The Theory of the Ideal Design of a Compound Vessel

1960 ◽  
Vol 82 (2) ◽  
pp. 136-142 ◽  
Author(s):  
S. J. Becker ◽  
L. Mollick
Keyword(s):  
General Theory ◽  
Young’S Modulus ◽  
Elastic Moduli ◽  
Young's Modulus ◽  
Compound Cylinder ◽  
Concentric Cylinders ◽  
Elastic Design ◽  
The Ideal

A general theory for the elastic design of a compound cylinder made by shrinking together many concentric cylinders is described. Each cylinder may have entirely different strength and operate at any temperature under any pressure, internal or external. The only assumptions, in addition to the usual homogeneity and isotropy in each member, are that they have the same Young’s modulus, although even different elastic moduli could be accommodated, and that they are not so thin that stability becomes a problem.

scholarly journals Workflow to build a continuous static elastic moduli profile from the drilling data using artificial intelligence techniques

2021 ◽  
Author(s):  
Osama Siddig ◽  
Salaheldin Elkatatny
Keyword(s):  
Young’S Modulus ◽  
Elastic Moduli ◽  
Young's Modulus ◽  
Correlation Coefficients ◽  
Wellbore Stability ◽  
Machine Learning Techniques ◽  
Support Vector ◽  
Ann Model ◽  
Weight On Bit ◽  
Data Points

AbstractRock mechanical properties play a crucial role in fracturing design, wellbore stability and in situ stresses estimation. Conventionally, there are two ways to estimate Young’s modulus, either by conducting compressional tests on core plug samples or by calculating it from well log parameters. The first method is costly, time-consuming and does not provide a continuous profile. In contrast, the second method provides a continuous profile, however, it requires the availability of acoustic velocities and usually gives estimations that differ from the experimental ones. In this paper, a different approach is proposed based on the drilling operational data such as weight on bit and penetration rate. To investigate this approach, two machine learning techniques were used, artificial neural network (ANN) and support vector machine (SVM). A total of 2288 data points were employed to develop the model, while another 1667 hidden data points were used later to validate the built models. These data cover different types of formations carbonate, sandstone and shale. The two methods used yielded a good match between the measured and predicted Young’s modulus with correlation coefficients above 0.90, and average absolute percentage errors were less than 15%. For instance, the correlation coefficients for ANN ranged between 0.92 and 0.97 for the training and testing data, respectively. A new empirical correlation was developed based on the optimized ANN model that can be used with different datasets. According to these results, the estimation of elastic moduli from drilling parameters is promising and this approach could be investigated for other rock mechanical parameters.

Differences between static and dynamic elastic moduli: Importance of experimental methods

2020 ◽  
Author(s):  
Elisabeth Bemer ◽  
Noalwenn Dubos-Sallée ◽  
Patrick N. J. Rasolofosaon
Keyword(s):  
Bulk Modulus ◽  
Young’S Modulus ◽  
Elastic Moduli ◽  
Young's Modulus ◽  
Local Strain ◽  
Experimental Methods ◽  
Triaxial Tests ◽  
Strain Gauges ◽  
Strain Measurements ◽  
Dynamic Elastic Moduli

<p>The differences between static and dynamic elastic moduli remain a controversial issue in rock physics. Various empirical correlations can be found in the literature. However, the experimental methods used to derive the static and dynamic elastic moduli differ and may entail substantial part of the discrepancies observed at the laboratory scale. The representativeness and bias of these methods should be fully assessed before applying big data analytics to the numerous datasets available in the literature.</p><p>We will illustrate, discuss and analyze the differences inherent to static and dynamic measurements through a series of triaxial and petroacoustic tests performed on an outcrop carbonate. The studied rock formation is Euville limestone, which is a crinoidal grainstone composed of roughly 99% calcite and coming from Meuse department located in Paris Basin. Sister plugs have been cored from the same quarry block and observed under CT-scanner to check their homogeneity levels.</p><p>The triaxial device is equipped with an internal stress sensor and provides axial strain measurements both from strain gauges glued to the samples and LVDTs placed inside the confinement chamber. Two measures of the static Young's modulus can thus be derived: the first one from the local strain measurements provided by the strain gauges and the second one from the semi-local strain measurements provided by the LVDTs. The P- and S-wave velocities are measured both through first break picking and the phase spectral ratio method, providing also two different measures of the dynamic Young's modulus.</p><p>The triaxial tests have been performed in drained conditions and the measured static elastic moduli correspond to drained elastic moduli. The petroacoustic tests have been performed using the fluid substitution method, which consists in measuring the acoustic velocities for various saturating fluids of different bulk modulus. No weakening or dispersion effects have been observed. Gassmann's equation can then be used to derive the dynamic drained elastic moduli and the solid matrix bulk modulus, which is otherwise either taken from the literature for pure calcite or dolomite samples, or computed using Voigt-Reuss-Hill or Hashin-Shtrikman averaging of the mineral constituents.</p><p>For the studied carbonate formation, we obtain similar values for static and dynamic elastic moduli when derived from careful lab experiments. Based on the obtained results, we will finally make recommendations, emphasizing the necessity of using relevant experimental techniques for a consistent characterization of the relation between static and dynamic elastic moduli.</p>

