DOCSLIB.ORG

Study on Characteristics of Energy Storage and Acoustic Emission of Rock Under Different Moisture Content

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Study on Characteristics of Energy Storage and Acoustic Emission of Rock Under Different Moisture Content sustainability Article Study on Characteristics of Energy Storage and Acoustic Emission of Rock under Different Moisture Content Chuanming Li 1,2, Nan Liu 1,2,* , Wanrong Liu 3 and Ruimin Feng 4 1 Key Laboratory of Safety and High-Efficiency Coal Mining, Ministry of Education, Anhui University of Science and Technology, Huainan 232001, China; [email protected] 2 School of Mining and Safety Engineering, Anhui University of Science and Technology, Huainan 232001, China 3 School of Architecture & Civil engineering, Liaocheng University, Liaocheng 252059, China; [email protected] 4 Department of Civil Engineering, University of Arkansas, Fayetteville, AR 72701, USA; [email protected] * Correspondence: [email protected] Abstract: In order to study the energy storage and sound emission characteristics of rocks under different water content, uniaxial compression test, cyclic loading, unloading test and sound emission test were carried out using RMT-150B rock mechanics test system and DS5 acoustic emission system. The results show that the total strain energy of saturated rock samples and the area of hysteresis loop are the largest in the same period number, which indicates that the presence of water can reduce the elastic limit of rock samples, making the rock very easy to deform and even damage. Acoustic emission tests show that the damage energy of water-bearing rocks is small. The higher the water content, the smaller the peak damage energy. The bending energy index WET of the rock sample under saturated and natural state is smaller than that under dry state, which further indicates that the presence of water can reduce the elastic limit of the rock and soften it. The results can provide a basis for the prediction of underground engineering construction and rock failure instability. Citation: Li, C.; Liu, N.; Liu, W.; Feng, R. Study on Characteristics of Keywords: moisture content; sandstone; acoustic emission; energy storage Energy Storage and Acoustic Emission of Rock under Different Moisture Content. Sustainability 2021, 13, 1041. https://doi.org/10.3390/ 1. Introduction su13031041 In recent years, with the increase of intensity and depth of coal mining, dynamic dis- Academic Editor: Guang-Liang Feng asters such as rock burst seriously threaten production safety [1,2]. As water is common in Received: 9 December 2020 the coal mining environment and many deformations of engineering rock mass are related Accepted: 18 January 2021 to the water in the rock, and the elastic energy index is one of the critical measurement Published: 20 January 2021 indicators for the evaluation of impact tendency, accurate calculation of the elastic energy index is crucial to estimate the strength of coal rock impact tendency [3–5]. Therefore, the Publisher’s Note: MDPI stays neutral study of characteristics of mechanical properties and energy storage of rock under different with regard to jurisdictional claims in water-bearing conditions has very important engineering significance. published maps and institutional affil- The water inside the rock mass is the leading cause of rock softening and strength iations. reduction. Many scholars [6–9] have studied the influence of water content on rock de- formation, strength characteristics, and energy storage characteristics. Z. Pan et al. [10] analyzed the influence of water content on compressive strength and elastic modulus of sandstone through loading and unloading tests. Eberhardt et al. [11] studied the fracture Copyright: © 2021 by the authors. damage mechanical behavior of brittle rock samples through uniaxial loading and unload- Licensee MDPI, Basel, Switzerland. ing tests and acoustic emission monitoring. Su [12] carried out uniaxial cyclic loading This article is an open access article and unloading tests on saturated diorite, and found that the energy storage capacity and distributed under the terms and brittleness of sandstone were greatly weakened and plasticity was significantly enhanced conditions of the Creative Commons after saturating water. Xia [13] found the energy dissipated and the number of cycles was Attribution (CC BY) license (https:// approximately linear. Zhang [14] studied the stress–strain curve and energy evolution creativecommons.org/licenses/by/ law of sandstone under different water content and found that the curve was sparse in 4.0/). Sustainability 2021, 13, 1041. https://doi.org/10.3390/su13031041 https://www.mdpi.com/journal/sustainability Sustainability 2021, 13, 1041 2 of 15 the saturated state, and the volume energy was small; and in the drying state, the curve was denser and the volume energy is the largest. Li [15] discusses the influence of water content and anisotropy on the strength and deformability of two meta-sedimentary rocks by triaxial compressive tests, and the experimental studies show that the anisotropy associ- ated with bedding in rock specimens plays a weakening effect on the triaxial compressive strength for both