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.
