Introduction to Dislocation Mechanics
|
|
- Rafe Henderson
- 6 years ago
- Views:
Transcription
1 Introduction to Dislocation Mechanics
2 What is Dislocation Mechanics? (as meant here) The study of the stress state and deformation of continua whose elastic response is mediated by the nucleation, presence, motion, and interaction of distributions of crystal defects called dislocations
3 For the moment, Dislocation? An imaginary curve in an elastic continuum that induces a stress field in the elastic body is capable of moving and altering its shape kinetics driven by stress Multiple dislocations interact through their stress fields The stress field of one dislocation modifies the stress acting on another thus affecting the latter s placement Cell walls in OFHC Cu, fatigue loading Zhang, Jiang, 07 Dislocation loops in Si
4 What is a Dislocation? Edge dislocation (after G. I. Taylor, 1934) Burgers vector Also Polanyi 34; Orowan, 34 Line direction books.lardbucket.org coefs.uncc.edu/hzhang3/w-o-m/
5 What is a Dislocation? Screw dislocation (after J. M. Burgers, 1939) Burgers vector coefs.uncc.edu/hzhang3/w-o-m/ Line direction
6 What is a Dislocation? Edge-Screw dislocation (after J. M. Burgers) Burgers vector for entire dislocation Dislocation line coefs.uncc.edu/hzhang3/w-o-m/
7 7 Why should Dislocation Mechanics be studied? Dislocations in crystalline materials are an inevitable consequence of the storage of elastic energy Once formed, they critically affect mechanical electrical electronic optical performance of devices and structures built from crystalline materials
8 8 Electronic Materials Mechanical stress is a central factor in Fabrication Performance Reliability Source of generation and motion of undesirable threading dislocations Easy diffusion paths for dopants short circuits across layers Electron-hole recombination centers Sites for defect nucleation, growth and multiplication Strain engineering Altering electronic band-gaps of devices by suitably positioning defects
9 9 Semiconductor Technology: Thin film-substrate Heterostructure Slip plane Interface misfit segment Semiconductor (GaInAs, SiGe, GaN) thin film ~ 10 nm thick film ~ 600 nm Threading segment Interface misfit dislocation Bulk substrate (Si, SiC)
10 10 Semiconductor Technology: Thin Film-Compliant Substrate System X-grid of screw dislocations InSb, InGaP film ~ nm Twist-bonded Compliant substrate GaAs ~3-10 nm Bulk substrate
11 11 IC, MEMS Technology Interconnects: Thermal and residual stress Voids and cracks in metallization layers leading to failure - stress migration Dislocation motion induces stress relaxation Important to understand magnitude of relaxation for quantitative failure estimates (reliability) Fatigue failure of MEMS components Experimental results indicate evolving dissipative mechanisms Residual dislocation stress + relaxation by dislocation motion need to be modeled to understand plasticity at micron length-scales.
12 12 Interconnects grain Passivation layer SiO 2 Al metallization ~500nm X 1000 nm Si substrate
13 13 MEMS frequency cycles Macroscopic plasticity does not work for structural dimensions of ~10 m m Gradient plasticity inadequate for detailed analysis of local stress concentrations that drive failure processes Dislocation mechanics required to understand stress concentration and relaxation in MEMS structures
14 14 Structural Components Inhomogeneous deformation - precursor to failure Strength Formability - Ductility Residual Stress Fatigue
15 Target Predictions of Dislocation Mechanics Capability: Fine Features Dislocation nucleation due to elastic instability s 15 c cohesive reaction b/4 0 b slip Instability leading to nucleation max b Simple cubic lattice shear traction c cohesive reaction
16 16 Nucleation vs. Motion a) AA, Beaudoin, Miller, 08 b) c) Figure 1. Schematic illustration of dislocation motion and nucleation; a) motion of an existing edge dislocation resulting in an advance of the slipped region; b) nucleation of an edge dislocation; c) nucleation of an edge dislocation dipole. Red lines indicate slipped regions of the crystal; green lines represent unslipped (but possibly deformed) regions; and black lines represent dislocations as the boundary between slipped and unslipped regions.
17 17 Nucleation vs. Motion AA, Beaudoin, Miller, 08 Figure 6: Nucleation and motion of a dislocation dipole during nano-indentation, with contours showing relative magnitudes of atomic motion (Å). (a) the undefected cystal. (b) nucleation (c) growth to a full Burgers vector and (d)-(f) motion.
