Nonlinear viscoelastic behavior of sedimentary rocks, Part II: Hysteresis effects and influence of type of fluid on elastic moduli

Geophysics ◽  
1998 ◽  
Vol 63 (1) ◽  
pp. 195-203 ◽  
Author(s):  
Azra N. Tutuncu ◽  
Augusto L. Podio ◽  
Mukul M. Sharma
Keyword(s):  
Strain Amplitude ◽  
Elastic Moduli ◽  
Pore Space ◽  
Viscoelastic Behavior ◽  
Uniaxial Stress ◽  
Amplitude Dependence ◽  
Stress Strain ◽  
Stick Slip ◽  
Young’S Moduli ◽  
Tangent Moduli

Uniaxial stress cycling experiments were conducted on dry, brine saturated and hexadecane saturated Berea sandstone samples to observe in detail the hysteresis in stress‐strain diagrams and to understand the influence of different fluids on the strain amplitude dependence of elastic moduli and attenuation. Cycling experiments were also conducted with sandstone samples saturated with CTAB, a cationic surfactant that renders the mineral surfaces hydrophobic. Hexadecane and CTAB were selected so as to investigate the relative contributions of adhesion hysteresis and stick‐slip sliding on attenuation in sedimentary granular rocks. Young’s moduli and Poisson’s ratios obtained from the cycling tests show a significant dependence on strain amplitude on dry as well as water and hexadecane saturated samples. Bow‐tie‐shaped diagrams are obtained when loading and unloading tangent moduli are plotted against strain. The type of fluid in the pore space and at the grain contacts has a large influence on the hysteresis observed in the stress‐strain diagrams.

Nonlinear viscoelastic behavior of sedimentary rocks, Part I: Effect of frequency and strain amplitude

Geophysics ◽  
1998 ◽  
Vol 63 (1) ◽  
pp. 184-194 ◽  
Author(s):  
Azra N. Tutuncu ◽  
Augusto L. Podio ◽  
Alvin R. Gregory ◽  
Mukul M. Sharma
Keyword(s):  
Strain Amplitude ◽  
Sedimentary Rocks ◽  
Low Frequency ◽  
Viscoelastic Behavior ◽  
Uniaxial Stress ◽  
Companion Paper ◽  
Elastic Behavior ◽  
Amplitude Dependence ◽  
Frequency Measurements ◽  
Young’S Moduli

Sedimentary rocks display nonlinear elastic behavior. This nonlinearity is a strong function of frequency, strain amplitude, and the properties of the saturating fluid. Experimental observations and potential mechanisms that cause these nonlinearities are presented in this and a companion paper. Young’s moduli and Poisson’s ratios obtained from ultrasonic laboratory measurements (50 kHz, 100 kHz, 180kHz and 1 MHz), low‐frequency measurements (1–2000 Hz) and static measurements (0.001–0.05 Hz) show significant differences under identical stress conditions. A comparison of the laboratory‐measured quantities with log‐derived moduli measured at 20 kHz indicates that [Formula: see text]. This shows clearly that a wide variety of sandstones demonstrate frequency‐dependent elastic behavior (viscoelastic behavior) over a range of frequencies. Differences between static (low‐frequency, high‐strain amplitude) velocities and ultrasonic velocities can be explained partially by differences in frequency as predicted by grain contact models. Such models, however, do not explain the strain amplitude dependence observed in our data. A series of uniaxial stress cycling measurements were carried out to investigate the influence of strain amplitude on elastic moduli. These low‐frequency measurements (0.01 Hz) clearly show that the Young’s modulus decreases with strain amplitude for a wide variety of sandstones. Attenuation increases with strain amplitude. The strain amplitude dependence does not change when the rocks are saturated with brine although the rocks soften measureably.

