Ultrasonic evaluation of filled polymers II. Elastic moduli of a resin filled with iron inclusions of different aspect ratios

1987 ◽  
Vol 8 (1) ◽  
pp. 22-28 ◽  
Author(s):  
L. Piché ◽  
A. Hamel
Keyword(s):  
Elastic Moduli ◽  
Filled Polymers ◽  
Ultrasonic Evaluation ◽  
Aspect Ratios

Modes of Wave Propagation and Dispersion Relations in Inclusion Reinforced Composite Plates

2010 ◽  
Author(s):  
Yu Cheng Liu ◽  
Jin Huang Huang
Keyword(s):  
Composite Plate ◽  
Elastic Moduli ◽  
Lamb Waves ◽  
Plate Thickness ◽  
Composite Plates ◽  
Dispersion Relations ◽  
Elastic Behavior ◽  
Effective Elastic Moduli ◽  
Aspect Ratios ◽  
Reinforced Composite

This paper mainly analyzes the wave dispersion relations and associated modal pattens in the inclusion-reinforced composite plates including the effect of inclusion shapes, inclusion contents, inclusion elastic constants, and plate thickness. The shape of inclusion is modeled as spheroid that enables the composite reinforcement geometrical configurations ranging from sphere to short and continuous fiber. Using the Mori-Tanaka mean-field theory, the effective elastic moduli which are able to elucidate the effect of inclusion’s shape, stiffness, and volume fraction on the composite’s anisotropic elastic behavior can be predicted explicitly. Then, the dispersion relations and the modal patterns of Lamb waves determined from the effective elastic moduli can be obtained by using the dynamic stiffness matrix method. Numerical simulations have been given for the various inclusion types and the resulting dispersions in various wave types on the composite plate. The types (symmetric or antisymmetric) of Lamb waves in an isotropic plate can be classified according to the wave motions about the midplane of the plate. For an orthotropic composite plate, it can also be classified as either symmetric or antisymmetric waves by analyzing the dispersion curves and inspecting the calculated modal patterns. It is also found that the inclusion contents, aspect ratios and plate thickness affect propagation velocities, higher-order mode cutoff frequencies, and modal patterns.

Modeling squirt dispersion and attenuation in fluid-saturated rocks using pressure dependency of dry ultrasonic velocities

Geophysics ◽  
2012 ◽  
Vol 77 (3) ◽  
pp. WA157-WA168 ◽  
Author(s):  
Osni Bastos de Paula ◽  
Marina Pervukhina ◽  
Dina Makarynska ◽  
Boris Gurevich
Keyword(s):  
Aspect Ratio ◽  
Elastic Properties ◽  
Elastic Moduli ◽  
Pore Space ◽  
Geometrical Parameters ◽  
Laboratory Measurements ◽  
Significant Linear Trend ◽  
Aspect Ratios ◽  
Pressure Dependency ◽  
Dispersion And Attenuation

Modeling dispersion and attenuation of elastic waves in fluid-saturated rocks due to squirt flow requires the knowledge of a number of geometrical parameters of the pore space, in particular, the characteristic aspect ratio of the pores. These parameters are usually inferred by fitting measurements on saturated rocks to model predictions. To eliminate such fitting and thus make the model more predictive, we propose to recover the geometrical parameters of the pore space from the pressure dependency of elastic moduli on dry samples. Our analysis showed that the pressure dependency of elastic properties of rocks (and their deviation from Gassmann’s prediction) at ultrasonic frequencies is controlled by the squirt flow between equant, stiff, and so-called intermediate pores (with aspect ratios between [Formula: see text]). Such intermediate porosity is expected to close at confining pressures of between 200 and 2000 MPa, and thus cannot be directly obtained from ultrasonic experiments performed at pressures below 50 MPa. However, the presence of this intermediate porosity is inferred from the significant linear trend in the pressure dependency of elastic properties of the dry rock and the difference between the bulk modulus of the dry rock computed for spherical pores and the measured modulus at 50 MPa. Moreover, we can infer the magnitude of the intermediate porosity and its characteristic aspect ratio. Substituting these parameters into the squirt model, we have computed elastic moduli and velocities of the water-saturated rock and compared these predictions against laboratory measurements of these velocities. The agreement is good for a number of clean sandstones, but not unexpectedly worse for a broad range of shaley sandstones. Our predictions showed that dispersion and attenuation caused by the squirt flow between compliant and stiff pores may occur in the seismic frequency band. Confirmation of this prediction requires laboratory measurements of elastic properties at these frequencies.