18 Target Predictions of Dislocation Mechanics Capability: Fine Features Dislocation multiplication - Frank-Read source 18 Screw dislocation
19 19 Target Predictions of Dislocation Mechanics Capability: Fine Features Hardening due to interactions Short range stress field Forest hardening Dissociation energetically favorable Partial dislocation Stacking fault in crystal Long range stress field Lomer-Cottrell lock
20 Orientation dependence of work hardening 20 Clarebrough and Hargreaves, AJP, 1960
21 Stress Target Predictions of Dislocation Mechanics Capability: Coarse Features Arising from lattice stretching Due to presence of dislocations (residual or internal stress) Due to applied loads Hardening Retardation of dislocation motion due to modification of local stress field acting on dislocation due to stress field of others Deformation Elastic stretching Slip due to dislocation motion (permanent deformation) deformation microstructure Time dependence of mechanical response 21
22 22 Patchy Slip brass Piercy, Cahn & Cottrell, 1955
23 23 Slip bands, localization Chang & Asaro, 1980 Al Cu
24
25
26
27
28
29
30
31 W O S { O } q : = q -q Related kinematical question + - W \ = : W * C + - Characterize the possible jumps in q field on S such that grad q on W \ where A is a given C vector field * = A on W satisfying curl A = 0. * q =-ò A d x C for any closed curve C surrounding O, and this is constant on S. S 1
32 a d e b c
33
34
35
36
37
38
39
40 Discontinuity of a Discontinuity Terminating curve of Displacement discontinuity = DISLOCATION Polar angle of director discontinuity = DISCLINATION
41 The classical question (Volterra - dislocations, Frank nematic disclinations) W O S { O } + - W \ = : W * 2 üï Minimize ò grad q dv W or ï ý solve div grad q = 0 on W \ S ï ïþ + - subject to q - q = : q = 2 pk on grad q n = 0 on S and say grad q n = 0 on W S 1 # grad q has to blow up like as r 1 # energy density like 2 r total energy in W is unbounded x O
42 Classical field of a screw dislocation/nematic wedge disclination x 2 x 3 x 1 u e e æx ö 2 = q = arctan ç çèx ø 1 b sinq = q, = - 2 4p r 1 b cos q = q, = 2 4p r 1 Discontinuous Displacement (even apart from origin) Except origin, smooth strain field!!!! Moral So, dislocation strain fields are not really the ones from taking a deriv. of the displacement field BUT derivative fields obtained on the Simply-connected domain Induced by the cut
43 A slightly different, partial, alternate formulation As an alternate problem for grad q, ask to find A s.t. How to do this? curl A =-do2pk e ü z ï ïýï div A = 0 ïþ A n = 0 on W on W Punctured domain etc. not physical and Impossible for practical computation However, this does not say anything about determining q with the required properties. Need formulation that produces finite energy AND an associated q field without requiring cuts, holes etc.
44 Dislocation-Eigendeformation Formulation # Infinite TOTAL energy classical solution t core n q + q - l is troublesome. Can the problem be forced so as to give finite energy, keeping most global features intact? # Regularize jump across S (but not only q) S l + - ( )( q q ) # l = g t - l n in Sl; 0 otherwise. t = x t and g constant in layer outside core and decays to zero inside core So, l( n ) is only non-zero component \ l( t) = 0 and l( n), t ¹ l( t), n # b : = curl l ¹ 0 and localized in core, and ò curl l ezda = q = 2pK A for any area patch A containing core
45 Dislocation-Eigendeformation formulation # Replace grad q in classical defect theory by E d : = grad q -l # Replace div grad q = 0 on W \ S by a) div E = 0 on W # Replace grad q n = 0 on W by b) E n = 0 on W # 2 pk smeared over core =- b = curle Recall, alternate problem for grad q field in classical theory curl A =-do2pk e ü z ï ïýï on W div A = 0 ïþ A n = 0 on W morally E = A (where A is a classical construct). but E has finite energy. # \ since we also have that outside S E = gradq by construction, we have managed to define a potential field q whose gradient field grad q matches A in most of the domain. l Main utility of eigendeformation formulation is it provides a new field for specification of dynamics of dislocation lines. d d d
46 Connection of eigendeformation formulation with classical picture # classical question: solve div é grad qù êc = 0 on W \ S ë úû + - subject to q - q = q = 2 pk on S Cgrad q n = 0 on S and say Cgrad q n = 0 on W without assumption A =gradq t core n S l c q + q - l # Write l = grad z + g üï ï curl g = b = curl l ï ý ïïï div g = 0 ïþ g n = 0 on W SH on W d+ d- q - q = z = q " values of l ³ 0, c ³ 0 g is a smooth field except at origin for c = 0. z + - z - = ò l æ = q + -q - l ö dx as l 0 p : é0,1ù y x 0 yl ë û ' t p 2 n ç è ø x0 > c d # div é ù = div é grad ( q - z ) ù = div é ù ëê CE ûú 0 ëê C ûú ë Cg û d 1 1 q - z = q s.t. div é grad q ù = div é ù for c ¹ 0 ëê C úû ë Cg û d 1 T : = CE (say with q = 0 on W) with q smooth for c ¹ 0 d T = 0 across any surface
47 Connection of eigendeformation formulation and classical picture c as l 0 In W \ S T = C gradq ; divt = 0 d ( d grad q l) T = C -, but in W \ S l = 0 l d d d \ In W \ Sl T = C gradq ; divt = 0 d d q = q ; T = 0 c But did not require cut surface punctures etc.
