Bounding elastic constants of an orthotropic polycrystal using measurements of the microstructure

Beran, Mark J.; Mason, Thomas A.; Adams, Brent L.; Olsen, Tyler

doi:10.1016/0022-5096(96)00052-x

Cited by 73 publications

(55 citation statements)

References 12 publications

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“…Beran, 1968) is the most complete description and has been extensively used for model calculations (e.g. Beran et al, 1996;Mason and Adams, 1999). Until recently it has been considered too complicated for practical application.…”

mentioning

confidence: 99%

The Seismic anisotropy of the Earth's mantle: From single crystal to polycrystal

Mainprice¹,

Barruol²,

Ismaı̈l³

2000

Earth's Deep Interior: Mineral Physics and Tomography From the Atomic to the Global Scale

220

172

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The anisotropic single crystal seismic properties are reviewed in the light of recent experimental and theoretical determinations. Although considerable progress has been made on the determination of single crystal properties, data are still lacking, particularly for the temperature derivatives of transition zone and lower mantle phases. The common types of LPO of olivine, opx and cpx are presented together with their associated seismic properties. It is emphasized that simple seismic symmetry pattern of upper mantle rocks are a direct result of the interaction of olivine, opx and cpx. Using the standard structural frame (X lineation, Z pole to foliation) for typical LPOs of olivine, opx and cpx have the maximum Vp parallel to X, in the XZ plane and parallel to Y respectively. Destructive interference occurs between these minerals and hence P-wave anisotropy should be sensitive to the aggregate composition. For shear wave splitting (dVs) typical olivine and opx LPOs result in similar patterns with the maximum dVs in the YZ plane and the fast split shear wave (Vs1) polarized parallel to the foliation. A typical cpx LPO on the other hand produces destructive interference as the max dVs is close to X. By comparison with experiments and numerical simulations, it is estimated that upper mantle samples have an olivine LPO strength which recorded shear strain gamma of between 0.25 and 2.0. Pyrolite and piclogite models are compared with global transverse isotropic models. The slowly reducing P-wave anisotropy in the first 200 km can be explained by a model with constant composition and LPO strength. The sharp decrease in the observed anisotropy in the global models cannot be explained by the transformation of opx to cpx at 300 km, it is proposed that this decrease is due to a reduction in LPO strength from 200 to 350 km at the base of the lithosphere.

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mentioning

confidence: 99%

The Seismic anisotropy of the Earth's mantle: From single crystal to polycrystal

Mainprice¹,

Barruol²,

Ismaı̈l³

2000

Earth's Deep Interior: Mineral Physics and Tomography From the Atomic to the Global Scale

220

172

View full text Add to dashboard Cite

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“…Several authors have speculated that longer-range correlations may exist [10][11][12], but apart from our most recent study on quadruple junction character [9], there has been no quantitative exploration of this issue. In this note, we offer the first study of correlations at the second and third nearest-neighbor levels in two-dimensional (2D) grain boundary networks, and point to critical issues for the development of a comprehensive percolation theory for grain boundary networks.…”

Section: Introductionmentioning

confidence: 90%

Correlations beyond the nearest-neighbor level in grain boundary networks

Schuh

Frary

2006

Scripta Materialia

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This is an author-produced, peer-reviewed version of this article. © 2009, Elsevier. Licensed under the Creative Commons AttributionNonCommercial-NoDerivatives 4.0 International License (https://creativecommons.org/licenses/by-nc-nd/4.0/). The final, definitive version of this document can be found online at Scripta Materialia, doi: 10.1016Materialia, doi: 10. /j.scriptamat.2005 This is an author-produced, peer-reviewed version of this article. The final, definitive version of this document can be found online at Scripta Materialia Abstract Correlations among 'special' and 'general' grain boundaries are studied on two-dimensional networks, by examining the configurational entropy of boundary structures as well as percolation thresholds. Consideration of crystallographic constraints at various length scales reveals that higher-order constraints play a role in boundary connectivity and network structure. Implications for grain boundary engineering are discussed and directions for future work highlighted.

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“…The prediction of mechanical properties from details of the microstructure such as phase, crystalline grain orientation distribution, and microstructural morphology has received a special attention in the mechanics and materials community [Torquato and Stell 1982;Adams et al 1987]. The mathematical description of heterogeneity has received some breakthroughs in the last few decades with the works [Beran 1968;Kröner 1972;. More progress has been achieved in calculating the effective properties by making simple assumptions about the microstructure distribution (random, isotropic, and periodic microstructures) or the shape of the second phase (spherical, ellipsoidal, etc.).…”

Section: Introductionmentioning

confidence: 99%

“…Extension of this effort to nonrandom microstructures requires proper definition of n-th degree statistical correlation functions. For a detailed description of the theoretical discussion and the derivations please refer to [Adams et al 1987;Beran et al 1996;Garmestani et al 1998b;Saheli et al 2004]. A statistical continuum mechanics approach for both elastic and inelastic deformation of composites was introduced earlier [Garmestani et al 1998b;1998a;.…”

Section: Introductionmentioning

confidence: 99%

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Untitled

2008

JOMMS

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See inside back cover or http://www.jomms.org for submission guidelines.Regular subscription rate: $500 a year. We study an axially symmetric frictionless contact problem between a nonhomogeneous elastic halfspace and a rigid base that has a small axisymmetric surface recess. We reduce the problem to solving Fredholm integral equations, solve these equations numerically, and establish a relationship between the applied pressure and the gap radius. We find and graph the effects of nonhomogeneity on the normal pressure, critical pressure and on the surface displacement.

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Bounding elastic constants of an orthotropic polycrystal using measurements of the microstructure

Cited by 73 publications

References 12 publications

The Seismic anisotropy of the Earth's mantle: From single crystal to polycrystal

The Seismic anisotropy of the Earth's mantle: From single crystal to polycrystal

Correlations beyond the nearest-neighbor level in grain boundary networks

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