tested rocks. Roshan [16] discussed the X-ray computed tomography which was conducted on the representative samples from each type of sandstone to assess the porosity, rock composition, and texture, and the experimental studies show that volume and effective porosity is more accurately correlated to mechanical properties. Meng [17] studied sedimentary rock and the models and correlations between moisture content and bursting potential are established, and the rock after peak strength of stress–strain curve represents brittleness and shear failure and has obvious strain softening behavior in the condition of dried or with small moisture content. Acoustic emission (A.E.) technology is capable of dynamically monitoring the genera- tion and expansion of micro-cracks in rock materials and reflecting the damage evolution process. Therefore, it has been widely used in geotechnical engineering such as coal mining, slopes, tunnels and bridges [18–20]. Mansurov et al. [21] used acoustic emission to measure the information of rock failure process and predict the failure type of rock. Xiao [22] stud- ied the characteristic parameters of acoustic emission, and the plastic piecewise functions through the cyclic loading and unloading and acoustic emission experiments. Fu [23] conducted uniaxial compression tests and acoustic emission tests on the rock, and the results showed that the rock deformation rate has a good correspondence with the number of acoustic emission events. Liang et al. [24] studied the influence of the cyclic loading and unloading on the mechanical properties of the rock at the post-peak stage, and verified that the deformation behavior of the rock was in good agreement with the acoustic emission parameters. He et al. [25] studied the A.E. cumulative energy release phenomenon in the process of rock unloading, loading and failure. The aforementioned studies have greatly deepened the understanding of the law of energy changes in the process of rock instability and failure. However, the combined effect of periodic loads and water is common in actual underground engineering construction. Therefore, typical sandstone materials were selected to perform the uniaxial compression test, cyclic loading and unloading test, and acoustic emission test on rock samples with three different water content, and conduct research on the characteristics of mechanical properties and energy storage of the rock samples with water to provide a theoretical reference for rock fracture and instability. 2. Sample Preparation The white sandstone samples were produced from a sandstone mine in Renshou County, Sichuan Province, China. The main mineral components of white sandstone are quartz 60%, feldspar 20%, clay 15%, and a small amount of muscovite. All samples were manufactured in accordance with the standard of the International Society of Rock Mechanics and Rock Engineering. SC-200 core machine was firstly used to drill a cylindrical core with a diameter of 50 mm, and SCQ automatic stone cutter was then used to cut a sample with a length of 100 mm. Finally, the two ends of each specimen were polished to be smooth and parallel using SCQM automatic cutting and grinding machine. The specimens were divided into three groups: saturated state (a), natural state (b), and dry state (c). The average water content of the as-received sandstone is 0.202%. In order to obtain dry and saturated sandstone specimens, the white sandstone is dried and saturated with water, respectively. The sandstone specimens under two states are measured until the mass difference between the two consecutive times’ weighing is less than 0.05%. During tests, the rock samples under natural state are not processed; other rock samples are dried in an oven at 100 ◦C for 48 h, and then taken out, placed in a drying oven to cool to the room temperature, and finally weighed. When the change in weight is constant, the rock sample is considered to be completely dried, and an appropriate amount of rock sample Sustainability 2021, 13, 1041 3 of 15 will be selected as the drying group (c). The sample under the saturated state is prepared by using a proper amount of dried rock samples to absorb water by natural immersion method. Take out rock samples at regular intervals, wipe off the surface moisture of the rock sample with a towel, and weigh until the water content becomes stable. Figure1 shows the variation curve of the average water content of all saturated rock samples with the immersion time. It can be seen that white sandstone has strong water absorption, and the water content increases exponentially with the immersion time. In the initial stage of immersion (0–4 h), the water absorption rate is large, and the water content increases rapidly as time elapses; then (4–7 h) the water absorption rate gradually decreases, and the water content increases slowly; after more than 7 h, the average water content of the rock sample tends to stabilize, indicating that the sandstone is close to saturation with the average water content of 2.483%. The curve in Figure1 is the fitting equation with the correlation coefficient R2 of 0.9890. This equation is only applicable when white sandstone with φ50 mm and L100 mm is selected in this test.