3, MSE 791 Mechanical Properties of Nanostructured Materials
3, MSE 791 Mechanical Properties of Nanostructured Materials Module 3: Fundamental Physics and Materials Design Lecture 1 1. What is strain (work) hardening? What is the mechanism for strain hardening?
More informationDislocations in Materials. Dislocations in Materials
Pose the following case scenario: Consider a block of crystalline material on which forces are applied. Top Force (111) parallel with top surface Bottom Force Sum Sum of of the the applied forces give
More informationmuch research (in physics, chemistry, material science, etc.) have been done to understand the difference in materials properties.
1.1: Introduction Material science and engineering Classify common features of structure and properties of different materials in a well-known manner (chemical or biological): * bonding in solids are classified
More informationChapter Outline Dislocations and Strengthening Mechanisms. Introduction
Chapter Outline Dislocations and Strengthening Mechanisms What is happening in material during plastic deformation? Dislocations and Plastic Deformation Motion of dislocations in response to stress Slip
More informationA Combined Discrete-dislocation/Scaledependent Crystal Plasticity Analysis of Deformation and Fracture in Nanomaterials. Presented by: Derek Columbus
MS Thesis Defense A Combined Discrete-dislocation/Scaledependent Crystal Plasticity Analysis of Deformation and Fracture in Nanomaterials Presented by: Derek Columbus Advisor: Dr. Mica Grujicic Department
More informationIMPERFECTIONSFOR BENEFIT. Sub-topics. Point defects Linear defects dislocations Plastic deformation through dislocations motion Surface
IMPERFECTIONSFOR BENEFIT Sub-topics 1 Point defects Linear defects dislocations Plastic deformation through dislocations motion Surface IDEAL STRENGTH Ideally, the strength of a material is the force necessary
More informationSECTION A. NATURAL SCIENCES TRIPOS Part IA. Friday 4 June to 4.30 MATERIALS AND MINERAL SCIENCES
NATURAL SCIENCES TRIPOS Part IA Friday 4 June 1999 1.30 to 4.30 MATERIALS AND MINERAL SCIENCES Answer five questions; two from each of sections A and B and one from section C. Begin each answer at the
More informationDislocations and Plastic Deformation
Dislocations and Plastic Deformation Edge and screw are the two fundamental dislocation types. In an edge dislocation, localized lattice distortion exists along the end of an extra half-plane of atoms,
More information(a) Would you expect the element P to be a donor or an acceptor defect in Si?
MSE 200A Survey of Materials Science Fall, 2008 Problem Set No. 2 Problem 1: At high temperature Fe has the fcc structure (called austenite or γ-iron). Would you expect to find C atoms in the octahedral
More informationECE236A Semiconductor Heterostructure Materials Defects in Semiconductor Crystals Lecture 6 Oct. 19, 2017
ECE236A Semiconductor Heterostructure Materials Defects in Semiconductor Crystals Lecture 6 Oct. 19, 2017 Stacking sequence in simple crystals. Stacking faults (intrinsic, extrinsic) Twin boundaries Dislocations
More informationDefects and Diffusion
Defects and Diffusion Goals for the Unit Recognize various imperfections in crystals Point imperfections Impurities Line, surface and bulk imperfections Define various diffusion mechanisms Identify factors
More informationImperfections in the Atomic and Ionic Arrangements
Objectives Introduce the three basic types of imperfections: point defects, line defects (or dislocations), and surface defects. Explore the nature and effects of different types of defects. Outline Point
More informationInstructor: Yuntian Zhu. Lecture 8
MSE 791: Mechanical Properties of Nanostructured Materials Module 3: Fundamental Physics and Materials Design Instructor: Yuntian Zhu Office: 308 RBII Ph: 513-0559 ytzhu@ncsu.edu Lecture 8 Deformation
More information3. Anisotropic blurring by dislocations
Dynamical Simulation of EBSD Patterns of Imperfect Crystals 1 G. Nolze 1, A. Winkelmann 2 1 Federal Institute for Materials Research and Testing (BAM), Berlin, Germany 2 Max-Planck- Institute of Microstructure
More informationMechanical Properties
Mechanical Properties Elastic deformation Plastic deformation Fracture II. Stable Plastic Deformation S s y For a typical ductile metal: I. Elastic deformation II. Stable plastic deformation III. Unstable
More informationCME 300 Properties of Materials. ANSWERS Homework 2 September 28, 2011
CME 300 Properties of Materials ANSWERS Homework 2 September 28, 2011 1) Explain why metals are ductile and ceramics are brittle. Why are FCC metals ductile, HCP metals brittle and BCC metals tough? Planes
More informationLecture contents. Heteroepitaxy Growth technologies Strain Misfit dislocations. NNSE 618 Lecture #24
