DOCSLIB.ORG

Notes on Physical Metallurgy

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Notes on Physical Metallurgy Notes on Physical Metallurgy Ju Li, MIT, December 10, 2015 1 Structures3 2 Metallic Bonding, Ideal Strength and the Dislocations Machinery 19 3 Linear Response Theory and Long-Range Diffusion 45 4 Capillary Energy Effects 70 5 Elastic Energy Effects 95 6 Interfacial Mobility 103 7 Nucleation, Growth and Coarsening 109 8 Solidification 128 9 Point defects: Climb, Anelasticity, Strain aging 138 A Review of Bulk Thermodynamics 142 B Spinodal Decomposition and Gradient Thermodynamics Description of the 1 Interface 168 2 Chapter 1 Structures The connections between structures - properties - processing, as illustrated on the cover of Acta Materialia, is the basis of materials science and engineering. Because of the relatively simple atomic structure of metals and the wide applications of metals (Bronze Age, Iron Age, copper interconnects in microprocessors), these connections were first discovered and distilled by metallurgists, and such methods and outlook are then extended to other kinds of materials: ceramics, polymers, semiconductors, biomaterials, etc. Although details vary a lot across different materials classes, especially in synthesis, the spirit and outlook are preserved a great deal in most areas of materials science and engineering - including the reliance on thermodynamic (Josiah Gibbs) and kinetic (Lars Onsager, John Cahn) theories, the realization of the importance of intervening scales (\microstructure" controls properties), the respect for processing details (physicists don't appreciate the detailed recipe- and history- dependencies of processing as much as materials scientists). The narrowest definition of Physical Metallurgy was the control of materials properties by thermo-mechanical processing (\heat and beat"), as distinguished from Chemical Metallurgy (changing the chemical composition), and Mechanical Metallurgy (\just beat, no heat"). Such definition is quite arbitrary, however, fundamentally. By \heat", people mean raising temperature T significantly above Troom = 300K, as most applications (let's say ∼ 90% of where metals are applied in tonnage) are at Troom. But 300K for steel is quite different from 300K for Sn. And even though kBTroom = 1=40 eV is quite \small" compared to the primary bond energies in steel (vacancy formation energy in α-Fe is 1.5 eV, which is about 4 bonds' worth), it turns out thermal fluctuations still cannot be ignored for most 3 processes of interest. 1 Also, physical metallurgists rely a lot on chemical thermodynamics and phase diagram in treating diffusion and phase transformations, so the boundary between Physical and Chemical Metallurgy is not sharp. For this reason, I would like to regard Physical Metallurgy as Physical, Chemical and Mechanical Metallurgy combined, but with emphasis on thermo-mechanical processing. The students in this class are expected to have taken 3.022 Microstructural Evolution in Ma- terials and 3.032 Mechanical Behavior of Materials or their equivalents already. Some topics of our class may overlap with ealier courses. But because we are 3.14 (upper undergrads) / 3.40J / 22.71J (grad student), this course is expected to be offered at a somewhat higher level, and also will have an integrative flavor. If all goes well, at end of this course you may agree that materials science is a very subtle science: one may think one understands something, until one looks at it once again from another angle, or at a different time/lengthscale. We begin with the word \structure". By now you have heard about (a) atomic structure, (b) molecular structure, as in double-stranded helical DNA, (c) microstructure, as in the (perhaps somewhat chauvinistic) old-school metallurgical matra \microstructure controls properties", (d) nanostructure, as in \One nanometer (one billionth of a meter) is a magical point on the dimensional scale. Nanostructures are at the confluence of the smallest of human-made devices and the largest molecules of living systems..." - yes, they did use the word \magical" - from a call for proposal from the US National Science Foundation 2. You may have also heard the word electronic structure from researchers doing so- called ab initio or first-principles calculations, in solving Schrodinger equation for many electrons, to obtain atomic interactions and interatomic forces numerically. So, which of these \structures" is the most important? The modern view is that none of the above structures, electronic structure - atomic structure (molecular structure) - nanostructure - microstructure, and even macro-structures (such as a trussed roof), could be ignored. In other words, all these structures potentially could be \equally" important. According to this \multiscale materials" view, there is no need to be particularly chauvinistic about any particular lengthscale, from the A˚ to the m. There are interesting physics and theory about these physics at all these scales, and they cascade through each other (\handshake"). Like a chain, no link can be missed on this chain of logic. According to [1], p.1, microstructure is what