Elastic properties of polycrystals—influence of texture and stereology

Abstract

The macroscopic elastic properties of polycrystalline materials depend on the elastic properties of the crystallites and the way how these are ‘arranged’ in the polycrystalline aggregate. This comprises the volume fraction of crystal orientations (texture) as well as their arrangement in space (stereology). It is estimated that the stereological aggregate parameters may contribute up to 25% of the maximum texture influence. Model calculations of the effective macroscopic elastic properties were carried out using a grain cluster model which is a finite discretization of the aggregate function g( x) describing the complete ‘orientation-stereology’ of the polycrystalline material. The most important stereological parameters influencing the effective elastic constants are grain shape expressed by two axis ratios, grain packing expressed by the space filling factor of the lattice of grain centres and orientation pair correlation of neighbouring grains expressed by the misorientation distribution function. By rotating the orientation of only one grain it can be shown that grain interaction strains decrease rapidly and may be neglected beyond the second order neighbours.