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Continuum Dislocation Dynamics Based on the Second Order Alignment Tensor

Published online by Cambridge University Press:  14 January 2014

Thomas Hochrainer
Thomas Hochrainer*
Affiliation:
Universität Bremen, IW3, Am Biologischen Garten 2,28359 Bremen, Germany.
*
*Contact e-mail: hochrainer@mechanik.uni-bremen.de
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Abstract

In the current paper we present a continuum theory of dislocations based on the second-order alignment tensor in conjunction with the classical dislocation density tensor (Kröner-Nye-tensor) and a scalar dislocation curvature measure. The second-order alignment tensor is a symmetric second order tensor characterizing the orientation distribution of dislocations in elliptic form. It is closely connected to total densities of screw and edge dislocations introduced in the literature. The scalar dislocation curvature density is a conserved quantity the integral of which represents the total number of dislocations in the system. The presented evolution equations of these dislocation density measures partly parallel earlier developed theories based on screw-edge decompositions but handle line length changes and segment reorientation consistently. We demonstrate that the presented equations allow predicting the evolution of a single dislocation loop in a non-trivial velocity field.

Keywords

dislocationsmicrostructuremetal
Type
Articles
Information
MRS Online Proceedings Library (OPL) , Volume 1651: Symposium KK – Adaptive Soft Matter through Molecular Networks , 2014 , mrsf13-1651-kk06-02
Copyright
Copyright © Materials Research Society 2014 

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References

REFERENCES

Groma, I., Csikor, F. F. and Zaiser, M., Acta Mater. 51, 1271–1281 (2003).CrossRefGoogle Scholar
Arsenlis, A. et al. ., J. Mech. Phys. Solids 52, 1213–1246 (2004).CrossRefGoogle Scholar
Zaiser, M. and Hochrainer, T., Scripta Mater. 54, 717–721 (2006)CrossRefGoogle Scholar
Hochrainer, T. MRS Proceedings, 1535, mmm2012-a-0343 doi:10.1557/opl.2013.451. (2013)CrossRefGoogle Scholar
Hochrainer, T., Zaiser, M. and Gumbsch, P., Philos. Mag. 87, 1261–1282 (2007)CrossRefGoogle Scholar
Hochrainer, T., Sandfeld, S., Zaiser, M. and Gumbsch, P., J. Mech. Phys. Solids. (in print)Google Scholar
Ebrahimi, A., Monavari, M. and Hochrainer, T., MRS Proceedings (this volume)Google Scholar
Acharya, A., J. Mech. Phys. Solids 49, 761–784 (2001).CrossRefGoogle Scholar
Sedlacek, R., Kratochvil, J. and Werner, E., Philos. Mag. 83, 3735–3752 (2003)CrossRefGoogle Scholar