Effect of variations in microstructure on clay elastic anisotropy

Geophysics ◽  
2020 ◽  
Vol 85 (2) ◽  
pp. MR73-MR82 ◽  
Author(s):  
Colin M. Sayers ◽  
Lennert D. den Boer
Keyword(s):  
Elastic Properties ◽  
Volume Fraction ◽  
Elastic Anisotropy ◽  
Rock Physics ◽  
Elastic Stiffness ◽  
Single Domain ◽  
Model Parameters ◽  
Stiffness Tensor ◽  
Elastic Stiffness Tensor ◽  
Clay Platelets

Rock physics provides a crucial link between seismic and reservoir properties, but it requires knowledge of the elastic properties of rock components. Whereas the elastic properties of most rock components are known, the anisotropic elastic properties of clay are not. Scanning electron microscopy studies of clay in shales indicate that individual clay platelets vary in orientation but are aligned locally. We present a simple model of the elastic properties of a region (domain) of locally aligned clay platelets that accounts for the volume fraction, aspect ratio, and elastic-stiffness tensor of clay platelets, as well as the effective elastic properties of the interplatelet medium. Variations in clay anisotropy are quantified by examining the effects of varying model parameters upon the effective transverse-isotropic (TI) elastic-stiffness tensor of a domain. Statistics of these distributions and correlations between stiffnesses and anisotropy parameters enable the most probable sets of stiffnesses to be identified for rock physics calculations. The mean of these distributions is on the order of twice the mode for in-plane stiffnesses ([Formula: see text], [Formula: see text], [Formula: see text]), but it is of the same order as the mode for out-of-plane stiffnesses ([Formula: see text], [Formula: see text], [Formula: see text]). Despite random sampling, well-defined relations emerge, consistent with similar shale relations reported in the literature. Expressing these relations in terms of [Formula: see text] for a single domain of aligned clay platelets facilitates their general application. In the limit that the volume fraction approaches unity, the elastic stiffnesses thus derived reproduce those of the clay mineral assumed as platelets. Given the elastic-stiffness tensor of a single domain of aligned clay platelets, the effective TI elastic-stiffness tensor of clay is obtained by integrating over the clay-platelet orientation-distribution function.

The elastic anisotropy of clay minerals

Geophysics ◽  
2016 ◽  
Vol 81 (5) ◽  
pp. C193-C203 ◽  
Author(s):  
Colin M. Sayers ◽  
Lennert D. den Boer
Keyword(s):  
Clay Minerals ◽  
Elastic Properties ◽  
Elastic Moduli ◽  
Elastic Anisotropy ◽  
Elastic Stiffness ◽  
Stiffness Tensor ◽  
Covalent Bonds ◽  
Best Fitting ◽  
Anisotropy Parameters ◽  
Elastic Stiffness Tensor

The layered structure of clay minerals produces large elastic anisotropy due to the presence of strong covalent bonds within layers and weaker electrostatic bonds in between. Technical difficulties associated with small grain size preclude experimental measurement of single-crystal elastic moduli. However, theoretical calculations of the complete elastic tensors of several clay minerals have been reported, using either first-principle calculations based on density functional theory or molecular dynamics. Because of the layered microstructure, the elastic stiffness tensor obtained from such calculations can be approximated to good accuracy as a transversely isotropic (TI) medium. The TI-equivalent elastic moduli of clay minerals indicate that Thomsen’s anisotropy parameters [Formula: see text] and [Formula: see text] are large and positive, whereas [Formula: see text] is small or negative. A least-squares inversion for the elastic properties of a best-fitting equivalent TI medium consisting of two isotropic layers to the elastic properties of clay minerals indicates that the shear modulus of the stiffest layer is considerably larger than the softest layer, consistent with the expected high compliance of the interlayer region in clay minerals. It is anticipated that the elastic anisotropy parameters derived from the best-fitting TI approximation to the elastic stiffness tensor of clay minerals will find applications in rock physics for seismic imaging, amplitude variation with offset analysis, and geomechanics.

scholarly journals Hydrostatic Parameters and Domain Effects in Novel 2-2 Composites Based on PZN-0.12PT Single Crystals

2011 ◽  
Vol 2011 ◽  
pp. 1-10
Author(s):  
Vitaly Yu. Topolov ◽  
Sergei V. Glushanin ◽  
Alexander A. Panich
Keyword(s):  
Electromechanical Coupling ◽  
Volume Fraction ◽  
Elastic Anisotropy ◽  
Electromechanical Coupling Factor ◽  
Coupling Factor ◽  
Single Domain ◽  
Absolute Minimum ◽  
Component Orientation ◽  
Record Value

A novel 0.88Pb(Zn1/3Nb2/3)O3-0.12PbTiO3 crystal/polymer composite with 2-2 connectivity is studied at variable orientations of spontaneous polarisation vector of the crystal component. Orientation and volume-fraction dependences of the hydrostatic piezoelectric coefficients dh*, eh*, and gh* and hydrostatic electromechanical coupling factor kh* are related to the important role of the piezoelectric and elastic anisotropy of single-domain layers of the 2-2 composite. The record value of |eh∗|≈77 C/m2 near the absolute-minimum point and the correlation between the hydrostatic (eh*) and piezoelectric (e3j*) coefficients and between the hydrostatic (gh*) and piezoelectric (g3j*) coefficients are first established. This discovery is of value for hydrostatic and piezotechnical applications. The hydrostatic performance of the composite based on the single-domain 0.88Pb(Zn1/3Nb2/3)O3-0.12PbTiO3 crystal is compared to the performance of the 2–2 composites based on either the same polydomain crystal or the related single-domain crystal.

scholarly journals Combining AFM and Acoustic Probes to Reveal Changes in the Elastic Stiffness Tensor of Living Cells