1 Lecture contents Heteroepitaxy Growth technologies Strain Misfit dislocations Epitaxy Heteroepitaxy 2 Single crystalline layer on Single crystalline substrate Strong layer-substrate interaction orientation
More informationLearning Objectives. Chapter Outline. Solidification of Metals. Solidification of Metals
Learning Objectives Study the principles of solidification as they apply to pure metals. Examine the mechanisms by which solidification occurs. - Chapter Outline Importance of Solidification Nucleation
More informationImperfections: Good or Bad? Structural imperfections (defects) Compositional imperfections (impurities)
Imperfections: Good or Bad? Structural imperfections (defects) Compositional imperfections (impurities) 1 Structural Imperfections A perfect crystal has the lowest internal energy E Above absolute zero
More informationThe story so far: Isolated defects
The story so far: Infinite, periodic structures have Bloch wave single-particle states, labeled by a wavenumber k. Translational symmetry of the lattice + periodic boundary conditions give discrete allowed
More informationPlanar Defects in Materials. Planar Defects in Materials
Classification of Defects in Solids: Planar defects: Stacking faults o {311} defects in Si o Inversion domain boundaries o Antiphase boundaries (e.g., super dislocations): analogous to partials but in
More informationTwins & Dislocations in HCP Textbook & Paper Reviews. Cindy Smith
Twins & Dislocations in HCP Textbook & Paper Reviews Cindy Smith Motivation Review: Outline Crystal lattices (fcc, bcc, hcp) Fcc vs. hcp stacking sequences Cubic {hkl} naming Hcp {hkil} naming Twinning
More informationIntroduction to Engineering Materials ENGR2000 Chapter 7: Dislocations and Strengthening Mechanisms. Dr. Coates
Introduction to Engineering Materials ENGR2000 Chapter 7: Dislocations and Strengthening Mechanisms Dr. Coates An edge dislocation moves in response to an applied shear stress dislocation motion 7.1 Introduction
More informationCHAPTER 4 INTRODUCTION TO DISLOCATIONS. 4.1 A single crystal of copper yields under a shear stress of about 0.62 MPa. The shear modulus of
CHAPTER 4 INTRODUCTION TO DISLOCATIONS 4.1 A single crystal of copper yields under a shear stress of about 0.62 MPa. The shear modulus of copper is approximately. With this data, compute an approximate
More informationImperfections, Defects and Diffusion
Imperfections, Defects and Diffusion Lattice Defects Week5 Material Sciences and Engineering MatE271 1 Goals for the Unit I. Recognize various imperfections in crystals (Chapter 4) - Point imperfections
More informationChapter 7 Dislocations and Strengthening Mechanisms. Dr. Feras Fraige
Chapter 7 Dislocations and Strengthening Mechanisms Dr. Feras Fraige Chapter Outline Dislocations and Strengthening Mechanisms What is happening in material during plastic deformation? Dislocations and
More informationLecture # 11. Line defects (1D) / Dislocations
Lecture # 11 - Line defects (1-D) / Dislocations - Planer defects (2D) - Volume Defects - Burgers vector - Slip - Slip Systems in FCC crystals - Slip systems in HCP - Slip systems in BCC References: 1-
More informationImperfections in atomic arrangements
MME131: Lecture 9 Imperfections in atomic arrangements Part 2: 1D 3D Defects A. K. M. B. Rashid Professor, Department of MME BUET, Dhaka Today s Topics Classifications and characteristics of 1D 3D defects
More informationCREEP CREEP. Mechanical Metallurgy George E Dieter McGraw-Hill Book Company, London (1988)
CREEP CREEP Mechanical Metallurgy George E Dieter McGraw-Hill Book Company, London (1988) Review If failure is considered as change in desired performance*- which could involve changes in properties and/or
More informationChapter 4. Introduction to Dislocations
Chapter 4 Introduction to Dislocations The discrepancy between the theoretical and observed yield stresses of crystals Dislocations The Burgers vector Vector notation for dislocations Dislocations in the
More informationLecture # 11 References:
Lecture # 11 - Line defects (1-D) / Dislocations - Planer defects (2D) - Volume Defects - Burgers vector - Slip - Slip Systems in FCC crystals - Slip systems in HCP - Slip systems in BCC Dr.Haydar Al-Ethari
More information1. Introduction. What is implantation? Advantages
Ion implantation Contents 1. Introduction 2. Ion range 3. implantation profiles 4. ion channeling 5. ion implantation-induced damage 6. annealing behavior of the damage 7. process consideration 8. comparison
More informationMultiscale models of metal plasticity Part II: Crystal plasticity to subgrain microstructures
Multiscale models of metal plasticity Part II: Crystal plasticity to subgrain microstructures M. Ortiz California Institute of Technology MULTIMAT closing meeting Bonn, Germany, September 12, 2008 Dislocation
More informationLectures on: Introduction to and fundamentals of discrete dislocations and dislocation dynamics. Theoretical concepts and computational methods