Evaluation of Effective Elastic Mechanical Properties of Graphene Sheets

2012 ◽  
Author(s):  
Khalid I. Alzebdeh
Keyword(s):  
Boundary Conditions ◽  
Young’S Modulus ◽  
Graphene Sheet ◽  
Poisson’S Ratio ◽  
Elastic Moduli ◽  
Young's Modulus ◽  
Unit Cell ◽  
Poisson's Ratio ◽  
Graphene Sheets ◽  
Numerical Predictions

The mechanical behaviour of a single-layer nanostructured graphene sheet is investigated using an atomistic-based continuum model. This is achieved by equating the stored energy in a representative unit cell for a graphene sheet at atomistic scale to the strain energy of an equivalent continuum medium under prescribed boundary conditions. Proper displacement-controlled (essential) boundary conditions which generate a uniform strain field in the unit cell model are applied to calculate one elastic modulus at a time. Three atomistic finite element models are adopted with an assumption that force interactions among carbon atoms can be modeled by either spring-like or beam elements. Thus, elastic moduli for graphene structure are determined based on the proposed modeling approach. Then, effective Young’s modulus and Poisson’s ratio are extracted from the set of calculated elastic moduli. Results of Young’s modulus obtained by employing the different atomistic models show a good agreement with the published theoretical and numerical predictions. However, Poisson’s ratio exhibits sensitivity to the considered atomistic model. This observation is supported by a significant variation in estimates as can be found in the literature. Furthermore, isotropic behaviour of in-plane graphene sheets was validated based on current modeling.

Young’s Modulus and Hardness of Zr0.5Hf0.5CoxRh1−xSb0.99Sn0.01 and Zr0.5Hf0.5CoxIr1−xSb0.99Sn0.01 Half-Heusler Alloys

2010 ◽  
Author(s):  
Melody A. Verges ◽  
Paul J. Schilling ◽  
Jeffrey D. Germond ◽  
Puja Upadyhay ◽  
William K. Miller ◽  
...  
Keyword(s):  
Young’S Modulus ◽  
Elastic Moduli ◽  
Young's Modulus ◽  
Heusler Alloys ◽  
Thermal Conversion ◽  
Elastic Stiffness ◽  
Depth Sensing ◽  
Microhardness Testing ◽  
Compositional Changes ◽  
Conversion Efficiencies

Mechanical testing was performed to determine the influence of compositional changes on the Young’s modulus and hardness of half-Heusler compounds of the base composition Zr0.5Hf0.5CoSb0.99Sn0.01. In the efforts to decrease the thermal conductivity of the composition toward the development of thermoelectric materials with high thermal conversion efficiencies, specimens were fabricated with varying amounts of rhodium and iridium at the cobalt site. In addition to the general Zr0.5Hf0.5CoSb0.99Sn0.01 composition, six hot-pressed samples of the Zr0.5Hf0.5CoxRh1−xSb0.99Sn0.01 (0.0≤x≤1.0) composition and four hot-pressed samples of the Zr0.5Hf0.5CoxIr1−xSb0.99Sn0.01 (0.0≤x≤0.7) composition were synthesized. Indentation measurements were obtained using both microhardness testing and depth-sensing nanoindentation. The general Zr0.5Hf0.5CoSb0.99Sn0.01 composition was observed to have a hardness and elastic modulus around 896HV0.2 and 247GPa, respectively. For all of the compositions tested the hardness range was observed to lie between 347HV0.2 and 951HV0.2. The elastic moduli for these compositions were found to range between 97GPa and 247GPa. The effects of the rhodium substitution and iridium substitution at the cobalt site on the elastic stiffness and hardness are examined.

A Numerical Evaluation of the Influence of Atomic Modifications on the Elastic and Shear Behavior of Connected Carbon Nanotubes with Parallel Longitudinal Axes

2014 ◽  
Vol 29 ◽  
pp. 93-104 ◽  
Author(s):  
Sadegh Imani Yengejeh ◽  
Seyedeh Alieh Kazemi ◽  
Andreas Öchsner
Keyword(s):  
Mechanical Properties ◽  
Carbon Nanotubes ◽  
Shear Modulus ◽  
Young’S Modulus ◽  
Young's Modulus ◽  
Shear Behavior ◽  
Second Phase ◽  
Perfect Form ◽  
Perfect Models ◽  
The Ideal

This study deals with the investigation of the tensile and shear behavior of connected carbon nanotubes (CNTs) with parallel longitudinal axes by performing several computational tests. In particular, the effect of imperfections on the mechanical properties, i.e. Young’s modulus and shear modulus, of these nanoconfigurations was analyzed. For this purpose, straight hetero-junctions were simulated in their perfect form and different boundary conditions were considered. In the second phase the three most likely atomic defects, i.e. impurities (doping with Si atoms), vacant sites (carbon vacancy) and introduced perturbations of the ideal geometry in different amounts to the perfect models, were simulated. Finally, the mechanical properties of imperfect hetero-junctions were numerically evaluated and compared with the behavior of perfect ones. It was concluded that the existence of any type of imperfections in the structure of connected CNTs leads to a reduction in the Young’s modulus as well as the shear modulus, and as a result, lower stiffness of these straight nanostructures.