Binder/Filler Interaction and the Nonlinear Behavior of Highly-Filled Elastomers

1990 ◽  
Vol 63 (4) ◽  
pp. 488-502 ◽  
Author(s):  
R. G. Stacer ◽  
C. Hübner ◽  
D. M. Husband
Keyword(s):  
Surface Area ◽  
Strain Amplitude ◽  
Nonlinear Response ◽  
Volume Fraction ◽  
Viscoelastic Behavior ◽  
Interaction Model ◽  
Nonlinear Behavior ◽  
Small Deformation ◽  
Amplitude Dependence ◽  
Filled Rubbers

Abstract 1. The small-deformation-viscoelastic response of elastomers containing nonreinforcing filler has been investigated. Nonlinear viscoelastic behavior was observed as a pronounced strain-amplitude dependence. The degree of this dependence was quantified using a power-law representation as a single nonlinear parameter, m. 2. The magnitude of m was a function of formulation variables. It was found that m increased with the volume fraction and particle size of filler material, as well as the volume fraction of plasticizer. Reduced values of m were observed in the presence of bonding agent and with greater degrees of apparent crosslinking. The latter was controlled in this study through imbalanced urethane cures. 3. Nonlinear behavior of elastomers containing nonreinforcing filler has been compared and contrasted with the data base for carbon-black-reinforced elastomers. The major difference is in the effect of the surface area of filler particles. Nonlinear response in black-filled rubbers increases with surface area, while the opposite is reported in this study. Additionally, the relationship between viscoelastic dissipation and the magnitude of nonlinear response, well established for black-filled rubbers, was not observed. These results indicate that the response of elastomers containing nonreinforcing filler, although nearly identical in appearance to that seen with reinforcing filler, is not driven by the same mechanism. 4. A binder/filler interaction model is proposed for materials containing nonreinforcing filler. This model is based on the ideal adhesive strength of the binder/filler interface. In this model, greater attraction between polymer and particle surfaces reduces molecular slippage during deformation, leading to a decreased dependence of the modulus on strain amplitude, or decreased nonlinearity. It is shown that the model provides reasonable predictions for the observed phenomena.

Application of rock physics modelling to investigate the differences between static and dynamic elastic moduli of carbonates

2020 ◽  
Vol 222 (3) ◽  
pp. 1992-2023
Author(s):  
M F Ghasemi ◽  
I O Bayuk
Keyword(s):  
Acoustic Wave ◽  
Elastic Moduli ◽  
Pore Space ◽  
Structural Characteristics ◽  
Rock Physics ◽  
Core Sample ◽  
Poisson's Ratio ◽  
Microstructural Parameters ◽  
Wave Velocities ◽  
Young’S Moduli

SUMMARY The elastic moduli estimated through geophysical studies carried out in wells (logging data) differ from those obtained from the triaxial tests conducted in laboratory on the available core samples. Terminologically former and latter are referred to as dynamic and static elastic moduli, respectively. Since the structural characteristics of rocks at the different scales, from micrometre to larger scales (tens of metre), are the controlling parameters of their dynamic and static moduli and their difference at the respective scale, in this study we aim to investigate the influence of the measurable (or quantifiable) parameters of the pore space on these elastic moduli. To do so, 19 dry carbonate samples of different structural characteristics were collected. Their basic petrophysical properties such as porosity and permeability were measured in laboratory. The ultra-sonic tomography was carried out to determine the heterogeneity degree, anisotropy system and average acoustic wave velocities for each core sample. SEM images were analysed to investigate the visual textural properties. The mineralogical composition of these samples was determined by the X-ray diffraction method. Based on the conducted experimental studies and using of the effective medium theory, a unique rock physics model (‘petroelastic model’) was constructed for each core sample. The average (effective) microstructural parameters characterizing the pore space of the studied carbonate samples, along with their elastic moduli were estimated through solving the inverse problem and the measured acoustic wave velocities. A multistage statistical approach, including computation of correlation coefficients, optimized regression analysis, factor analysis and bootstrap resampling, was suggested to investigate the effect of each microstructural parameters on the static and dynamic Young's moduli, ratio of dynamic to static Young's moduli (k-value), dynamic Poisson's ratio and mechanical properties (including unconfined compressive strength and internal friction angle). The obtained results show that the microstructural characteristics have different degrees of influence on the elastic moduli and can be successfully classified based on their physical nature. It was also concluded that the dynamic Poisson's ratio is independent of the studied, in this work, microstructural parameters.

scholarly journals Effects of CNT Diameter on the Uniaxial Stress-Strain Behavior of CNT/Epoxy Composites