Lectures on: Introduction to and fundamentals of discrete dislocations and dislocation dynamics. Theoretical concepts and computational methods Hussein M. Zbib School of Mechanical and Materials Engineering
More informationDept.of BME Materials Science Dr.Jenan S.Kashan 1st semester 2nd level. Imperfections in Solids
Why are defects important? Imperfections in Solids Defects have a profound impact on the various properties of materials: Production of advanced semiconductor devices require not only a rather perfect
More informationMovement of edge and screw dislocations
Movement of edge and screw dislocations Formation of a step on the surface of a crystal by motion of (a) n edge dislocation: the dislocation line moves in the direction of the applied shear stress τ. (b)
More informationAtomistic Modeling of Thermally Activated Processes for Crystal Dislocations
IPAM Workshop ELWS 2 UCLA, Oct 16-20, 2017 Atomistic Modeling of Thermally Activated Processes for Crystal Dislocations Oct 16, 2017 Wei Cai, Xiaohan Zhang, William Kuykendall* Department of Mechanical
More informationPlastic Deformation in Crystalline Materials. Lecture 1: Overview. Kamyar Davoudi Fall 2015
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
More informationStrengthening Mechanisms
ME 254: Materials Engineering Chapter 7: Dislocations and Strengthening Mechanisms 1 st Semester 1435-1436 (Fall 2014) Dr. Hamad F. Alharbi, harbihf@ksu.edu.sa November 18, 2014 Outline DISLOCATIONS AND
More informationDefect in crystals. Primer in Materials Science Spring
Defect in crystals Primer in Materials Science Spring 2017 11.05.2017 1 Introduction The arrangement of the atoms in all materials contains imperfections which have profound effect on the behavior of the
More informationCristian Teodosiu. Elastic Models. of Crystal Defects. With 58 Figures. Editura Academiei Bucure~ti
Cristian Teodosiu Elastic Models of Crystal Defects With 58 Figures Editura Academiei Bucure~ti Springer-Verlag Berlin Heidelberg GmbH 1982 Cristian Teodosiu Department of Solid Mechanics Institute for
More informationE45 Midterm 01 Fall 2007! By the 0.2% offset method (shown on plot), YS = 500 MPa
1.!Mechanical Properties (20 points) Refer to the following stress-strain plot derived from a standard uniaxial tensile test of a high performance titanium alloy to answer the following questions. Show
More informationIndex. Cambridge University Press Introduction to Elasticity Theory for Crystal Defects R. W. Balluffi. Index.
Airy stress functions formulation of 60 1 table of 426 alternator operator 419 Brown s formula 255 Burgers equation 264 5 Christoffel stiffness tensor 34 corresponding elastic fields 25 7 curvature tensor,
More informationIntroduction to Materials Science
EPMA Powder Metallurgy Summer School 27 June 1 July 2016 Valencia, Spain Introduction to Materials Science Prof. Alberto Molinari University of Trento, Italy Some of the figures used in this presentation
More informationChapter 8. Deformation and Strengthening Mechanisms
Chapter 8 Deformation and Strengthening Mechanisms Chapter 8 Deformation Deformation and Strengthening Issues to Address... Why are dislocations observed primarily in metals and alloys? How are strength
More information4-Crystal Defects & Strengthening
4-Crystal Defects & Strengthening A perfect crystal, with every atom of the same type in the correct position, does not exist. The crystalline defects are not always bad! Adding alloying elements to a
More informationEPITAXY extended single-crystal film formation on top of a crystalline substrate. Homoepitaxy (Si on Si) Heteroepitaxy (AlAs on GaAs)
extended single-crystal film formation on top of a crystalline substrate Homoepitaxy (Si on Si) Heteroepitaxy (AlAs on GaAs) optoelectronic devices (GaInN) high-frequency wireless communication devices
More informationRecent development of modelling techniques in nano- and meso-scale simulations of dislocation dynamics
Recent development of modelling techniques in nano- and meso-scale simulations of dislocation dynamics Department for Microstructure Physics and Alloy Design, Düsseldorf, Germany S.M. Hafez Haghighat,
More informationStrengthening Mechanisms
Strengthening Mechanisms The ability of a metal/ alloy to plastically deform depends on the ability of dislocations to move. Strengthening techniques rely on restricting dislocation motion to render a
More informationSTRENGTHENING MECHANISM IN METALS
Background Knowledge Yield Strength STRENGTHENING MECHANISM IN METALS Metals yield when dislocations start to move (slip). Yield means permanently change shape. Slip Systems Slip plane: the plane on which
More informationMetallurgy 101 (by popular request)
Metallurgy 101 (by popular request) Metals are crystalline materials Although electrons are not shared between neighboring atoms in the lattice, the atoms of a metal are effectively covalently bonded.
