Elastic constants of polycrystals

Morris, Peter R.

doi:10.1016/0020-7225(70)90014-5

Cited by 158 publications

(53 citation statements)

References 9 publications

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“…The first model uses only a well-established self-consistent method (e.g., Kröner, 1958;Budiansky, 1965;Hill, 1965;Morris, 1970) based on Eshelby's (1957) inclusion principle. We use the same GeoMIXself (GMS) algorithm (Matthies, 2010(Matthies, , 2012 as Vasin et al (2013).…”

Section: Self-consistent Geomixself Modelmentioning

confidence: 99%

Linking preferred orientations to elastic anisotropy in Muderong Shale, Australia

et al. 2015

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The significance of shales for unconventional hydrocarbon reservoirs, nuclear waste repositories, and geologic carbon storage has opened new research frontiers in geophysics. Among many of its unique physical properties, elastic anisotropy had long been investigated by experimental and computational approaches. Here, we calculated elastic properties of Cretaceous Muderong Shale from Australia with a self-consistent averaging method based on microstructural information. The volume fraction and crystallographic preferred orientation distributions of constituent minerals were based on synchrotron x-ray diffraction experiments. Aspect ratios of minerals and pores, determined from scanning electron microscopy, were introduced in the self-consistent averaging. Our analysis suggested that phyllosilicates (i.e., illite-mica, illite-smectite, kaolinite, and chlorite) were dominant with [Formula: see text]. The shape of clay platelets displayed an average aspect ratio of 0.05. These platelets were aligned parallel to the bedding plane with a high degree of preferred orientation. The estimated porosity at ambient pressure was [Formula: see text] and was divided into equiaxial pores and flat pores with an average aspect ratio of 0.01. Our model gave results that compared satisfactorily with values derived from ultrasonic velocity measurements, confirming the validity and reliability of our approximations and averaging approach.

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Section: Self-consistent Geomixself Modelmentioning

confidence: 99%

Linking preferred orientations to elastic anisotropy in Muderong Shale, Australia

et al. 2015

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“…These averages are not able to take grain shapes into account. Consideration of grain shapes (approximated by ellipsoids) is possible within a self-consistent scheme (e.g., Kröner, 1958;Morris, 1970;Kocks et al [2000], Chapter 7) based on Eshelby's (1957) concept of ellipsoidal inclusions in a homogeneous matrix. Here, we use two slightly different variants of the self-consistent approach.…”

Section: Calculation Of Bulk Elastic Properties and Elastic Wave Velomentioning

confidence: 99%

The influence of grain shape and volume fraction of sheet silicates on elastic properties of aggregates: Biotite platelets in an isotropic matrix

et al. 2014

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Elastic anisotropy of sheet-silicate-rich rocks such as shales and slates strongly depends on the orientation distribution of platelet-shaped minerals, as well as shape and orientation of pores. Bulk elastic anisotropy of the rock results in the anisotropy with respect to the propagation of elastic waves, and consequently, the fastest P-waves can travel with velocities exceeding the slowest velocities by a factor of two or even greater. An important factor is the sheet-silicate's grain shapes. We approached a model system of biotite platelets in an isotropic matrix with different methods: A mean-field self-consistent method that considered ellipsoidal particles in an effective anisotropic matrix, and a full-field method based on fast Fourier transforms that considered the microstructure, the topology of the polycrystal, and local interactions. Both methods provided numerically very close results. Using these results, we predicted that the aggregate with more oblate grain shape (thinner platelets) was elastically more anisotropic than the material with grains of less oblate shape, but only for small volume fractions of oriented platelets. For large fractions of platelets, the opposite was true. This switchover in the elastic anisotropy depended on texture strength, platelet shape, and elastic properties of the isotropic matrix.

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“…Originally, spherical inclusions only were considered by Morris [6]. For ellipsoidal shaped inclusions Asaro and Barnett [7] and Kocks et al [8] have established the following relations for numerical calculation of each ijkl subscripted component of Morris' tensor:…”

Section: Microscopic Mechanical Statesmentioning

confidence: 99%

Prediction of local hygroscopic stresses for composite structures – Analytical and numerical micro-mechanical approaches

Jacquemin¹,

Fréour²,

Guillén³

2009

Composites Science and Technology

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Elastic constants of polycrystals

Cited by 158 publications

References 9 publications

Linking preferred orientations to elastic anisotropy in Muderong Shale, Australia

Linking preferred orientations to elastic anisotropy in Muderong Shale, Australia

The influence of grain shape and volume fraction of sheet silicates on elastic properties of aggregates: Biotite platelets in an isotropic matrix

Prediction of local hygroscopic stresses for composite structures – Analytical and numerical micro-mechanical approaches

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