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

Journal Article · Thu Sep 16 04:00:00 EDT 2004 · Journal of the Mechanics and Physics of Solids

OSTI ID:875664

Berryman, J G

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.

• Research Organization: Lawrence Livermore National Laboratory (LLNL), Livermore, CA
• Sponsoring Organization: USDOE
• DOE Contract Number: W-7405-ENG-48
• OSTI ID: 875664
• Report Number(s): UCRL-JRNL-206669
• Journal Information: Journal of the Mechanics and Physics of Solids, Journal Name: Journal of the Mechanics and Physics of Solids Journal Issue: 10 Vol. 53; ISSN JMPSA8; ISSN 0022-5096
• Country of Publication: United States
• Language: English

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ALGORITHMS
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