More informationSolid. Imperfection in solids. Examples of Imperfections #2. Examples of Imperfections #1. Solid
Solid Imperfection in solids By E-mail: Patama.V@chula.ac.th Solid State of materials Rigid Strong bonding ionic, van der aals, metal bonding normally has crystal structure Examples of Imperfections #
More informationModule #8. Defects in Crystalline Materials. READING LIST DIETER: Ch. 4, Pages
HOMEWORK From Dieter 4-6 Module #8 Defects in Crystalline Materials READING LIST DIETER: Ch. 4, Pages 103-114 Ch. 4, Pages 103-117 in Meyers & Chawla, 1 st ed. Ch. 1, Pages 1-26 in Argon Property Structure,
More informationHigh-resolution electron microscopy of grain boundary structures in yttria-stabilized cubic zirconia
Mat. Res. Soc. Symp. Proc. Vol. 654 2001 Materials Research Society High-resolution electron microscopy of grain boundary structures in yttria-stabilized cubic zirconia K. L. Merkle, L. J. Thompson, G.-R.
More informationMT 348 Outline No MECHANICAL PROPERTIES
MT 348 Outline No. 1 2009 MECHANICAL PROPERTIES I. Introduction A. Stresses and Strains, Normal and Shear Loading B. Elastic Behavior II. Stresses and Metal Failure A. ʺPrincipal Stressʺ Concept B. Plastic
More informationChapter 8 Strain Hardening and Annealing
Chapter 8 Strain Hardening and Annealing This is a further application of our knowledge of plastic deformation and is an introduction to heat treatment. Part of this lecture is covered by Chapter 4 of
More informationModule #0. Introduction. READING LIST DIETER: Ch. 1, pp. 1-6
Module #0 Introduction READING LIST DIETER: Ch. 1, pp. 1-6 Introduction Components used in engineering structures usually need to bear mechanical loads. Engineers are mainly interested in design rules
More informationSingle vs Polycrystals
WEEK FIVE This week, we will Learn theoretical strength of single crystals Learn metallic crystal structures Learn critical resolved shear stress Slip by dislocation movement Single vs Polycrystals Polycrystals
More informationTOPIC 2. STRUCTURE OF MATERIALS III
Universidad Carlos III de Madrid www.uc3m.es MATERIALS SCIENCE AND ENGINEERING TOPIC 2. STRUCTURE OF MATERIALS III Topic 2.3: Crystalline defects. Solid solutions. 1 PERFECT AND IMPERFECT CRYSTALS Perfect
More informationThe role of geometrically necessary dislocations in giving material strengthening
Scripta Materialia 48 (2003) 179 183 www.actamat-journals.com The role of geometrically necessary dislocations in giving material strengthening N.A. Fleck a, *, M.F. Ashby a, J.W. Hutchinson b a Department
More informationDislocations Linear Defects
Dislocations Linear Defects Dislocations are abrupt changes in the regular ordering of atoms, along a line (dislocation line) in the solid. They occur in high density and are very important in mechanical
More informationDISLOCATIONS. Edge dislocation Screw dislocation Dislocations in crystals
Edge dislocation Screw dislocation Dislocations in crystals Further reading DISLOCATIONS Part of Introduction to Dislocations D. Hull and D.J. Bacon Pergamon Press, Oxford (1984) Advanced reading (comprehensive)
More informationCHAPTER 5: DIFFUSION IN SOLIDS
CHAPTER 5: DIFFUSION IN SOLIDS ISSUES TO ADDRESS... How does diffusion occur? Why is it an important part of processing? How can the rate of diffusion be predicted for some simple cases? How does diffusion
More information9.1 Refinement of dangling bond densities calculations
I 9 9.1 Refinement of dangling bond densities calculations However, a situation when the combined case takes place may be also theoretically possible. For the instance, when condition of core at the 30
More informationFundamentals of Plastic Deformation of Metals
We have finished chapters 1 5 of Callister s book. Now we will discuss chapter 10 of Callister s book Fundamentals of Plastic Deformation of Metals Chapter 10 of Callister s book 1 Elastic Deformation
More informationPart IA Paper 2: Structures and Materials MATERIALS Examples Paper 3 Stiffness-limited Design; Plastic Deformation and Properties
Engineering Part IA Paper 2: Structures and Materials MATERIALS FIRST YEAR Examples Paper 3 Stiffness-limited Design; Plastic Deformation and Properties Straightforward questions are marked with a Tripos
More informationDepartment of Materials Science and Engineering Massachusetts Institute of Technology 3.14 Physical Metallurgy Fall 2003 Exam I
Department of Materials Science and Engineering Massachusetts Institute of Technology 3.14 Physical Metallurgy Fall 2003 Exam I 3 2.5 2 Frequency 1.5 1 0.5 0 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
More informationUNIVERSITY OF CALIFORNIA College of Engineering Department of Materials Science and Engineering
Midterm 2 Solution Problem 1 1a) Acceptable answers: Crack deflection, where the crack path is deflected by either hardened particles or weak interfaces. This occurs in composite structures like wood.
