On the Generation of Discrete Isotropic Orientation Distributions for Linear Elastic Cubic Crystals |
| |
Authors: | A Bertram T Böhlke N Gaffke B Heiligers R Offinger |
| |
Institution: | (1) Faculty of Engineering, University of Magdeburg, Magdeburg, Germany;(2) Faculty of Mathematics, University of Magdeburg, Magdeburg, Germany |
| |
Abstract: | We consider a model for the elastic behavior of a polycrystalline material based on volume averages. In this case the effective
elastic properties depend only on the distribution of the grain orientations. The aggregate is assumed to consist of a finite
number of grains each of which behaves elastically like a cubic single crystal. The material parameters are fixed over the
grains. An important problem is to find discrete orientation distributions (DODs) which are isotropic, i.e., whose Voigt and
Reuss averages of the grain stiffness tensors are isotropic. We succeed in finding isotropic DODs for any even number of grains
N≥4 and uniform volume fractions of the grains. Also, N=4 is shown to be the minimum number of grains for an isotropic DOD.
This revised version was published online in August 2006 with corrections to the Cover Date. |
| |
Keywords: | anisotropy cubic symmetry discrete orientation distribution invariant subspace isotropy linear elasticity polycrystals Reuss average special orthogonal group Voigt average |
本文献已被 SpringerLink 等数据库收录! |