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Shells and Plates with Surface Effects Read chapter Read first chapter

2013 | OriginalPaper | Chapter

A Theory of Disclination and Dislocation Fields for Grain Boundary Plasticity

Authors : V. Taupin, L. Capolungo, C. Fressengeas, A. Das, M. Upadhyay

Published in: Generalized Continua as Models for Materials

Publisher: Springer Berlin Heidelberg

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Abstract

A continuum mechanics model is introduced for a core and structure sensitive modeling of grain boundary mediated plasticity. It accounts for long range elastic strain and curvature incompatibilities due to the presence of dislocation and disclination densities. The coupled spatio-temporal evolution of the crystal defects is also accounted for by transport equations. Based on atomistic structures, copper tilt boundaries are modeled with periodic sequences of wedge disclination dipoles. Their self-relaxation by transport leads to grain boundary configurations with lower elastic energies, which are compared to molecular statics values. The characteristic internal length inherent to strain gradient elasticity, which relates the elastic energy weight of couple-stresses to that of stresses, is chosen to retrieve the elastic energy obtained by atomistic simulations. This length is found to be lower than interatomic distances. In agreement with atomistic modeling, couple-stress elasticity is thought to be relevant for the modeling of highly heterogeneous defect microstructures at atomic resolution scales only.

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Footnotes
1
It is found from Frank’s formula that the separation distance \(\displaystyle l\) between the edge dislocations in a dislocation-made tilt boundary of misorientation \(\displaystyle 46.40^{\circ }\) is \(\displaystyle l = 0.34\,nm\), a distance much too short to be realistic. Such a result supports the view that a consistent description of high-angle tilt boundaries should recourse to disclination dipole walls rather than edge dislocation walls.
 
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Metadata
Title
A Theory of Disclination and Dislocation Fields for Grain Boundary Plasticity
Authors
V. Taupin
L. Capolungo
C. Fressengeas
A. Das
M. Upadhyay
Copyright Year
2013
Publisher
Springer Berlin Heidelberg
Book
Generalized Continua as Models for Materials

Print ISBN: 978-3-642-36393-1

Electronic ISBN: 978-3-642-36394-8

Copyright Year: 2013

DOI
https://doi.org/10.1007/978-3-642-36394-8_18

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