More informationThree-dimensional epitaxy: Thermodynamic stability range of coherent germanium nanocrystallites in silicon
Three-dimensional epitaxy: Thermodynamic stability range of coherent germanium nanocrystallites in silicon S. Balasubramanian, a) G. Ceder, and K. D. Kolenbrander Department of Materials Science and Engineering,
More informationEngineering 45: Properties of Materials Final Exam May 9, 2012 Name: Student ID number:
Engineering 45: Properties of Materials Final Exam May 9, 2012 Name: Student ID number: Instructions: Answer all questions and show your work. You will not receive partial credit unless you show your work.
More informationLectures on: Introduction to and fundamentals of discrete dislocations and dislocation dynamics. Theoretical concepts and computational methods
Lectures on: Introduction to and fundamentals of discrete dislocations and dislocation dynamics. Theoretical concepts and computational methods Hussein M. Zi School of Mechanical and Materials Engineering
More informationPh.D. Admission 20XX-XX Semester X
Ph.D. Admission 20XX-XX Semester X Written Examination Materials Science & Engineering Department, IIT Kanpur Date of Examination: XX XXXX 20XX Timing: XX:XX XX:XX XX Application# Please read these instructions
More informationSome thoughts on the nonlinearity of cracks in structural materials
The Modelling and Simulation Centre The University of Manchester Some thoughts on the nonlinearity of cracks in structural materials John R Yates Where, and what is, the crack tip? 2.0 mm 7.0 mm 2.0 mm
More informationA discrete dislocation plasticity analysis of grain-size strengthening
Materials Science and Engineering A 400 401 (2005) 186 190 A discrete dislocation plasticity analysis of grain-size strengthening D.S. Balint a,, V.S. Deshpande a, A. Needleman b, E. Van der Giessen c
More informationThermally Activated Mechanisms in Crystal Plasticity
PERGAMON MATERIALS SERIES Thermally Activated Mechanisms in Crystal Plasticity by D. Caillard CEMES/CNRS-BP4347, F 31055 Toulouse Cedex J. L. Martin IPMC/EPFL-CH 1015 Lausanne 2003 PERGAMON An Imprint
More informationCHAPTER 6 OUTLINE. DIFFUSION and IMPERFECTIONS IN SOLIDS
CHAPTER 6 DIFFUSION and IMPERFECTIONS IN SOLIDS OUTLINE 1. TYPES OF DIFFUSIONS 1.1. Interdiffusion 1.2. Selfdiffusion 1.3.Diffusion mechanisms 1.4.Examples 2. TYPES OF IMPERFECTIONS 2.1.Point Defects 2.2.Line
More informationMSE 6020: Defects and Microstructure in Materials Spring 2015, Tuesday and Thursday, 3:30-4:45 pm, Rice Hall 032
MSE 6020: Defects and Microstructure in Materials Spring 2015, Tuesday and Thursday, 3:30-4:45 pm, Rice Hall 032 Contact Information: Instructor: Leonid Zhigilei Office: Wilsdorf Hall 303D Office Hours:
More informationMICROMAGNETISM AND THE MICROSTRUCTURE OF FERROMAGNETIC SOLIDS
MICROMAGNETISM AND THE MICROSTRUCTURE OF FERROMAGNETIC SOLIDS HELMUT KRONMULLER MANFRED FÄHNLE Max-Planck-lnstitut fiir Metallforschung, Stuttgart, Germany CAMBRIDGE UNIVERSITY PRESS Acknowledgements page
More informationa. 50% fine pearlite, 12.5% bainite, 37.5% martensite. 590 C for 5 seconds, 350 C for 50 seconds, cool to room temperature.