can be observed under an optical microscope 1If in doubt, some properties of steel at 300K, such as ductility, can be really different from at 0K. 2Nanoscale Science & Engineering Center program, U.S. National Science Foundation, 2001 4 (such as grains in a polycrystal), with 100× to 1000× magnification power. However, when the grain size D shrinks to say, 80nm, optical microscope can't see the grains (one has to use electron microscopes), but the dependence of properties such as yield strength σY on D −1=2 (so called Hall-Petch relation: σ(D) = σ0 + kD ) is no less sensitive than when D is 10 µm when optical microscope can see them [2]. Thus, putting a hard lengthscale bound on a concept based on the resolution limit of some observation instrument is convenient but not very enlightening. In this course, we intentionally smear the concept of microstructure to make the concept inclusive. We would not separate nanostructure from microstructure. Dislocations, cracks, grain boundaries, surfaces, phase boundaries, etc. are all components of the microstructure. In our course, the term microstructure just denotes some structural order or descriptor, beyond the Angstrom-level atomic structure. The term \Microstructural Evolution" is one of the most frequently used word in metal- lurgy. The choice of the word \Evolution" is intriguing. What is common between Darwin's Evolution in Earth's biosphere, and \Microstructural Evolution" inside a piece of metal? A modern view, mostly coming from physicists, is that biological evolution and microstruc- tural evolution all belong to so-called emergent phenomena (also called self-organization, spontaneous order) or emergence in dissipative systems. A dissipative system is a system out of equilibrium, where free energy is being spent (∆Suniverse > 0) instead of conserved (∆Suniverse = 0). In thermodynamics, we know that an isolated system at equilibrium, such as a canister of gas with no energy or mass in or out, will reach the state of max- imum disorder (homogeneous in density, temperature, no flow), or maximum entropy, for the given constraints (the adiabatic, mechanically strong and impermeable box that con- tains the gas molecules). However, Earth is not an isolated system: there is high-quality sunlight (Tblackbody = 5800K) coming in, and lower-quality light emission going out (think Tblackbody = 2:7K for cosmic background radiation). So Earth is in effect a giant heat en- gine, enjoying the great benefits of a huge free-energy influx, even though the raw energy flux is nearly balanced (energy in = energy out). This free-energy dissipation is what supports biosphere, from the smallest plankton to whales, and Darwin's Evolution, where order emerges - the species - with some highly conserved traits, despite of rich and intricate interactions between the species. The same principle is true for a piece of metal. When one \heats and beats" a metal, or react oxygen or hydrogen or lithium with it, or irradiate it with high-energy neutrons, one is injecting free energy into the system, or \dissipating good energy". In exchange for such wasteful behavior, one gets to see beautiful patterns that emerge spontaneously inside the 5 metals, the \microstructures". Like \following the money" in All the President's Men, it is crucial to account for the flows of free energy G = E + PV − TS (1.1) in a metal, because the flow/dissipation of G generates the microstructures. Indeed, without a large flux of outside free energy, most \microstructures" cannot form. From the Boltzmann formula c0 / exp(−Ef =kBT ) (1.2) where c0 is the equilibrium concentration of some defect, and Ef is its formation energy, one cannot explain the presence of extended defects like dislocations or grain boudaries since their Ef ! 1, if based on just equilibrium thermal fluctuations. In other words, most defects except the point defects (like vacancies) are manifestations of out-of-equilibrium- ness. And oftentimes even the vacancy concentrations themselves are out-of-equilibrium (such as quenched-in vacancies in aluminum alloys, or materials under irradiation). One needs to beat the metal, quench the metal, irradiate the metal with 1MeV neutrons, do something more \dramatic" like the above, to create the extended defects. Just like plants tend to cover everywhere there is sunlight, dislocations tend to multiply (there is a word \dislocation breeding" in the field as if dislocations were animals), and cracks tend to grow, to take advantage of elastic strain energy density stored in the material. Dislocations or 2 cracks \feed" on elastic strain energy density: estrain(x) = σ(x) =2C, where C is the elastic constant, σ(x) is the stres at location x, and estrain(x) is the elastic strain energy density. Free energy to a metal is like money to a society, or food/ATP to biosphere. When one stops heating/quenching, beating on or irradiating the metals, one stops injecting more \good energy" into the system. But there is often still some free energy stored inside the system to drive further evolution, for instance in the form of residual stress (due to - surprise - microstructures!), which induces residual elastic strain energy.
