Methods of Mechanical Testing1
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Lecture 13: Earth Materials
Earth Materials Lecture 13 Earth Materials GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD Hooke’s law of elasticity Force Extension = E × Area Length Hooke’s law σn = E εn where E is material constant, the Young’s Modulus Units are force/area – N/m2 or Pa Robert Hooke (1635-1703) was a virtuoso scientist contributing to geology, σ = C ε palaeontology, biology as well as mechanics ij ijkl kl ß Constitutive equations These are relationships between forces and deformation in a continuum, which define the material behaviour. GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD Shear modulus and bulk modulus Young’s or stiffness modulus: σ n = Eε n Shear or rigidity modulus: σ S = Gε S = µε s Bulk modulus (1/compressibility): Mt Shasta andesite − P = Kεv Can write the bulk modulus in terms of the Lamé parameters λ, µ: K = λ + 2µ/3 and write Hooke’s law as: σ = (λ +2µ) ε GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD Young’s Modulus or stiffness modulus Young’s Modulus or stiffness modulus: σ n = Eε n Interatomic force Interatomic distance GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD Shear Modulus or rigidity modulus Shear modulus or stiffness modulus: σ s = Gε s Interatomic force Interatomic distance GNH7/GG09/GEOL4002 EARTHQUAKE SEISMOLOGY AND EARTHQUAKE HAZARD Hooke’s Law σij and εkl are second-rank tensors so Cijkl is a fourth-rank tensor. For a general, anisotropic material there are 21 independent elastic moduli. In the isotropic case this tensor reduces to just two independent elastic constants, λ and µ. -
Guide to Rheological Nomenclature: Measurements in Ceramic Particulate Systems
NfST Nisr National institute of Standards and Technology Technology Administration, U.S. Department of Commerce NIST Special Publication 946 Guide to Rheological Nomenclature: Measurements in Ceramic Particulate Systems Vincent A. Hackley and Chiara F. Ferraris rhe National Institute of Standards and Technology was established in 1988 by Congress to "assist industry in the development of technology . needed to improve product quality, to modernize manufacturing processes, to ensure product reliability . and to facilitate rapid commercialization ... of products based on new scientific discoveries." NIST, originally founded as the National Bureau of Standards in 1901, works to strengthen U.S. industry's competitiveness; advance science and engineering; and improve public health, safety, and the environment. One of the agency's basic functions is to develop, maintain, and retain custody of the national standards of measurement, and provide the means and methods for comparing standards used in science, engineering, manufacturing, commerce, industry, and education with the standards adopted or recognized by the Federal Government. As an agency of the U.S. Commerce Department's Technology Administration, NIST conducts basic and applied research in the physical sciences and engineering, and develops measurement techniques, test methods, standards, and related services. The Institute does generic and precompetitive work on new and advanced technologies. NIST's research facilities are located at Gaithersburg, MD 20899, and at Boulder, CO 80303. -
Making and Characterizing Negative Poisson's Ratio Materials
Making and characterizing negative Poisson’s ratio materials R. S. LAKES* and R. WITT**, University of Wisconsin–Madison, 147 Engineering Research Building, 1500 Engineering Drive, Madison, WI 53706-1687, USA. 〈[email protected]〉 Received 18th October 1999 Revised 26th August 2000 We present an introduction to the use of negative Poisson’s ratio materials to illustrate various aspects of mechanics of materials. Poisson’s ratio is defined as minus the ratio of transverse strain to longitudinal strain in simple tension. For most materials, Poisson’s ratio is close to 1/3. Negative Poisson’s ratios are counter-intuitive but permissible according to the theory of elasticity. Such materials can be prepared for classroom demonstrations, or made by students. Key words: Poisson’s ratio, deformation, foam, honeycomb 1. INTRODUCTION Poisson’s ratio is the ratio of lateral (transverse) contraction strain to longitudinal extension strain in a simple tension experiment. The allowable range of Poisson’s ratio ν in three 1 dimensional isotropic solids is from –1 to 2 [1]. Common materials usually have a Poisson’s 1 1 ratio close to 3 . Rubbery materials, however, have values approaching 2 . They readily undergo shear deformations, governed by the shear modulus G, but resist volumetric (bulk) deformation governed by the bulk modulus K; for rubbery materials G Ӷ K. Even though textbooks can still be found [2] which categorically state that Poisson’s ratios less than zero are unknown, or even impossible, there are in fact a number of examples of negative Poisson’s ratio solids. Although such behaviour is counter-intuitive, negative Poisson’s ratio structures and materials can be easily made and used in lecture demonstrations and for student projects. -
Determination of Shear Modulus of Dental Materials by Means of the Torsion Pendulum