Estimating 3D elastic moduli of rock from 2D thin-section images using differential effective medium theory

Geophysics ◽  
2018 ◽  
Vol 83 (4) ◽  
pp. MR211-MR219 ◽  
Author(s):  
Sadegh Karimpouli ◽  
Pejman Tahmasebi ◽  
Erik H. Saenger
Keyword(s):  
Porous Media ◽  
Thin Section ◽  
Elastic Moduli ◽  
Effective Medium ◽  
Physical Parameters ◽  
Reconstruction Method ◽  
Digital Rock ◽  
Aspect Ratios ◽  
Rock Structure ◽  
2D Images

Standard digital rock physics (DRP) has been extensively used to compute rock physical parameters such as permeability and elastic moduli. Digital images are captured using 3D microcomputed tomography scanners that are not widely available and often come with an excessive cost and expensive computation. Alternative DRP methods, however, benefit from the highly available low-cost 2D thin-section images and require a small amount of computer memory use and CPU. We have developed another alternative DRP method to compute 3D elastic parameters based on differential effective medium (DEM) theory. Our investigations indicate that the pore aspect ratio (PAR) is the most crucial factor controlling the elastic moduli of rock. Based on digital rock modeling in a dry calcite sample with 20% porosity, the bulk modulus is reduced by 51%, 80.7%, and 96.8% for aspect ratios of 1, 0.2, and 0.05, respectively. Similarly, the shear modulus is reduced by 52%, 73.8%, and 92.8% for the same PARs. These findings confirm the importance of the PAR in wave propagation through porous media. Such an evaluation, however, can be very expensive for 3D images because one requires using several of them for drawing a reliable conclusion. Therefore, we aim to capture the PAR distribution from 2D images. This distribution is, then, used to estimate 3D elastic moduli of sample by DEM equations. Three orthogonal 2D images were used and results indicated that 2D PARs in orthogonal orientations could address pore shapes more effectively. Moreover, a stochastic porous media reconstruction method was also used to generate more scenarios of rock structure and those of which that are not seen in 2D images. Results from Berea sandstone and Grosmont carbonate indicated that using only 2D images our proposed method could effectively estimate 3D elastic moduli of rock samples.

The elastic moduli of particulate-filled polymers

1984 ◽  
Vol 29 (10) ◽  
pp. 2997-3011 ◽  
Author(s):  
P. S. Theocaris ◽  
E. Sideridis
Keyword(s):  
Elastic Moduli ◽  
Filled Polymers

Ellipsoidal Bounds of Elastic Composites

2012 ◽  
Vol 79 (2) ◽  
Author(s):  
X. Frank Xu
Keyword(s):  
Physical Properties ◽  
Elastic Moduli ◽  
Applied Mechanics ◽  
Explicit Formulas ◽  
Aspect Ratios ◽  
Multiphase Composites ◽  
Rigorous Bounds ◽  
Elastic Composites ◽  
Asymptotic Analyses ◽  
Properties Of Composites

The formulation of rigorous bounds for the physical properties of composites constitutes one of the most fundamental parts of applied mechanics. In this work, the so-called ellipsoidal bounds, as a generalization of the Hashin-Shtrikman spherical bounds, are formulated for elastic moduli of multiphase composites. Explicit formulas are derived to estimate the bounds for the elastic moduli of isotropic composites. Asymptotic analyses are conducted for composites containing needlelike and disklike fillers with aspect ratios approaching infinity and zero, respectively. The new bounds and estimates are expected to be useful for polycrystals and composites containing fillers, especially with large or small aspect ratios, such as nanowires, nanotubes, and nanoplatelets.

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