Load more

Recommended publications
  • Frank Nabarro: a Journey Through Science and Society
    Obituary South African Journal of Science 103, March/April 2007 99 search Group (AORG), an amazing gathering of talented individuals who Frank Nabarro: A journey through included Maurice Wilkes, Patrick Black- ett, Andrew Huxley and Nevill Mott. The head of AORG was Brigadier Basil science and society Schonland, who was later to become the first president of the South African Coun- A.G. Every* cil for Scientific and Industrial Research (CSIR) and to play an important role in the recruitment of Nabarro to the Univer- N A CAREER SPANNING ALMOST SEVENTY YEARS, FRANK NABARRO ACHIEVED WORLD RENOWN sity of the Witwatersrand (Wits). Nabarro for his pioneering contributions to the theory of crystal lattice dislocations and their role in reminisces how in AORG he ‘helped Mott Ithe plastic deformation of solids. He wielded enormous influence on materials science on problems of diffraction affecting the through his acclaimed monograph, Theory of Crystal Dislocations, the encyclopaedic series of accuracy of anti-aircraft radar, studied the books, Dislocations in Solids, which he edited, and innumerable personal ties. In the various effectiveness of anti-aircraft shells and offices he held at the University of the Witwatersrand in Johannesburg, and through his worked out the consequences of Solly membership of numerous scientific societies and committees, he played an important role in the development of science in South Africa and the transformation of our society. Nabarro Zuckerman’s experiments on the pene- possessed to a remarkable degree the ability to bridge cultures, whether scientific, political or tration of shell fragments into telephone social, and was sought out by many for his knowledge and wise counsel.
    [Show full text]
  • Iron, Steel and Swords Script - Page 1 Johannes (Jan) Martinus Burgers
    Heroes of Dislocation Science Here are some notes about some of the (early) "Heroes" of Dislocation Science. It is a purely subjective collection and does not pretend to do justice to the history of the field or the people involved. I will not even remotely try to establish a "ranking", and that's why names appear in alphabetical order. To put things in perspective, let's start with a short history of the invention of the dislocation, followed by their actual discovery. Dislocations were invented long before they were discovered. They came into being in 1934 by hard thinking and not by observation. As ever so often, three people came up with the concept independently and pretty much at the same time. The three inventors were Egon Orowan, Michael Polanyi and Geoffrey Taylor. What they invented was the edge dislocation; the general concept of dislocations had to wait a little longer. Of course, they all knew a few things that gave them the right idea. They knew about atoms and crystals since X- ray diffraction was already in place since 1912. They also knew that plastic deformation occurred by slip on special lattice planes if some shear stress was large enough, and they knew that the stress needed for slip was Advanced far lower than what one would need if complete planes would be slipping on top of each other. They were also aware of the work of others. Guys with big names then and still today, like T. v. Kármán, Jakow Iljitsch Frenkel, or Ludwig Prandtl, had put considerable effort into theories dealing, in modern parlor, with the collective movements of atoms in crystals.
    [Show full text]
  • Solid Mechanics at Harvard University
    SOLID MECHANICS James R. Rice School of Engineering and Applied Sciences, and Department of Earth and Planetary Sciences Harvard University, Cambridge, MA 02138 USA Original version: October 1994 This revision: February 2010 Downloadable at: http://esag.harvard.edu/rice/e0_Solid_Mechanics_94_10.pdf TABLE OF CONTENTS provided on last three pages, pp. 87-89 INTRODUCTION The application of the principles of mechanics to bulk matter is conventionally divided into the mechanics of fluids and the mechanics of solids. The entire subject is often called continuum mechanics, particularly when we adopt the useful model of matter as being continuously divisible, making no reference to its discrete structure at microscopic length scales well below those of the application or phenomenon of interest. Solid mechanics is concerned with the stressing, deformation and failure of solid materials and structures. What, then, is a solid? Any material, fluid or solid, can support normal forces. These are forces directed perpendicular, or normal, to a material plane across which they act. The force per unit of area of that plane is called the normal stress. Water at the base of a pond, air in an automobile tire, the stones of a Roman arch, rocks at base of a mountain, the skin of a pressurized airplane cabin, a stretched rubber band and the bones of a runner all support force in that way (some only when the force is compressive). We call a material solid rather than fluid if it can also support a substantial shearing force over the time scale of some natural process or technological application of interest.
