and Werner, E., Phil. Mag. 83, 3735 (2003).CrossRefGoogle Scholar
Arsenlis, A.A., Parks, D.M., Becker, R. and Bulatov, V.V., J. Mech. Phys. Solids 52, 1213 (2004).CrossRefGoogle Scholar
Acharya, A. and Roy, A., J. Mech. Phys. Solids 54, 1687 (2006).CrossRefGoogle Scholar
Hochrainer, T., Zaiser, M. and Gumbsch, P., Phil. Mag. 87, 1261 (2007).CrossRefGoogle Scholar
Sandfeld, S., Hochrainer, T., Gumbsch, P. and Zaiser, M., Phil. Mag. 90, 3697 (2010).CrossRefGoogle Scholar
Sandfeld, S., Hochrainer, T., Zaiser, M. and Gumbsch, P., J. Mater. Res. 26, 623 (2011).CrossRefGoogle Scholar
Hochrainer, T., Sandfeld, S., Zaiser, M. and Gumbsch, P., J. Mech. Phys. Solids (2013), DOI:10.1016/j.jmps.2013.09.012.Google Scholar
Hochrainer, T., MRS Proceedings (Proceedings of the MMM2012-6th International Conference on Multiscale Materials Modeling), 04/2013; 1355.Google Scholar
Ebrahimi, A., Monavari, M. and Hochrainer, T., MRS Proceedings of the fall 2013 meeting Google Scholar