ISSN:
1573-2681
Keywords:
anisotropy
;
cubic symmetry
;
discrete orientation distribution
;
invariant subspace
;
isotropy
;
linear elasticity
;
polycrystals
;
Reuss average
;
special orthogonal group
;
Voigt average
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
,
Physics
Notes:
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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1007655817328
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