    [Show full text]
  • RHEOLOGY BULLETIN Publication of the Society of Rheology
    RHEOLOGY BULLETIN Publication of the Society of Rheology Volume 28, No. 3 Fall, 1959 THE BINGHAM MEDAL, 1959 THIRTIETH ANNIVERSARY The Bingham Medal of the Society of Rheology for MEETING — 1959 1959 will be awarded to Dr. Egon Orowan, George Plans are now being completed for the Thirtieth Westinghouse Professor of Mechanical Engineering in Anniversary Meeting of the Society, to be held at the Massachusetts Institute of Technology. The re- Lehigh University on Wednesday, Thursday and Fri- cipient was chosen by a special Bingham Award Com- day, November 4, 5 and 6. A block of rooms has been mittee, consisting of the following members: J. D. reserved for the Society at the Hotel Bethlehem in Dienes (Chairman), T. Alfrey, Jr., H. Leaderman, Bethlehem, Pa., and Society members are strongly A. S. Nowick, and F. D. Dexter. urged to make their room reservations immediately, Dr. Orowan was born in 1902 in Budapest, Hungary, if they have not already done so. Bus service will be where he also attended school. He studied at the Uni- available between the Hotel and the Lehigh campus. versity of Vienna for two years, and then transferred A very full program of papers has been scheduled to the Technical University of Berlin-Charlottenburg, by the Program Committee, under the chairmanship of where he obtained an Engineering Diploma and a Doc- J. T. Bergen, as will be seen from the detailed program tor's degree in Applied Physics. which follows. Two special symposia are included. We He then returned to Budapest, and was for a time in are also fortunate to have as a foreign guest Prof.
    [Show full text]
  • John Frederick Nye. 26 February 1923—8 January 2019
    JOHN FREDERICK NYE 26 February 1923 — 8 January 2019 Biogr. Mems Fell. R. Soc. JOHN FREDERICK NYE 26 February 1923 — 8 January 2019 Elected FRS 1976 By Sir Michael Berry FRS* H. H. Wills Physics Laboratory, Tyndall Avenue, Bristol BS8 1TL, UK John Nye was an internationally renowned physicist who made fundamental contributions to the understanding of crystals, ice and light. He explored defects in crystal structures, in particular continuous distributions of dislocations. He explained the mechanics of the flow of glaciers: their advance and retreat, and how this depends on the underlying topography; and how water flows beneath and within them. He was a pioneer in the study of optical singularities on three levels: stable caustics in geometrical optics; phase singularities (wavefront dislocations) in scalar waves; and lines of circular and linear polarization in electromagnetic fields. Early life and education John Frederick Nye, born on 26 February 1923 in Hove, Sussex, England, was the second child of Haydn Percival Nye and Jessie Mary Nye. John’s elder brother, Peter Hague Nye, became a distinguished soil scientist, and was elected FRS in 1987. Haydn was a chartered surveyor who earned a Military Cross in the First World War for his bravery as an engineer in the trenches. He combined the high principles of the Catholic Apostolic Church, of which he was a devout member, with kindness and generosity. He was a stickler for precision and correctness in the use of words, and John writes: ‘I am sure that my own interest in language comes from that time.’ John’s mother, ‘Mamie’, worshipped at the Church of England, and the boys divided their Sundays between ‘Daddy’s church’ and ‘Mamie’s church’.† According to John, ‘Although not at all intellectual herself, [Mamie] believed firmly in the virtues of a good education and was very ambitious for her two sons.’ * [email protected] † See the Acknowledgements section for details of the sources for personal reminiscences.