scholarly journals Elastic Moduli of Avian Eggshell

Biology ◽  
2021 ◽  
Vol 10 (10) ◽  
pp. 989
Author(s):  
Pei-Lin Chiang ◽  
Yu-Chien Tseng ◽  
Hsiao-Jou Wu ◽  
Shu-Han Tsao ◽  
Shang-Ping Wu ◽  
...  
Keyword(s):  
Young’S Modulus ◽  
Zebra Finch ◽  
Elastic Moduli ◽  
Mineral Content ◽  
Electron Backscatter Diffraction ◽  
Young's Modulus ◽  
Egg Mass ◽  
Avian Reproduction ◽  
Crystallographic Characteristics ◽  
Chicken Eggshell

We analyze 700 freshly-laid eggs from 58 species (22 families and 13 orders) across three orders of magnitude in egg mass. We study the elastic moduli using three metrics: (i) effective Young’s modulus, EFEM, by a combined experimental and numerical method; (ii) elastic modulus, Enano, by nanoindentation, and (iii) theoretical Young’s modulus, Etheory. We measure the mineral content by acid-base titration, and crystallographic characteristics by electron backscatter diffraction (EBSD), on representative species. We find that the mineral content ranges between 83.1% (Zebra finch) and 96.5% (ostrich) and is positively correlated with EFEM—23.28 GPa (Zebra finch) and 47.76 GPa (ostrich). The EBSD shows that eggshell is anisotropic and non-homogeneous, and different species have different degrees of crystal orientation and texture. Ostrich eggshell exhibits strong texture in the thickness direction, whereas chicken eggshell has little. Such anisotropy and inhomogeneity are consistent with the nanoindentation tests. However, the crystal characteristics do not appear to correlate with EFEM, as EFEM represents an overall “average” elasticity of the entire shell. The experimental results are consistent with the theoretical prediction of linear elasticity. Our comprehensive investigation into the elastic moduli of avian eggshell over broad taxonomic scales provides a useful dataset for those who work on avian reproduction.

Size-Dependent Elastic Moduli of FCC Crystal Nanofilms

2006 ◽  
Vol 924 ◽  
Author(s):  
Shih-Hsiang Chang ◽  
I-Ling Chang
Keyword(s):  
Young’S Modulus ◽  
Size Effects ◽  
Continuum Model ◽  
Elastic Moduli ◽  
Young's Modulus ◽  
Current Model ◽  
Continuum Theory ◽  
Thickness Direction ◽  
Size Dependent ◽  
Discrete Nature

ABSTRACTA semi-continuum model is constructed to study the size effects on the mechanical properties of face-cubic-center crystal structure nanofilms. Unlike the classical continuum theory, the current model directly takes the discrete nature in the thickness direction into consideration. In-plane and out-plane Poisson's ratios as well as in-plane Young's modulus are investigated with this model. It is found that the values of the Young's modulus and Poisson's ratio depend on the film thickness and approach the respective bulk values asymptotically.

scholarly journals In-situ curing mechanism of Portland cement

2019 ◽  
Vol 221 ◽  
pp. 01001
Author(s):  
Yurii Abzaev ◽  
Aleksei Gnyrya ◽  
Sergei Korobkov ◽  
Danil Dudov ◽  
Dmitrii Mihailov ◽  
...  
Keyword(s):  
Portland Cement ◽  
Young’S Modulus ◽  
Elastic Moduli ◽  
Solid Phase ◽  
Young's Modulus ◽  
Pore Space ◽  
Predictive Modelling ◽  
Effective Elastic Moduli ◽  
Curing Mechanism ◽  
Microstructural Model

The paper presents the results of predictive modelling of the curing mechanism of the type CEM I 42.5B Portland cement using the VCCTL tool. The curing lasts during 28 days at 20 оС and the water-cement (W/C) ratio of 0.26, 0.30, 0.35 and 0.40. It is shown that the degree of Portland cement hydration is ~0.70 after 28-day curing. The growth in the W/C ratio significantly intensifies the hydration rate and the dissolution of clinker minerals. The amount of the main hydration products calcium silicate hydrate (C-S-H) and portlandite considerably increases with the W/C ratio. In Portland cement, the fraction of hydrated cement achieves 0.60 of the solid phase and the pore space. It is found that the effective elastic moduli rapidly increase during 400 hours, and then monotonely lower down to 16.79 GPa for the bulk modulus, 8.90 GPa for the shear modulus and 22.69 GPa for Young’s modulus. Relatively high values of the effective elastic moduli are explained by the higher content of the clinker phases and, probably, the higher degree of C-S-H crystallinity. The dependence between the yield stress and Young’s modulus is in good agreement with the VCCTL microstructural model of Portland cement curing.

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