NATIONAL BUREAU OF STANDARDS REPORT 10 068 Progress Report on DETERMINATION OF SHEAR MODULUS OF DENTAL MATERIALS BY MEANS OF THE TORSION PENDULUM U.S. DEPARTMENT OF COMMERCE NATIONAL BUREAU OF STANDARDS NATIONAL BUREAU OF STANDARDS The National Bureau of Standards ' was established by an act of Congress March 3, 1901. Today, in addition to serving as the Nation’s central measurement laboratory, the Bureau is a principal focal point in the Federal Government for assuring maximum application of the physical and engineering sciences to the advancement of technology in industry and commerce. To this end the Bureau conducts research and provides central national services in four broad program areas. These are: (1) basic measurements and standards, (2) materials measurements and standards, (3) technological measurements and standards, and (4) transfer of technology. The Bureau comprises the Institute for Basic Standards, the Institute for Materials Research, the Institute for Applied Technology, the Center for Radiation Research, the Center for Computer Sciences and Technology, and the Office for Information Programs. THE INSTITUTE FOR BASIC STANDARDS provides the central basis within the United States of a complete and consistent system of physical measurement; coordinates that system with measurement systems of other nations; and furnishes essential services leading to accurate and uniform physical measurements throughout the Nation’s scientific community, industry, and com- merce. The Institute consists of an Office of Measurement Services -
Chapter 14 Solids and Fluids Matter Is Usually Classified Into One of Four States Or Phases: Solid, Liquid, Gas, Or Plasma
Chapter 14 Solids and Fluids Matter is usually classified into one of four states or phases: solid, liquid, gas, or plasma. Shape: A solid has a fixed shape, whereas fluids (liquid and gas) have no fixed shape. Compressibility: The atoms in a solid or a liquid are quite closely packed, which makes them almost incompressible. On the other hand, atoms or molecules in gas are far apart, thus gases are compressible in general. The distinction between these states is not always clear-cut. Such complicated behaviors called phase transition will be discussed later on. 1 14.1 Density At some time in the third century B.C., Archimedes was asked to find a way of determining whether or not the gold had been mixed with silver, which led him to discover a useful concept, density. m ρ = V The specific gravity of a substance is the ratio of its density to that of water at 4oC, which is 1000 kg/m3=1 g/cm3. Specific gravity is a dimensionless quantity. 2 14.2 Elastic Moduli A force applied to an object can change its shape. The response of a material to a given type of deforming force is characterized by an elastic modulus, Stress Elastic modulus = Strain Stress: force per unit area in general Strain: fractional change in dimension or volume. Three elastic moduli will be discussed: Young’s modulus for solids, the shear modulus for solids, and the bulk modulus for solids and fluids. 3 Young’s Modulus Young’s modulus is a measure of the resistance of a solid to a change in its length when a force is applied perpendicular to a face. -
Me 212 Laboratory Experiment #3 Hardness Testing And
ME 212 LABORATORY EXPERIMENT #3 HARDNESS TESTING AND AGE HARDENING 1. OBJECTIVE: Our primary aim is to measure the Rockwell Hardness values for different materials and estimate ultimate tensile strengths by the aid of conversion tables. We will also focus on age hardening, the info on which can be found in the last part of this experiment sheet. 2. HARDNESS TESTING THEORY: Hardness is usually defined as the resistance of a material to plastic penetration of its surface. There are three main types of tests used to determine hardness: • Scratch tests are the simplest form of hardness tests. In this test, various materials are rated on their ability to scratch one another. Mohs hardness test is of this type. This test is used mainly in mineralogy. • In Dynamic Hardness tests, an object of standard mass and dimensions is bounced back from a surface after falling by its own weight. The height of the rebound is indicated. Shore hardness is measured by this method. • Static Indentation tests are based on the relation of indentation of the specimen by a penetrator under a given load. The relationship of total test force to the area or depth of indentation provides a measure of hardness. The Rockwell, Brinell, Knoop, Vickers, and ultrasonic hardness tests are of this type. For engineering purposes, only the static indentation tests are used. BRINELL HARDNESS TEST: This test consists of applying a constant load, usually between 500 and 3000 kgf for a specified time (10 to 30 s) using a 5- or 10-mm diameter hardened steel or tungsten carbide ball on the flat surface of a workpiece. -
5. Mechanical Properties and Performance of Materials