    [Show full text]
  • A Method to Obtain Macroscopic Plastic Strain Values with Electron Backscatter Diffraction Data and a Comparison with FEM Remy Ripandelli S2249855
    Master Thesis A method to obtain macroscopic plastic strain values with Electron Backscatter Diffraction data and a comparison with FEM Remy Ripandelli s2249855 Supervisors: Dr. ir. I. Basu Dr. ir. V. Ocelík Prof. Dr. J. Th. M. De Hosson 2018 Rijksuniversiteit Groningen Abstract In this study EBSD scanned misorientations of a highly deformed ferritic metal was used to calculate quantitative macroscopic plastic strain values using a statistical approach. By using EBSD measurements on tensile test samples, a correlation between the misorientation values and macroscopic plastic strain was found. Misorientation values measured on various highly deformed bent samples were translated in macroscopic plastic strain values using the correlation equation. The bent samples were simulated with a finite element model and the experimental values agreed very well with the computed data. Furthermore an attempt was made to calculate the microscopic misorientation data with a very simplified dislocation density model which treats all misorientation values as measures for glide dislocations. The resulting microscopic strain values obtained were in the order of 101. This approach was too straight forward because misorientations result from a very complex interaction of different kind of dislocations. It was therefore rejected. Finally a study of the reliability of the used equipment was done in the form of a gage repeat and reproducibility study which revealed a total relative error of misorientations that did not exceed 0.8 %. Contents 1 Introduction .........................................................................................................................................
    [Show full text]
  • LD5655.V855 1968.G62.Pdf (3.872Mb)
    ,'.·:' .. .... ' . .·THE APPLICATION OF THE DUGDALE MODEL ... ~ ~- · ·.. TO AN ORTHOTROPIC PLATE by Henry G9nzalez, Jr. Thesis submitted to the Graduate Faculty of the Virginia Polytechnic .. Institute .in partial . fulfillment for the· degree of MASTER OF SCIENCE in . Engineering Nechanics APPROVED: Dr. H. F. Brinson, Chairman ..--~"----~~~~~---...-~~---~.-~-~ ~-l·r~ . Prof.\ c. w. Smith Dr. G... Swift . :. .. December, 1968 Blacksburg, Virginia '\ _;··.. ''. ... TABLE OF CONTENTS PAGE AC~OWLEDGEf1Er.lTS ••••• ~.a ... -.......... -..- ........... ~ ...........-......... iv LIST OF ILLUSTRATIONS. ..... ' ....................................... v NOTATION. ···············•••••••'!'•······················-·••ct••·······vi L INTRODUCTION ••••••••• 1 1.1 General •.•••• ...................................... ' ...... • 1 1.2 Specific Objective .••••..•.•••..•••••••.• 2 2. LITERATURE REVI Et"7 • ••••..•..... ,, ......... -. ••.•••••. • • • • • • • •. • • •- e • • • 3 2.1 Cl.as sic Theory ••••••••.....••••• 3 2.2 Irwin and Orowan ~·fodification ••••••.•..••••••••••••.•••••• 7 2.3 Dug-_dale ,- s ~·fodel . •................... ·· •..................... 10 ·2.4 Orthotropic Effects on the Classical Theory ••.••..•••••••. 14 ANALYS·IS .••.•. ..•..•...... •· .... •·• .. '. " ........• II ••••• 5 •••••• •.••• 15 3.1 D.evelopment of the General Orthotropic Problem..• 15 3.2 Statement of Problem ...... ·- ........ e ••••••• •.• 20 3.3 Elliptical Hole Part of Which is Subjected to a Normal Pressure .•..•..••..••.•.••••••• 20 3.4. Superposition of State
    [Show full text]
  • Lawrence Bragg's Interest in the Deformation of Metals and 1950
    Bragg centennial Acta Crystallographica Section A Foundations of Lawrence Bragg’s interest in the deformation of Crystallography metals and 1950–1953 in the Cavendish – a ISSN 0108-7673 worm’s-eye view Received 24 May 2012 Accepted 2 August 2012 Anthony Kelly Churchill College, University of Cambridge, Storeys Way, Cambridge CB3 0DS, United Kingdom. Correspondence e-mail: [email protected] This paper recounts the atmosphere in the Cavendish Laboratory during Lawrence Bragg’s triumphant final years there through the eyes and the work of a young research student, and hence reflects some measure of Bragg’s personality. The opportunity is taken to deal in detail with Bragg’s contribution to our understanding of crystal plasticity, which is seldom described, being overshadowed by his many superb contributions to the determination of crystal structure. Bragg produced in 1940–1942, through his development of the bubble model of a crystal structure, the first demonstration of how crystal dislocations move. His suggestion of the use of microbeams led rather directly to the development of modern thin-film transmission electron microscopy. 1. Introduction Taylor was common at the time. I was assigned to this group, I believe, because when interviewed by Schonberg earlier in William Lawrence Bragg (WLB) came to Cambridge from the 1950 I had suggested that I was interested in sub-grains in National Physical Laboratory (NPL) in October 1938, metals and their analogues as Bitter patterns – in those days, succeeding Rutherford, the New Zealander, as he had done at prospective research students were expected to suggest a Manchester. He had been at the NPL only from November problem on which he or she would like to work (Kelly, 2005).