2014 ◽  
Vol 107 (7) ◽  
pp. 1502-1512 ◽  
Author(s):  
Nadja Nijenhuis ◽  
Xuegen Zhao ◽  
Alex Carisey ◽  
Christoph Ballestrem ◽  
Brian Derby
Keyword(s):  
Elastic Stiffness ◽  
Living Cells ◽  
Stiffness Tensor ◽  
Elastic Stiffness Tensor

First-Principles Study on Elastic Properties of AlN

2013 ◽  
Vol 821-822 ◽  
pp. 841-844 ◽  
Author(s):  
Xin Tan ◽  
Zhen Yang Xin ◽  
Xue Jie Liu ◽  
Qing Ge Mu
Keyword(s):  
Elastic Properties ◽  
Brittle Material ◽  
First Principles ◽  
Elastic Anisotropy ◽  
Three Dimensional ◽  
Elastic Stiffness ◽  
Wurtzite Structure ◽  
Shear Moduli ◽  
Young’S Moduli ◽  
Zinc Blende

Structural and elastic properties of AlN are investigated by using First-principles. Both of wurtzite and zinc-blende structures are investigated, respectively. The bulk moduli of the wurtzite structure and zinc blende AlN are 194.2GPa and 187GPa, which obtained by the elastic stiffness constants respectively. Shear moduli are 136GPa and 124GPa. Young's moduli are 331GPa and 305GPa. Poisson's ratio and Pugh criterion suggests that both of them are brittle material. The brittleness of wurtzite AlN is higher than that of zinc-blende AlN. The elastic anisotropy of the bulk moduli and shear moduli were discussed. Three-dimensional anisotropic of the young's modulus were analyzed.

Structural and elastic properties of Cu6Sn5 and Cu3Snfrom first-principles calculations

2009 ◽  
Vol 24 (7) ◽  
pp. 2361-2372 ◽  
Author(s):  
Jiunn Chen ◽  
Yi-Shao Lai ◽  
Ping-Feng Yang ◽  
Chung-Yuan Ren ◽  
Di-Jing Huang
Keyword(s):  
Electronic Structure ◽  
Elastic Modulus ◽  
Elastic Properties ◽  
First Principles ◽  
Elastic Anisotropy ◽  
Lattice Structure ◽  
Elastic Stiffness ◽  
First Principles Calculations ◽  
Atomic Lattice ◽  
Microstructure Effect

We investigated the elastic properties of two tin-copper crystalline phases, the η′-Cu6Sn5 and ε-Cu3Sn, which are often encountered in microelectronic packaging applications. The full elastic stiffness of both phases is determined based on strain-energy relations using first-principles calculations. The computed results show the elastic anisotropy of both phases that cannot be resolved from experiments. Our results, suggesting both phases have the greatest stiffness along the c direction, particularly showed the unique in-plane elastic anisotropy associated with the lattice modulation of the Cu3Sn superstructure. The polycrystalline moduli obtained using the Voigt-Reuss scheme are 125.98 GPa for Cu6Sn5 and 134.16 GPa for Cu3Sn. Our data analysis indicates that the smaller elastic moduli of Cu6Sn5 are attributed to the direct Sn–Sn bond in Cu6Sn5. We reassert the elastic modulus and hardness of both phases using the nanoindentation experiment for our calculation benchmark. Interestingly, the computed polycrystalline elastic modulus of Cu6Sn5 seems to be overestimated, whereas that of Cu3Sn falls nicely in the range of reported data. Based on the observations, the elastic modulus of Cu6Sn5 obtained from nanoindentation tests admit the microstructure effect that is absent for Cu3Sn is concluded. Our analysis of electronic structure shows that the intrinsic hardness and elastic modulus of both phases are dominated by electronic structure and atomic lattice structure, respectively.

Comparison of Mixed and Kinematic Uniform Boundary Conditions in Homogenized Elasticity of Femoral Trabecular Bone Using Microfinite Element Analyses

2015 ◽  
Vol 137 (1) ◽  
Author(s):  
Jarunan Panyasantisuk ◽  
Dieter H. Pahr ◽  
Thomas Gross ◽  
Philippe K. Zysset
Keyword(s):  
Boundary Conditions ◽  
Trabecular Bone ◽  
Elastic Properties ◽  
Elastic Constants ◽  
Volume Fraction ◽  
Bone Fragility ◽  
Model Parameters ◽  
Bone Volume Fraction ◽  
Age Related ◽  
Future Work

Mechanical properties of human trabecular bone play an important role in age-related bone fragility and implant stability. Microfinite element (μFE) analysis allows computing the apparent elastic properties of trabecular bone for use in homogenized FE (hFE) analysis, but the results depend unfortunately on the type of applied boundary conditions (BCs). In this study, 167 human femoral trabecular cubic regions with a side length of 5.3 mm were extracted from three proximal femora and analyzed using μFE analysis to compare systematically their stiffness with kinematic uniform BCs (KUBCs) and periodicity-compatible mixed uniform BCs (PMUBCs). The obtained elastic constants were then used in the volume fraction and fabric-based orthotropic Zysset–Curnier model to identify their respective model parameters. As expected, PMUBCs lead to more compliant apparent elastic properties than KUBCs, especially in shear. The differences in stiffness decreased with bone volume fraction and mean intercept length (MIL). Unlike KUBCs, PMUBCs were sensitive to heterogeneity of the biopsies. The Zysset–Curnier model fitted the apparent elastic constants successfully in both cases with adjusted coefficients of determination (radj2) of 0.986 for KUBCs and 0.975 for PMUBCs. The proper use of these BCs for hFE analysis of whole bones will need to be investigated in future work.

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