Load more

Recommended publications
  • J-Integral Analysis of the Mixed-Mode Fracture Behaviour of Composite Bonded Joints
    J-Integral analysis of the mixed-mode fracture behaviour of composite bonded joints FERNANDO JOSÉ CARMONA FREIRE DE BASTOS LOUREIRO novembro de 2019 J-INTEGRAL ANALYSIS OF THE MIXED-MODE FRACTURE BEHAVIOUR OF COMPOSITE BONDED JOINTS Fernando José Carmona Freire de Bastos Loureiro 1111603 Equation Chapter 1 Section 1 2019 ISEP – School of Engineering Mechanical Engineering Department J-INTEGRAL ANALYSIS OF THE MIXED-MODE FRACTURE BEHAVIOUR OF COMPOSITE BONDED JOINTS Fernando José Carmona Freire de Bastos Loureiro 1111603 Dissertation presented to ISEP – School of Engineering to fulfil the requirements necessary to obtain a Master's degree in Mechanical Engineering, carried out under the guidance of Doctor Raul Duarte Salgueiral Gomes Campilho. 2019 ISEP – School of Engineering Mechanical Engineering Department JURY President Doctor Elza Maria Morais Fonseca Assistant Professor, ISEP – School of Engineering Supervisor Doctor Raul Duarte Salgueiral Gomes Campilho Assistant Professor, ISEP – School of Engineering Examiner Doctor Filipe José Palhares Chaves Assistant Professor, IPCA J-Integral analysis of the mixed-mode fracture behaviour of composite Fernando José Carmona Freire de Bastos bonded joints Loureiro ACKNOWLEDGEMENTS To Doctor Raul Duarte Salgueiral Gomes Campilho, supervisor of the current thesis for his outstanding availability, support, guidance and incentive during the development of the thesis. To my family for the support, comprehension and encouragement given. J-Integral analysis of the mixed-mode fracture behaviour of composite
    [Show full text]
  • Contact Mechanics in Gears a Computer-Aided Approach for Analyzing Contacts in Spur and Helical Gears Master’S Thesis in Product Development
    Two Contact Mechanics in Gears A Computer-Aided Approach for Analyzing Contacts in Spur and Helical Gears Master’s Thesis in Product Development MARCUS SLOGÉN Department of Product and Production Development Division of Product Development CHALMERS UNIVERSITY OF TECHNOLOGY Gothenburg, Sweden, 2013 MASTER’S THESIS IN PRODUCT DEVELOPMENT Contact Mechanics in Gears A Computer-Aided Approach for Analyzing Contacts in Spur and Helical Gears Marcus Slogén Department of Product and Production Development Division of Product Development CHALMERS UNIVERSITY OF TECHNOLOGY Göteborg, Sweden 2013 Contact Mechanics in Gear A Computer-Aided Approach for Analyzing Contacts in Spur and Helical Gears MARCUS SLOGÉN © MARCUS SLOGÉN 2013 Department of Product and Production Development Division of Product Development Chalmers University of Technology SE-412 96 Göteborg Sweden Telephone: + 46 (0)31-772 1000 Cover: The picture on the cover page shows the contact stress distribution over a crowned spur gear tooth. Department of Product and Production Development Göteborg, Sweden 2013 Contact Mechanics in Gears A Computer-Aided Approach for Analyzing Contacts in Spur and Helical Gears Master’s Thesis in Product Development MARCUS SLOGÉN Department of Product and Production Development Division of Product Development Chalmers University of Technology ABSTRACT Computer Aided Engineering, CAE, is becoming more and more vital in today's product development. By using reliable and efficient computer based tools it is possible to replace initial physical testing. This will result in cost savings, but it will also reduce the development time and material waste, since the demand of physical prototypes decreases. This thesis shows how a computer program for analyzing contact mechanics in spur and helical gears has been developed at the request of Vicura AB.