    [Show full text]
  • National Academy of Sciences Autumn Meeting
    National Academy of Sciences Autumn Meeting The National Academy of Sciences held its Autumn Meeting at Dartmouth College, Hanover, New Hampshire, on October 13-15, 1969. Three symposia and four sessions of contributed papers comprised the scientific sessions. Ab- stracts of contributed papers are printed in this issue. The following activities highlighted the program. Public Lecture- THE HONORABLE THOMAS J. \ICINTYRE, United States Senator: Power at the Pentagon and the Consent of the Governed: Congressional Control of Military Research and Development Award Presentation- The G. K. Warren Prize to BRIGADIER RALPH A. BAGNOLD (Ret.), F.R.S., "in recognition of his outstanding contributions to geology" SCIENTIFIC SESSIONS Monday Afternoon: SYMPOSIUM ON CHEMICAL AND BIOLOGICAL WARFARE Chairman: M\IATTHEW S. MIESELSON Harvard University, Cambridge, M\Jassachusetts GEORGE BUNN, University of Wisconsin, Madison, Wisconsin (formerly General Counsel, U. S. Arms Control and Disarmament Agency): International Legal History and Present Status HAN SWYTER, Arlington, Virginia (formerly U. S. Department of Defense): Political Considerations and Analysis of Military Requirements for Chemical and Biological Weapons IVAN L. BENNETT, JR., New York University MIedical Center, New York, New York (formerly Deputy Director, Office of Science and Technology): Significance of Chemical and Biological Warfare for the People Tuesday Morning: SYMPOSIUM ON THE EXPLORATION OF SPACE- MANNED VS. UNMANNED Chairman: MIILLETT G. 1\IORGAN Dartmouth College, Hanover, New Hampshire FRANK H. BORMAN, Colonel, USAF, M\1anned Spacecraft Center, NASA, Hous- toil, Texas: Discussion Leader, Manned Exploration 1419 Downloaded by guest on September 27, 2021 1420 N. A. S. AUTUMN MEETING 1969 PROC. N. A. S. HARRISON H. SCHMITT, Manned Spacecraft Center, NASA, Houston, Texas: Contributor, Manned Exploration WILLIAM G.
    [Show full text]
  • Plastic Deformation in Crystalline Materials Lecture 1
    Plastic Deformation in Crystalline Materials Lecture 1: Overview Kamyar Davoudi! Fall 2015! 1 Structure of Solids Single Crystalline Crystalline Poly Crystalline Solids: amorphous Quasi-crystalline* (ordered but not periodic; lacks translational symmetry) 2 Crystalline vs Amorphous Solids • Solids are often crystalline. • A solid may be found in a crystalline or amorphous form. Each may have its own applications! For example: • Crystalline silicon (Si) are used in ICs. • Amorphous silicon (Si) are sometimes used in Li-ion batteries and solar cells • Amorphous metals are often called metallic glasses • It is really hard to make some metals amorphous (e.g. Ag) 3 Let’s start with some ! ! elementary diagrams ! ! we saw in elementary mechanics of materials and ask ! ! Some questions 4 Stress-Strain Curve Stress-Strain Curve of a metal under uniaxial loading:! One of the first things we learned in mechanics of materials Low carbon steel Aluminum Alloy [Beer & Johnston et al, mechanics of materials] Questions: • Why do materials become plastic? What is the mechanism of plastic deformation? • Why stress-strain curves of different materials are different? • How can we model strain hardening (= work hardening)? 5 Stress-Strain Curve – Loading and Unloading Again what we saw in the first chapters of mechanics of materials [Beer & Johnston et al, mechanics of materials] 6 ‌Bauschinger Effect [Xiang, Vlassak, Acta Mater, 2006] Question: What causes the Bauschinger effect? 7 Effects of Orientation & Loading Rates! ] 2 Questions: • How does the orientation affect the deformation? • What is the difference between Nominal Shear Stress [kg/mm Stress Shear Nominal deformation of single crystal and Nominal Shear [%] polycrystal? Nominal stress strain curves (without correction • How does the loading rate for area changes and orientation changes) for affect the deformation?! 99.99% pure Al, at two tensile strain rates: three ! single crsytals of different orientations and one polycrystal of a grain size of 0.2 mm.