5. MECHANICAL PROPERTIES AND PERFORMANCE OF MATERIALS Samples of engineering materials are subjected to a wide variety of mechanical tests to measure their strength, elastic constants, and other material properties as well as their performance under a variety of actual use conditions and environments. The results of such tests are used for two primary purposes: 1) engineering design (for example, failure theories based on strength, or deflections based on elastic constants and component geometry) and 2) quality control either by the materials producer to verify the process or by the end user to confirm the material specifications. Because of the need to compare measured properties and performance on a common basis, users and producers of materials use standardized test methods such as those developed by the American Society for Testing and Materials (ASTM) and the International Organization for Standardization (ISO). ASTM and ISO are but two of many standards-writing professional organization in the world. These standards prescribe the method by which the test specimen will be prepared and tested, as well as how the test results will be analyzed and reported. Standards also exist which define terminology and nomenclature as well as classification and specification schemes. The following sections contain information about mechanical tests in general as well as tension, hardness, torsion, and impact tests in particular. Mechanical Testing Mechanical tests (as opposed to physical, electrical, or other types of tests) often involves the deformation or breakage of samples of material (called test specimens or test pieces). Some common forms of test specimens and loading situations are shown in Fig 5.1. -
Enghandbook.Pdf
785.392.3017 FAX 785.392.2845 Box 232, Exit 49 G.L. Huyett Expy Minneapolis, KS 67467 ENGINEERING HANDBOOK TECHNICAL INFORMATION STEELMAKING Basic descriptions of making carbon, alloy, stainless, and tool steel p. 4. METALS & ALLOYS Carbon grades, types, and numbering systems; glossary p. 13. Identification factors and composition standards p. 27. CHEMICAL CONTENT This document and the information contained herein is not Quenching, hardening, and other thermal modifications p. 30. HEAT TREATMENT a design standard, design guide or otherwise, but is here TESTING THE HARDNESS OF METALS Types and comparisons; glossary p. 34. solely for the convenience of our customers. For more Comparisons of ductility, stresses; glossary p.41. design assistance MECHANICAL PROPERTIES OF METAL contact our plant or consult the Machinery G.L. Huyett’s distinct capabilities; glossary p. 53. Handbook, published MANUFACTURING PROCESSES by Industrial Press Inc., New York. COATING, PLATING & THE COLORING OF METALS Finishes p. 81. CONVERSION CHARTS Imperial and metric p. 84. 1 TABLE OF CONTENTS Introduction 3 Steelmaking 4 Metals and Alloys 13 Designations for Chemical Content 27 Designations for Heat Treatment 30 Testing the Hardness of Metals 34 Mechanical Properties of Metal 41 Manufacturing Processes 53 Manufacturing Glossary 57 Conversion Coating, Plating, and the Coloring of Metals 81 Conversion Charts 84 Links and Related Sites 89 Index 90 Box 232 • Exit 49 G.L. Huyett Expressway • Minneapolis, Kansas 67467 785-392-3017 • Fax 785-392-2845 • [email protected] • www.huyett.com INTRODUCTION & ACKNOWLEDGMENTS This document was created based on research and experience of Huyett staff. Invaluable technical information, including statistical data contained in the tables, is from the 26th Edition Machinery Handbook, copyrighted and published in 2000 by Industrial Press, Inc. -
Compositional Effects on Ideal Shear Strength in Fe-Cr Alloys
Journal of Alloys and Compounds 720 (2017) 466e472 Contents lists available at ScienceDirect Journal of Alloys and Compounds journal homepage: http://www.elsevier.com/locate/jalcom Compositional effects on ideal shear strength in Fe-Cr alloys * Luis Casillas-Trujillo, Liubin Xu, Haixuan Xu University of Tennessee, Department of Materials Science and Engineering, Knoxville, TN 37996, USA article info abstract Article history: The ideal shear strength is the minimum stress needed to plastically deform a defect free crystal; it is of Received 8 August 2016 engineering interest since it sets the upper bound of the strength of a real crystal and connects to the Received in revised form nucleation of dislocations. In this study, we have employed spin-polarized density functional theory to 25 March 2017 calculate the ideal shear strength, elastic constants and various moduli of body centered cubic Fe-Cr Accepted 15 May 2017 alloys. We have determined the magnetic ground state of the Fe-Cr solid solutions, and noticed that Available online 17 May 2017 calculations without the correct magnetic ground state would lead to incorrect results of the lattice and elastic constants. We have determined the ideal shear strength along the 〈111〉{110} and 〈111〉{112} slip Keywords: Compositional effects systems and established the relationship between alloy composition and mechanical properties. We 〈 〉 Ideal shear stress observe strengthening in the 111 {110} system as a function of chromium composition, while there is no Density functional theory change in strength in the 〈111〉{112} system. The observed differences can be explained by the response Magnetism of the magnetic moments as a function of applied strain. -
Solids and Fluids
