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The evolution of the anisotropy of a polycrystalline aggregate. (English) Zbl 0786.73067
(From authors’ abstract and introduction.) The macroscopic properties of a polycrystalline aggregate depend upon the orientational distribution of the single crystals. Firstly, the authors derive the equation of evolution for the orientation of a single crystal of arbitrary type that deforms through the mechanism of rate independent crystallographic slip. Then they introduce an orientational distribution function \(f(\phi)\) to describe the distribution of orientations of the single crystals in the aggregate, and derive the evolutionary equation for this function.
An approximate representation of the orientational distribution function applied to cubic crystals and the differential equations for the evolution of the coefficients associated with the anisotropic term of the representation are given. Solutions of these equations can be obtained numerically. This work is an attempt to extend the results obtained by V. C. Prantil [Ph.D. Thesis, Cornell Univ. Ithaca, New York (1992)] for the texture, plastic spin and yield of two-dimensional polycrystalline aggregates to three dimensions.

MSC:
74A60 Micromechanical theories
74M25 Micromechanics of solids
74E10 Anisotropy in solid mechanics
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