Table of Contents
Textures and Microstructures
Volume 26 (1996)–27

Estimation of the Range of Elastic Interaction Due to Grain Misorientation

1Institute of Theoretical Physics B, Technical University Clausthal, Germany
2Department of Physical Metallurgy, Technical University Clausthal, Germany

Received 30 January 1996

Copyright © 1996 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The discontinuities of the elastic constants across grain boundaries in polycrystalline aggregates can be considered as sources of “compatibility” strains in the adjacent crystals under the action of an external stress. This effect was studied theoretically using the cluster model of Kiewel and Fritsche. In order to distinguish the contributions of individual grains, the orientation of only one grain was changed whereas all others in the cluster were kept constant. The orientation dependent part of the strain field thus allows to estimate the range over which the influence of an individual grain reaches. The results shows that this part decreases faster than 1/r3 with the distance from the centre of the considered grain. It has virtually vanished at two or three times the grain diameter.

The magnitude of the compatibility strains depends on grain shape. It was found higher in a cluster of cubic grains than in clusters consisting of dodecahedral or cubo-octahedral grains.

The compatibility strains vary systematically when the orientation of the considered grain is changed continuously. The influence of even small misorientations <5° is distinctly visible.

The results show that grain shape and orientation correlation must be taken into consideration additional to the texture in order to obtain narrower bounds for the effective elastic constants than those by Voigt and Reuss. They show, however, also that orientation correlations of higher than next-nearest neighbours have virtually no influence.