Bounds and self-consistent estimates for elastic constants of random polycrystals with hexagonal, trigonal, and tetragonal symmetries

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Peselnick, Meister, and Watt have developed rigorous methods for bounding elastic constants of random polycrystals based on the Hashin-Shtrikman variational principles. In particular, a fairly complex set of equations that amounts to an algorithm has been presented previously for finding the bounds on effective elastic moduli for polycrystals having hexagonal, trigonal, and tetragonal symmetries. The more analytical approach developed here, although based on the same ideas, results in a new set of compact formulas for all the cases considered. Once these formulas have been established, it is then straightforward to perform what could be considered an analytic continuation of the ... continued below

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Berryman, J G September 16, 2004.

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Peselnick, Meister, and Watt have developed rigorous methods for bounding elastic constants of random polycrystals based on the Hashin-Shtrikman variational principles. In particular, a fairly complex set of equations that amounts to an algorithm has been presented previously for finding the bounds on effective elastic moduli for polycrystals having hexagonal, trigonal, and tetragonal symmetries. The more analytical approach developed here, although based on the same ideas, results in a new set of compact formulas for all the cases considered. Once these formulas have been established, it is then straightforward to perform what could be considered an analytic continuation of the formulas (into the region of parameter space between the bounds) that can subsequently be used to provide self-consistent estimates for the elastic constants in all cases. These self-consistent estimates are easily shown (essentially by construction) to lie within the bounds for all the choices of crystal symmetry considered. Estimates obtained this way are quite comparable to those found by the Gubernatis and Krumhansl CPA (coherent potential approximation), but do not require any computations of scattering coefficients.

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PDF-file: 29 pages; size: 0.2 Mbytes

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  • Journal Name: Journal of the Mechanics and Physics of Solids; Journal Volume: 53; Journal Issue: 10

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  • Report No.: UCRL-JRNL-206669
  • Grant Number: W-7405-ENG-48
  • Office of Scientific & Technical Information Report Number: 875664
  • Archival Resource Key: ark:/67531/metadc874922

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  • September 16, 2004

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  • Sept. 21, 2016, 2:29 a.m.

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  • Nov. 22, 2016, 9:31 p.m.

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Berryman, J G. Bounds and self-consistent estimates for elastic constants of random polycrystals with hexagonal, trigonal, and tetragonal symmetries, article, September 16, 2004; Livermore, California. (digital.library.unt.edu/ark:/67531/metadc874922/: accessed October 22, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.