Elastic Constants Of Hcp
Authors: Publication Date: 2012-03-01 Research Org.: Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States) Sponsoring Org.: Earth Sciences Division OSTI Identifier: 1082188 Report Number(s): LBNL-5386E Journal ID: ISSN 1098-0121; PRBMDO DOE Contract Number: DE-AC02-05CH11231 Resource Type: Journal Article Journal Name: Physical Review. B, Condensed Matter and Materials Physics Additional Journal Information: Journal Volume: 85; Journal Issue: 9; Related Information: Journal Publication Date: 2012; Journal ID: ISSN 1098-0121 Publisher: American Physical Society (APS) Country of Publication: United States Language: English Subject: 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY.
GPa-1), Young modulus (Y, in GPa), Poisson`s ratio (), Pugh’s indicator (G/B. Ratio), machinability index (μM) and indexes of elastic anisotropy (A, f, and AU) for. Hcp-Re and hexagonal rhenium nitrides in comparison with available experimental. And theoretical data. Pv-CaIrO 3 and pPv-CaIrO 3 have orthorhombic symmetry and thus nine independent elastic constants. The six diagonal elastic constants (C 11, C 22, C 33, C 44, C 55, C 66) is related to nearly.
AbstractMethods for computing Hashin-Shtrikman bounds and related self-consistent estimates of elastic constants for polycrystals composed of crystals having orthorhombic symmetry have been known for about three decades. However, these methods are underutilized, perhaps because of some perceived difficulties with implementing the necessary computational procedures. Several simplifications of these techniques are introduced, thereby reducing the overall computational burden, as well as the complications inherent in mapping out the Hashin-Shtrikman bounding curves. The self-consistent estimates of the effective elastic constants are very robust, involving a quickly converging iteration procedure.
Elastic Constants Relation
Once these self-consistent values are known, they may then be used to speed up the computations of the Hashin-Shtrikman bounds themselves. It is shown furthermore that the resulting orthorhombic polycrystal code can be used as well to compute both bounds and self-consistent estimates for polycrystals of higher-symmetry tetragonal, hexagonal, and cubic (but not trigonal) materials. The self-consistent results found this way are shown to be the same as those obtained using the earlier methods, specifically those methods designed specially for each individual symmetry type. But the Hashin-Shtrikman bounds found using the orthorhombic code are either the same or (more typically) tighter than those found previously for these special cases (i.e., tetragonal, hexagonal, and cubic). The improvement in the Hashin-Shtrikman bounds is presumably due to the additional degrees of freedom introduced into the available search space. Authors: Publication Date: 2011-02-01 Research Org.: Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States) Sponsoring Org.: Earth Sciences Division OSTI Identifier: 1019302 Report Number(s): LBNL-4411E Journal ID: ISSN 1539-3755; TRN: US201114%%743 DOE Contract Number: DE-AC02-05CH11231 Resource Type: Journal Article Journal Name: Physical Review E Additional Journal Information: Journal Volume: 83; Journal Issue: 4; Related Information: Journal Publication Date: 2011; Journal ID: ISSN 1539-3755 Country of Publication: United States Language: English Subject: 54; 58; DEGREES OF FREEDOM; POLYCRYSTALS; SYMMETRY; VELOCITY.
Elastic Constants Of Hcp Research
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.
While the well-known Voigt and Reuss (VR) bounds, and the Voigt-Reuss-Hill (VRH) elastic constant estimators for random polycrystals are all straightforwardly calculated once the elastic constants of anisotropic crystals are known, the Hashin-Shtrikman (HS) bounds and related self-consistent (SC) estimators for the same constants are, by comparison, more difficult to compute. Recent work has shown how to simplify (to some extent) these harder to compute HS bounds and SC estimators. An overview and analysis of a subsampling of these results is presented here with the main point being to show whether or not this extra work (i.e., in calculating both the HS bounds and the SC estimates) does provide added value since, in particular, the VRH estimators often do not fall within the HS bounds, while the SC estimators (for good reasons) have always been found to do so. The quantitative differences between the SC and the VRH estimators in the eight cases considered are often quite small however, being on the order of ±1%.
Rubber Elastic Constant
These quantitative results hold true even though these polycrystal Voigt-Reuss-Hill estimators more typically (but not always) fall outside the Hashin-Shtrikman bounds, while the self-consistent estimators always fall inside (or on the boundaries of) these same bounds.