    [Show full text]
  • Methodological Developments in the Field of Structural Integrity Analyses of Large Scale Reactor Pressure Vessels in Hungary
    T. Fekete, Frattura ed Integrità Strutturale, 36 (2016) 78-98; DOI: 10.3221/IGF-ESIS.36.09 Focused on Fracture Mechanics in Central and East Europe Methodological developments in the field of structural integrity analyses of large scale reactor pressure vessels in Hungary Tamás Fekete HAS Centre for Energy Research, Department of Fuel and Reactor Materials, Structural Integrity Group [email protected] ABSTRACT. Buildings, structures and systems of large scale and high value (e.g. conventional and nuclear power plants, etc.) are designed for a certain, limited service lifetime. If the standards and guidelines of the time are taken into account during the design process, the resulting structures will operate safely in most cases. However, in the course of technical history there were examples of unusual, catastrophic failures of structures, even resulting in human casualties. Although the concept of Structural Integrity first appeared in industrial applications only two-three decades ago, its pertinence has been growing higher ever since. Four nuclear power generation units have been constructed in Hungary, more than 30 years ago. In every unit, VVER-440 V213 type light-water cooled, light-water moderated, pressurized water reactors are in operation. Since the mid-1980s, Pressurized Thermal Shock (PTS) analyses of Reactor Pressure Vessels (RPV) have been conducted in Hungary, where the concept of structural integrity was the basis of research and development. In the first part of the paper, a short historic overview is given, where the origins of the Structural Integrity concept are presented, and the beginnings of Structural Integrity in Hungary are summarized.
    [Show full text]
  • Dislocation Glide in Ringwoodite (20 Gpa)
    Rheology II Transport properties Patrick Cordier Mineral Physics Group - UMET - Université Lille 1 & CNRS CIDER Summer Program: Flow In the Deep Earth Santa Barbara CA July 2016 The unreachable Earth Mechanical properties of wadsleyite 10000 9000 8000 7000 6000 Nishihara et al., 2008 5000 Kawazoe et al., 2013 (MPa) Kawazoe et al., 2010 σ 4000 Hustoft et al., 2013 Farla et al., 2015 3000 2000 1000 0 0 500 1000 1500 2000 2500 3000 T (K) Mechanical properties of ringwoodite 10000 9000 8000 7000 6000 Hustoft et al., 2013 5000 Kavner et al., 2001 (MPa) Meade and Jeanloz, 1990 σ 4000 Miyagi et al., 2014 Nishiyama et al., 2005 3000 2000 1000 0 0 500 1000 1500 2000 2500 3000 T (K) Mechanical properties of bridgmanite 14000 12000 10000 8000 Merkel et al. 2003 (MPa) 6000 Meade et al. 1990 σ Girard et al. 2015 4000 2000 0 0 500 1000 1500 2000 2500 3000 T (K) Constitutive equations Q − ε∝ σ n. e kT Mackwell, 2008 Also need to take high- pressure into account: Q+PV Extrapolating to natural timescales Q − ε∝ σ n. e kT -7.0 -8.0 -9.0 Extrapolation to natural conditions -10.0 -11.0 -12.0 The pitch drop experiment The University of Queensland pitch drop experiment (started 1927) Here featuring, Professor John Mainstone (taken in 1990, two years after the seventh drop and 10 years before the eighth drop fell). Professor John Mainstone died on 23 August 2013, aged 78, after having watched the experiment 52 years Bitumen η = 2.3 1011 Pa.s What if….
    [Show full text]