Extension of the Vook–Witt and inverse Vook–Witt elastic grain-interaction models to general loading states

Abstract

The recently developed Vook–Witt and inverse Vook–Witt elastic grain-interaction models have been employed for the calculation of mechanical elastic constants and diffraction (X-ray) stress factors of, in particular, thin films. However, their applicability is limited to a planar, rotationally symmetric state of macroscopic, mechanical stress. For such a loading state (and an, at least, transversely, elastically isotropic specimen), only two mechanical elastic constants are necessary to describe mechanical elastic behaviour and only the sum of two diffraction (X-ray) stress factors is needed to relate lattice strains to the one independent component of the mechanical stress tensor. The restriction to a planar, rotationally symmetric state of mechanical stress will be removed in this work. Calculation of the full stiffness tensor and all six diffraction (X-ray) stress factors then becomes possible. It was found previously that the Vook–Witt and inverse Vook–Witt models become (but only approximately) equivalent to the Eshelby–Kröner model for certain ideal grain-shape textures. For this reason, results of numerical calculations of mechanical elastic constants and diffraction (X-ray) stress factors, based on the Vook–Witt and inverse Vook–Witt models, will be presented and compared to corresponding results obtained from the Eshelby--Kröner grain-interaction model considering ideal grain-shape (‘morphological’) textures.

Acknowledgments

The authors express their gratitude to Professor Dr Ir. E. J. Mittemeijer for constructive discussions.

Notes

†Present address: Institut de Recherche en Génie-Civil et Mécanique, GeM–CRTT, 37 Bd. de l'Université, 44602 Saint-Nazaire, France

†Of course, a real polycrystal cannot consist of ellipsoidal grains (only). The ellipsoidal shape is an idealized shape, which is adopted to represent grains with (average) aspect ratios different from 1, whereas a spherical shape is adopted for grains with an (average) aspect ratio of 1.

Additional information

Notes on contributors

S. Fréour†

†Present address: Institut de Recherche en Génie-Civil et Mécanique, GeM–CRTT, 37 Bd. de l'Université, 44602 Saint-Nazaire, France