    [Show full text]
  • Cookbook for Rheological Models ‒ Asphalt Binders
    CAIT-UTC-062 Cookbook for Rheological Models – Asphalt Binders FINAL REPORT May 2016 Submitted by: Offei A. Adarkwa Nii Attoh-Okine PhD in Civil Engineering Professor Pamela Cook Unidel Professor University of Delaware Newark, DE 19716 External Project Manager Karl Zipf In cooperation with Rutgers, The State University of New Jersey And State of Delaware Department of Transportation And U.S. Department of Transportation Federal Highway Administration Disclaimer Statement The contents of this report reflect the views of the authors, who are responsible for the facts and the accuracy of the information presented herein. This document is disseminated under the sponsorship of the Department of Transportation, University Transportation Centers Program, in the interest of information exchange. The U.S. Government assumes no liability for the contents or use thereof. The Center for Advanced Infrastructure and Transportation (CAIT) is a National UTC Consortium led by Rutgers, The State University. Members of the consortium are the University of Delaware, Utah State University, Columbia University, New Jersey Institute of Technology, Princeton University, University of Texas at El Paso, Virginia Polytechnic Institute, and University of South Florida. The Center is funded by the U.S. Department of Transportation. TECHNICAL REPORT STANDARD TITLE PAGE 1. Report No. 2. Government Accession No. 3. Recipient’s Catalog No. CAIT-UTC-062 4. Title and Subtitle 5. Report Date Cookbook for Rheological Models – Asphalt Binders May 2016 6. Performing Organization Code CAIT/University of Delaware 7. Author(s) 8. Performing Organization Report No. Offei A. Adarkwa Nii Attoh-Okine CAIT-UTC-062 Pamela Cook 9. Performing Organization Name and Address 10.
    [Show full text]
  • Idealized 3D Auxetic Mechanical Metamaterial: an Analytical, Numerical, and Experimental Study
    materials Article Idealized 3D Auxetic Mechanical Metamaterial: An Analytical, Numerical, and Experimental Study Naeim Ghavidelnia 1 , Mahdi Bodaghi 2 and Reza Hedayati 3,* 1 Department of Mechanical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Hafez Ave, Tehran 1591634311, Iran; [email protected] 2 Department of Engineering, School of Science and Technology, Nottingham Trent University, Nottingham NG11 8NS, UK; [email protected] 3 Novel Aerospace Materials, Faculty of Aerospace Engineering, Delft University of Technology (TU Delft), Kluyverweg 1, 2629 HS Delft, The Netherlands * Correspondence: [email protected] or [email protected] Abstract: Mechanical metamaterials are man-made rationally-designed structures that present un- precedented mechanical properties not found in nature. One of the most well-known mechanical metamaterials is auxetics, which demonstrates negative Poisson’s ratio (NPR) behavior that is very beneficial in several industrial applications. In this study, a specific type of auxetic metamaterial structure namely idealized 3D re-entrant structure is studied analytically, numerically, and experi- mentally. The noted structure is constructed of three types of struts—one loaded purely axially and two loaded simultaneously flexurally and axially, which are inclined and are spatially defined by angles q and j. Analytical relationships for elastic modulus, yield stress, and Poisson’s ratio of the 3D re-entrant unit cell are derived based on two well-known beam theories namely Euler–Bernoulli and Timoshenko. Moreover, two finite element approaches one based on beam elements and one based on volumetric elements are implemented. Furthermore, several specimens are additively Citation: Ghavidelnia, N.; Bodaghi, manufactured (3D printed) and tested under compression.