2008 ◽  
Vol 2008 ◽  
pp. 1-6 ◽  
Author(s):  
N. Yu ◽  
Y. W. Chang
Keyword(s):  
Epoxy Matrix ◽  
Weight Fraction ◽  
Uniaxial Stress ◽  
Epoxy Composites ◽  
Percentage Increase ◽  
Matrix Composites ◽  
Stress Strain ◽  
Strain Behavior ◽  
Young’S Moduli ◽  
Micromechanics Models

The present work studies the effects of the diameter of carbon nanotube (CNT) as well as CNT weight fraction on the uniaxial stress-strain behavior, stiffness, and strength of CNT-reinforced epoxy-matrix composites. The experimental results show that average Young's moduli of 5 wt%-CNT/epoxy composites with a CNT diameterD<20 nm andD=40∼60 nm are 4.56 GPa and 4.36 GPa, and the average tensile strengths are 52.89 MPa and 46.80 MPa, respectively, which corresponds to a percentage increase of 61.1%, 54.1%, 106%, and 82.3%, respectively. Two micromechanics models are employed and the predicted Young's moduli are benchmarked with the experimental data of MWCNT-reinforced epoxy-matrix composites.

Delamination in the scoring and folding of paperboard

TAPPI Journal ◽  
2012 ◽  
Vol 11 (1) ◽  
pp. 61-66 ◽  
Author(s):  
DOEUNG D. CHOI ◽  
SERGIY A. LAVRYKOV ◽  
BANDARU V. RAMARAO
Keyword(s):  
Finite Element ◽  
Plane Deformation ◽  
Strain Analysis ◽  
Local Strain ◽  
Uniaxial Stress ◽  
Material Model ◽  
Element Model ◽  
Plastic Behavior ◽  
Stress Strain ◽  
Strain Fields

Delamination between layers occurs during the creasing and subsequent folding of paperboard. Delamination is necessary to provide some stiffness properties, but excessive or uncontrolled delamination can weaken the fold, and therefore needs to be controlled. An understanding of the mechanics of delamination is predicated upon the availability of reliable and properly calibrated simulation tools to predict experimental observations. This paper describes a finite element simulation of paper mechanics applied to the scoring and folding of multi-ply carton board. Our goal was to provide an understanding of the mechanics of these operations and the proper models of elastic and plastic behavior of the material that enable us to simulate the deformation and delamination behavior. Our material model accounted for plasticity and sheet anisotropy in the in-plane and z-direction (ZD) dimensions. We used different ZD stress-strain curves during loading and unloading. Material parameters for in-plane deformation were obtained by fitting uniaxial stress-strain data to Ramberg-Osgood plasticity models and the ZD deformation was modeled using a modified power law. Two-dimensional strain fields resulting from loading board typical of a scoring operation were calculated. The strain field was symmetric in the initial stages, but increasing deformation led to asymmetry and heterogeneity. These regions were precursors to delamination and failure. Delamination of the layers occurred in regions of significant shear strain and resulted primarily from the development of large plastic strains. The model predictions were confirmed by experimental observation of the local strain fields using visual microscopy and linear image strain analysis. The finite element model predicted sheet delamination matching the patterns and effects that were observed in experiments.

Three Types of Stress-Strain Relationship’s Comparison of Circular Tubed Reinforced Concrete in FEA

2012 ◽  
Vol 204-208 ◽  
pp. 930-933
Author(s):  
Xiao Hu ◽  
Zhen Lin Chen
Keyword(s):  
Finite Element ◽  
Reinforced Concrete ◽  
Uniaxial Stress ◽  
Steel Tube ◽  
Finite Element Analyses ◽  
Stress Strain ◽  
Concrete Filled Steel Tube ◽  
Bearing Analysis

The paper introduces 3 types of uniaxial stress-strain relationships of concrete filled steel tube by Pan Youguang, Susantha and Saenz, and performs finite element analyses of the axial strengths of 18 CTRC columns, studies the characters of three models, and comprises between the axial strengths from FEA and existed experiments. Results show these 3 types of model are all suitable for bearing analysis, but Pan’s model is more accurate.

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