Final Exam Wednesday, March 21, noon to 3:00 pm (160 points total) 1. TTT Diagrams A U.S. steel producer has four quench baths, used to quench plates of eutectoid steel to 700 C, 590 C, 350 C, and 22 C
More informationMaterials Science and Engineering: An Introduction
Materials Science and Engineering: An Introduction Callister, William D. ISBN-13: 9780470419977 Table of Contents List of Symbols. 1 Introduction. 1.1 Historical Perspective. 1.2 Materials Science and
More informationConstitutive models: Elasto-Plastic Models
Plasticity is the property of the solid body to deform under applied external force and to possess permanent or temporal residual deformation after applied load is removed. Main feature of plasticity:
More informationMaterials and their structures
Materials and their structures 2.1 Introduction: The ability of materials to undergo forming by different techniques is dependent on their structure and properties. Behavior of materials depends on their
More information3. Solidification & Crystalline Imperfections
3. Solidification & Crystalline Imperfections solidification (casting process) of metals divided into two steps (1) nucleation formation of stable nuclei in the melt (2) growth of nuclei into crystals
More informationRecrystallization Theoretical & Practical Aspects
Theoretical & Practical Aspects 27-301, Microstructure & Properties I Fall 2006 Supplemental Lecture A.D. Rollett, M. De Graef Materials Science & Engineering Carnegie Mellon University 1 Objectives The
More informationFirst stages of plasticity in nano- and micro-objects: simulations and experiments
First stages of plasticity in nano- and micro-objects: simulations and experiments Sandrine BROCHARD, Jean-Luc DEMENET, Julien GODET, Julien GUENOLE (PhD student), Dominique EYIDI, Laurent PIZZAGALLI,
More informationNATURE OF PLASTIC DEFORMAIION
NATURE OF PLASTIC DEFORMAIION Plastic deformation is the deformation which is permanent and beyond the elastic range of the material often, metals are worked by plastic deformation because of the beneficial
More informationCHEM-E5225 :Electron Microscopy Imaging II
CHEM-E5225 :Electron Microscopy Imaging II D.B. Williams, C.B. Carter, Transmission Electron Microscopy: A Textbook for Materials Science, Springer Science & Business Media, 2009. Z. Luo, A Practical Guide
More informationIntroduction to Engineering Materials ENGR2000 Chapter 4: Imperfections in Solids. Dr. Coates
Introduction to Engineering Materials ENGR000 Chapter 4: Imperfections in Solids Dr. Coates Learning Objectives 1. Describe both vacancy and self interstitial defects. Calculate the equilibrium number
More informationChapter 14 Fracture Mechanics
Chapter 14 Fracture Mechanics Stress Concentrations - discontinuities typically exist in structures (holes, cross-section changes, keyways, etc) - discontinuities locally increase stress (stress raisers)
More informationKinematical theory of contrast
Kinematical theory of contrast Image interpretation in the EM the known distribution of the direct and/or diffracted beam on the lower surface of the crystal The image on the screen of an EM = the enlarged
More informationHigh temperature applications
3. CREEP OF METALS Lecturer: Norhayati Ahmad High temperature applications -Steel power plants -Oil refineries -Chemical plants High operating temperatures Engine jet ----1400 o C Steam turbine power plants:
More informationSemiconductors. The essential materials for microelectronics technology A key property: conductivity (or resistivity) - large dynamic range
Semiconductors The essential materials for microelectronics technology A key property: conductivity (or resistivity) - large dynamic range - controllable (or engineerable) Example of controllable conductivity
More informationA rigid model illustrating the formation of misfit dislocations at the (111) diamond/c-bn
Supplementary Figure 1 Rigid model describing the formation of misfit dislocations. A rigid model illustrating the formation of misfit dislocations at the (111) diamond/ interface. The red and green lattices
More informationC h a p t e r 4 : D e f e c t s i n C r y s t a l s
C h a p t e r 4 : D e f e c t s i n C r y s t a l s...perfection's a gift of The gods, few can boast they possess it - and most Of you, my dears, don't. - Ovid, The Art of Love Chapter 4: Defects in Crystals...
More informationThe Plastic Regime. Processes in Structural Geology & Tectonics. Ben van der Pluijm. WW Norton+Authors, unless noted otherwise 3/4/ :11
The Plastic Regime Processes in Structural Geology & Tectonics Ben van der Pluijm WW Norton+Authors, unless noted otherwise 3/4/2017 17:11 We Discuss The Plastic Regime Strain rate Viscosity Crystal defects
More informationHomework 4 on Dislocations, Yield Stress, Hardness, Creep, Grain Size
Homework 4 on Dislocations, Yield Stress, Hardness, Creep, Grain Size 27-301, A. D. Rollett, Fall 2002 Chemical processing plant sometimes uses nickel or nickel-based alloys because of their corrosion
More informationTutorial 2 : Crystalline Solid, Solidification, Crystal Defect and Diffusion
Tutorial 1 : Introduction and Atomic Bonding 1. Explain the difference between ionic and metallic bonding between atoms in engineering materials. 2. Show that the atomic packing factor for Face Centred
More informationMSE 170 Midterm review
MSE 170 Midterm review Exam date: 11/2/2008 Mon, lecture time Place: Here! Close book, notes and no collaborations A sheet of letter-sized paper with double-sided notes is allowed Material on the exam
More informationPart VII. Miscellaneous topics
Part VII. Miscellaneous topics Module 1 : Recovery and recrystallisation Part VII. Miscellaneous topics In this part, we discuss the recovery, recrystallisation and grain growth processes; though these
More informationImaging with Diffraction Contrast
Imaging with Diffraction Contrast Duncan Alexander EPFL-CIME 1 Introduction When you study crystalline samples TEM image contrast is dominated by diffraction contrast. An objective aperture to select either
More information