    [Show full text]
  • RHEOLOGY and DYNAMIC MECHANICAL ANALYSIS – What They Are and Why They’Re Important
    RHEOLOGY AND DYNAMIC MECHANICAL ANALYSIS – What They Are and Why They’re Important Presented for University of Wisconsin - Madison by Gregory W Kamykowski PhD TA Instruments May 21, 2019 TAINSTRUMENTS.COM Rheology: An Introduction Rheology: The study of the flow and deformation of matter. Rheological behavior affects every aspect of our lives. Dynamic Mechanical Analysis is a subset of Rheology TAINSTRUMENTS.COM Rheology: The study of the flow and deformation of matter Flow: Fluid Behavior; Viscous Nature F F = F(v); F ≠ F(x) Deformation: Solid Behavior F Elastic Nature F = F(x); F ≠ F(v) 0 1 2 3 x Viscoelastic Materials: Force F depends on both Deformation and Rate of Deformation and F vice versa. TAINSTRUMENTS.COM 1. ROTATIONAL RHEOLOGY 2. DYNAMIC MECHANICAL ANALYSIS (LINEAR TESTING) TAINSTRUMENTS.COM Rheological Testing – Rotational - Unidirectional 2 Basic Rheological Methods 10 1 10 0 1. Apply Force (Torque)and 10 -1 measure Deformation and/or 10 -2 (rad/s) Deformation Rate (Angular 10 -3 Displacement, Angular Velocity) - 10 -4 Shear Rate Shear Controlled Force, Controlled 10 3 10 4 10 5 Angular Velocity, Velocity, Angular Stress Torque, (µN.m)Shear Stress 2. Control Deformation and/or 10 5 Displacement, Angular Deformation Rate and measure 10 4 10 3 Force needed (Controlled Strain (Pa) ) Displacement or Rotation, 10 2 ( Controlled Strain or Shear Rate) 10 1 Torque, Stress Torque, 10 -1 10 0 10 1 10 2 10 3 s (s) TAINSTRUMENTS.COM Steady Simple Shear Flow Top Plate Velocity = V0; Area = A; Force = F H y Bottom Plate Velocity = 0 x vx = (y/H)*V0 .
    [Show full text]
  • What Engineers Should Know About Bending Steel
    bending and rolling What Engineers Should Know About Bending Steel With these tips under your belt, you’ll be ahead of the curve on your next bending or rolling project. BY TODD A. ALWOOD HOW MUCH DO YOU KNOW ABOUT BENDING STRUCTURAL STEEL? Do you know what you need to show on con- struction drawings to transfer the idea of what the result should actually look like? Do you know how tight of a radius you Hcan roll a W12×19, and what to expect it to look like? If you have bending questions, who do you ask? AISC’s bender-roller com- mittee is taking steps to address these ques- tions, which are coming up more and more within the structural steel industry. Bender = Fabricator? Not so! The bender is typically a spe- cialty subcontractor of the fabricator. Benders receive the steel from the fabri- cator (or sometimes furnish it themselves), and then ship the curved steel back to the fabricator. Benders usually have limited fabrication capabilities, such as hole drill- ing and plate welding, but they are gener- ally used for smaller jobs that usually are not structural in nature. Typical fabrication is still carried out through the main project fabricator who organizes the steel package from procurement through delivery to the site for erection. Kottler Metal Products, Inc. Kottler Metal Products, Todd Alwood is the senior advisor for AISC’s Steel Solutions Center and is Secretary of AISC’s Bender-Roller Committee. MODERN STEEL CONSTRUCTION MAY 2006 Common Terminology and Essential Dimensions for Curving Common Hot-Rolled Shapes There’s only one type of bending, right? Nope! There are five typical methods of bending in the industry: roll- ing, incremental bending, hot bending, rotary-draw bending, and induc- tion bending.
    [Show full text]
  • Elastic Metamaterials for Independent Realization of Negativity in Density
    Elastic metamaterials for independent realization of negativity in density and stiffness Joo Hwan Oh1, Young Eui Kwon2, Hyung Jin Lee3 and Yoon Young Kim1, 3* 1Institute of Advanced Machinery and Design, Seoul National University, 599 Gwanak-ro, Gwanak-gu, Seoul 151-744, Korea 2Korea Institute of Nuclear Safety, 62 Gwahak-ro, Yuseoung-gu, Daejeon 305-338, Korea 3School of Mechanical and Aerospace Engineering, Seoul National University, 599 Gwanak-ro, Gwanak-gu, Seoul 151-744, Korea Abstract In this paper, we present the realization of an elastic metamaterial allowing independent tuning of negative density and stiffness for elastic waves propagating along a designated direction. In electromagnetic (or acoustic) metamaterials, it is now possible to tune permittivity (bulk modulus) and permeability (density) independently. Apparently, the tuning methods seem to be directly applicable for elastic case, but no realization has yet been made due to the unique tensorial physics of elasticity that makes wave motions coupled in a peculiar way. To realize independent tunability, we developed a single-phased elastic metamaterial supported by theoretical analysis and numerical/experimental validations. Keywords: Elastic metamaterial, Independently tuning parameters, Negative density, Negative stiffness PACS numbers: 46.40.-f, 46.40.Ff, 62.30.+d * Corresponding Author, Professor, [email protected], phone +82-2-880-7154, fax +82-2-872-1513 -1- Interest in negative material properties has initially grown in electromagnetic field1-3, being realized by metamaterials. Since then, several interesting applications in antennas, lenses, wave absorbers and others have been discussed. The advances in electromagnetic metamaterials are largely due to independent tuning of the negativity in permittivity and permeability.
