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Higher order alignment tensors for continuum dislocation dynamics

Published online by Cambridge University Press:  05 April 2013

Thomas Hochrainer*
Affiliation:
Universität Bremen, IW3, Am Biologischen Garten 2,28359 Bremen, Germany.
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Abstract

Dislocation density based modeling of crystal plasticity remains one of the central challenges in multi scale materials modeling. A dislocation based theory requires sufficiently rich dislocation density measures which are capable of predicting their own evolution. Continuum dislocation dynamics is based on a higher dimensional dislocation density tensor comprised of two distribution functions on the space of local orientations, which are the density of dislocations per orientation and the density of dislocation curvature per orientation. We propose to expand these functions into series of symmetric tensors (alignment tensors), to be used in dislocation based theories without extra dimensions. The first two terms in the expansion of the density define the total dislocation density and the Kröner-Nye tensor. The first term in the expansion of the curvature density, the scalar total curvature density, turns out to be a conserved quantity; the integral of which corresponds to the total number of dislocations. The content of the next higher order tensors is discussed.

Type
Articles
Copyright
Copyright © Materials Research Society 2013 

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References

REFERENCES

Kröner, E., Int. J. Solids Struct. 38, 11151134 (2001).CrossRefGoogle Scholar
Acharya, A., J. Mech. Phys. Solids 49, 761784 (2001).CrossRefGoogle Scholar
Sedlacek, R., Kratochvil, J. and Werner, E., Philos. Mag. 83, 37353752 (2003)CrossRefGoogle Scholar
Kocks, M. F., J. Eng. Mater. Techn.-Trans. 98 (1), 76–-86 (1976)CrossRefGoogle Scholar
Roters, F. et al. ., Acta Mater. 58 11521211 (2010)Google Scholar
Arsenslis, A. et al. ., J. Mech. Phys. Solids 52, 12131246 (2004).CrossRefGoogle Scholar
Hochrainer, T., Zaiser, M. and Gumbsch, P., Philos. Mag. 87, 12611282 (2007)CrossRefGoogle Scholar
Hess, S., Z. Naturkunde 30a, 728738 (1975)Google Scholar
Pressly, A., Elemetary Diffenerential Geometry (Springer-Verlag, London 2010), p. 57 CrossRefGoogle Scholar
Advani, S.G. and Tucker, C.L., Journal of Rheology 31 (8), 751784 (1987)CrossRefGoogle Scholar
Kröger, M., Physica A 248, 332336 (1998)CrossRefGoogle Scholar
Hochrainer, T., Oberwolfach Reports 15, 3031 (2012) DOI: 10.4171/OWR/2012/15 Google Scholar