11/2/2010 Solids and Fluids Crystalline solid Amorphous solid Liquids Gases Plasmas Deformation in solids Stress is related to the force causing a deformation Strain is a measure of the degree of deformation stress Elastic modulus= strain 1 11/2/2010 Elasticity in length Tensile stress is the ratio force F of the magnitude of the Tensile stress= = external force per sectional area A area A: Units 1 Pa ≡1 Nm −2 Tensile strain is the ratio ∆ of the change of length to L Tensile strain= the original length L0 Young’s modulus is the F / A F L ratio of the tensile stress Y ≡ = 0 over the tensile strain: ∆ ∆ L / L0 L A Elastic limit 2 11/2/2010 Shear deformation Elasticity of Shape Shear stress is the ratio of F the parallel force to the area Shear stress= parallel A of the face being sheared: area Units 1 Pa ≡1 Nm −2 Shear strain is the ratio of the distance sheared to the ∆x Shear strain= height h Shear modulus is the ratio F / A F h of the shear stress over the S ≡ parallel = parallel shear strain: ∆x / h ∆x A 3 11/2/2010 Volume elasticity Elasticity in volume Volume stress is the ∆F change in the applied force ∆P ≡ per surface area Asurface Volume strain is the ratio of the change of volume to ∆V Volume strain= the original volume V Bulk modulus is the ratio ∆F / A ∆P of the volume stress over B ≡ − = − the volume strain: ∆V /V ∆V /V 4 11/2/2010 Elasticity in volume For the Bulk modulus to be positive, as an increase of pressure always produces a decrease of volume, one introduces a negative sign in its definition! Bulk modulus is the ratio -
Indentation Hardness Measurements at Macro-, Micro-, and Nanoscale: a Critical Overview
Tribol Lett (2017) 65:23 DOI 10.1007/s11249-016-0805-5 REVIEW Indentation Hardness Measurements at Macro-, Micro-, and Nanoscale: A Critical Overview Esteban Broitman1 Received: 25 September 2016 / Accepted: 15 December 2016 / Published online: 28 December 2016 Ó The Author(s) 2016. This article is published with open access at Springerlink.com Abstract The Brinell, Vickers, Meyer, Rockwell, Shore, 1 Introduction IHRD, Knoop, Buchholz, and nanoindentation methods used to measure the indentation hardness of materials at The hardness of a solid material can be defined as a mea- different scales are compared, and main issues and mis- sure of its resistance to a permanent shape change when a conceptions in the understanding of these methods are constant compressive force is applied. The deformation can comprehensively reviewed and discussed. Basic equations be produced by different mechanisms, like indentation, and parameters employed to calculate hardness are clearly scratching, cutting, mechanical wear, or bending. In metals, explained, and the different international standards for each ceramics, and most of polymers, the hardness is related to method are summarized. The limits for each scale are the plastic deformation of the surface. Hardness has also a explored, and the different forms to calculate hardness in close relation to other mechanical properties like strength, each method are compared and established. The influence ductility, and fatigue resistance, and therefore, hardness of elasticity and plasticity of the material in each mea- testing can be used in the industry as a simple, fast, and surement method is reviewed, and the impact of the surface relatively cheap material quality control method. -
Equation of State and Shear Strength at Multimegabar Pressures: Magnesium Oxide to 227 Gpa
VOLUME 74, NUMBER 8 PH YSICAL REVIEW LETTERS 20 FEBRUARY 1995 Equation of State and Shear Strength at Multimegabar Pressures: Magnesium Oxide to 227 GPa Thomas S. Duffy, Russell J. Hemley, and Ho-kwang Mao Geophysicai Laboratory and Center for High Pres-sure Research, Carnegie Institution of Washington, 5251 Broad Branch Road, NW, Washington, DC 20015 (Received 9 June 1994) The equation of state, elasticity, and shear strength of magnesium oxide were examined to 227 GPa using synchrotron x-ray diffraction in a diamond anvil cell. Static compression, ultrasonic elasticity, and shock data for MgO from ambient pressure to above 200 GPa can all be described by a single Birch-Murnaghan equation of state when the static shear strength, which is determined to be at least 11 GPa at 227 GPa, is taken into account. Our results show that there are significant changes in the degree and character of the elastic anisotropy of MgO at high pressure. PACS numbers: 62.50.+p, 64.30.+t, 64.70.Kb Understanding the physics of materials at ultrahigh pres- Structural studies of materials at multimegabar pres- sure is an important focus of current work in condensed sures have largely been restricted to high atomic weight matter science. The equation of state (EOS) and phase sta- materials, due to the difficulty of performing x-ray diffrac- bility are the most fundamental properties obtained from tion on the extremely small volumes which can be sub- these investigations. The reliability of equation of state jected to such pressures. We show that with synchrotron determinations at large compressions is uncertain because radiation methods x-ray diffraction can be carried out on the stress state at multimegabar static pressures is not well MgO, a low-Z oxide, to pressures in excess of 200 GPa.