    [Show full text]
  • Contact Mechanics and Friction
    Contact Mechanics and Friction Valentin L. Popov Contact Mechanics and Friction Physical Principles and Applications 1 3 Professor Dr. Valentin L. Popov Berlin University of Technology Institute of Mechanics Strasse des 17.Juni 135 10623 Berlin Germany [email protected] ISBN 978-3-642-10802-0 e-ISBN 978-3-642-10803-7 DOI 10.1007/978-3-642-10803-7 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2010921669 c Springer-Verlag Berlin Heidelberg 2010 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: WMXDesign GmbH Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com) Dr. Valentin L. Popov studied physics and obtained his doctorate from the Moscow State Lomonosow University. He worked at the Institute of Strength Physics and Materials Science of the Russian Academy of Sciences.
    [Show full text]
  • Bending of Beam
    BENDING OF BEAM When a beam is loaded under pure moment M, it can be shown that the beam will bend in a circular arc. If we assume that plane cross-sections will remain plane after bending, then to form the circular arc, the top layers of the beam have to shorten in length (compressive strain) and the bottom layers have to elongate in length (tensile strain) to produce the M curvature. The compression amount will gradually diminish as we go down from the Compressed top layer, eventually changing from layer compression to tension, which will then gradually increase as we reach the bottom layer. Elongated layer Thus, in this type of loading, the top layer M will have maximum compressive strain, the bottom layer will have maximum tensile Un-strained layer strain and there will be a middle layer where the length of the layer will remain unchanged and hence no normal strain. This layer is known as Neutral Layer, and in 2D representation, it is known as Neutral Axis (NA). NA= Neutral Axis Because the beam is made of elastic Compression A material, compressive and tensile strains will N also give rise to compressive and tensile stresses (stress and strain is proportional – Hook’s Law), respectively. Unchanged More the applied moment load more is Elongation the curvature, which will produce more strains and thus more stresses. Two Dimensional View Our objective is to estimate the stress from bending. We can determine the bending strain and stress from the geometry of bending. Let us take a small cross section of width dx, at a distance x from the left edge of the beam.
    [Show full text]
  • The Viscous Catenary
    J. Fluid Mech. (2003), vol. 478, pp. 71–80. c 2003 Cambridge University Press 71 DOI: 10.1017/S0022112002003038 Printed in the United Kingdom The viscous catenary By J. TEICHMAN AND L. MAHADEVAN Hatsopoulos Microfluids Laboratory, Massachusetts Institute of Technology,† 77 Massachusetts Avenue, Cambridge, MA 02139, USA (Received 29 September 2002 and in revised form 21 October 2002) A filament of an incompressible highly viscous fluid that is supported at its ends sags under the influence of gravity. Its instantaneous shape resembles that of a catenary, but evolves with time. At short times, the shape is dominated by bending deformations. At intermediate times, the effects of stretching become dominant everywhere except near the clamping boundaries where bending boundary layers persist. Finally, the filament breaks off in finite time via strain localization and pinch-off. 1. Introduction In 1690, Jacob Bernoulli issued the following challenge: determine the shape of a heavy filament or chain hanging between two points on the same horizontal line. Leibniz, Huygens and Johann Bernoulli independently discovered the equation for the shape of the catenary (derived from the Latin for chain), providing one of the first exact solutions of a nonlinear problem in continuum mechanics. Here we consider the fluid analogue of a catenary, shown in figure 1(a–f ). When a thin filament of an incompressible highly viscous fluid forms a bridge across the gap between two solid vertical walls, it will sag under the influence of gravity. After a very short initial transient when it falls quickly, it slows down in response to the resistance to extension.
    [Show full text]
  • SCK« CEN Stuimkchntrum VOOR Kl-.Rnfcnlrglt CTNTRF D'ftudl 1)1 I'fcnl-Rgil- MICI.FAIRF Precracking of Round Notched Bars
    BE9800004 SCK« CEN STUIMKChNTRUM VOOR Kl-.RNfcNLRGlt CTNTRF D'FTUDl 1)1 I'fcNl-RGIl- MICI.FAIRF Precracking of round notched bars Progress Report M. Scibetta SCK-CEN Mol* Belgium Precracking of round notched bars Progress Report M. Scibetta SCK»CEN Mol, Belgium February, 1996 BLG-708 Precracking of round notched bars 1 Abstract 3 2 Introduction 3 3 Overview of precracking techniques 4 3.1 Introduction 4 3.2 Equipment 4 3.3 Eccentricity 5 3.4 Time required to precrack 5 3.5 Crack depth determination 5 3.5.1 The compliance method 6 3.5.1.1 Measuring force 6 3.5.1.2 Measuring displacement 6 3.5.1.3 Measuring an angle with a laser 6 3.5.1.4 Measuring force and displacement 7 3.5.2 Optical methods 7 3.5.3 The potential drop method 7 3.5.4 The resonance frequency method 8 3.6 Summary 8 4 Stress intensity factor and compliance of a bar under bending 9 4.1 Analytical expression 9 4.2 Stress intensity factor along the crack front 10 4.4 Combined effect of contact and eccentricity 12 4.5 Effect of mode II 12 4.6 Compliance 13 5 Stress intensity factor and compliance of a bar under bending using the finite element method (FEM) 15 5.1 Stress intensity factors 15 5.2 Compliance 17 6 Precracking system 18 6.2 Schematic representation of the experimental system 19 6.3 Initial stress intensity factor 19 6.4 Initial force 20 6.5 Initial contact pressure 20 6.6 Final force 22 6.7 Final stress intensity factor 22 7 Stress intensity factor of a precracked bar under tension 23 7.1 Analytical formulations 23 7.2 Finite element method 24 8 Compliance of a precracked bar under tension 26 8.1 Analytical formulations 26 8.2 Finite element method 27 9 Conclusions 28 10 Future investigations 29 11 References 30 Annex 1 Stress intensity factor and compliance function of a precracked bar under bending 33 Annex 2 Neutral axis position and stress intensity factor correction due to contact .34 Annex 3 Stress intensity factor and compliance function of a precracked bar under tension 35 1 Abstract Precracking round notched bars is the first step before fracture mechanics tests.
    [Show full text]
  • Basic Mechanics
    93 Chapter 6 Basic mechanics BASIC PRINCIPLES OF STATICS All objects on earth tend to accelerate toward the Statics is the branch of mechanics that deals with the centre of the earth due to gravitational attraction; hence equilibrium of stationary bodies under the action of the force of gravitation acting on a body with the mass forces. The other main branch – dynamics – deals with (m) is the product of the mass and the acceleration due moving bodies, such as parts of machines. to gravity (g), which has a magnitude of 9.81 m/s2: Static equilibrium F = mg = vρg A planar structural system is in a state of static equilibrium when the resultant of all forces and all where: moments is equal to zero, i.e. F = force (N) m = mass (kg) g = acceleration due to gravity (9.81m/s2) y ∑Fx = 0 ∑Fx = 0 ∑Fy = 0 ∑Ma = 0 v = volume (m³) ∑Fy = 0 or ∑Ma = 0 or ∑Ma = 0 or ∑Mb = 0 ρ = density (kg/m³) x ∑Ma = 0 ∑Mb = 0 ∑Mb = 0 ∑Mc = 0 Vector where F refers to forces and M refers to moments of Most forces have magnitude and direction and can be forces. shown as a vector. The point of application must also be specified. A vector is illustrated by a line, the length of Static determinacy which is proportional to the magnitude on a given scale, If a body is in equilibrium under the action of coplanar and an arrow that shows the direction of the force. forces, the statics equations above must apply.
    [Show full text]