Dislocations

9 Key excerpts on "Dislocations"

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  Essentials of Materials Science and Engineering, SI Edition

  • Donald Askeland, Wendelin Wright(Authors)
  • 2018(Publication Date)
  • Cengage Learning EMEA

    (Publisher)

  The presence of domains influences the dielectric and magnetic properties of many electronic and magnetic chapters. 4-8 Importance of Defects Extended and point defects play a major role in influencing mechanical, electrical, opti-cal, and magnetic properties of engineered materials. In this section, we recapitulate the importance of defects on properties of materials. We emphasize that the effect of disloca-tions is most important in metallic materials. Effect on Mechanical Properties via Control of the Slip Process Any imperfection in the crystal raises the internal energy at the location of the imperfection. The local energy is increased because, near the imperfection, the atoms either are squeezed too closely together (compression) or are forced too far apart (tension). A dislocation in an otherwise perfect metallic crystal can move easily through the crystal if the resolved shear stress equals the critical resolved shear stress. If the dis-location encounters a region where the atoms are displaced from their usual positions, however, a higher stress is required to force the dislocation past the region of high local energy; thus, the material is stronger. Defects in materials, such as Dislocations, point defects, and grain boundaries, serve as “stop signs” for Dislocations . They provide resist-ance to dislocation motion, and any mechanism that impedes dislocation motion makes a metal stronger. Thus, we can control the strength of a metallic material by controlling the number and type of imperfections. Three common strengthening mechanisms are based on the three categories of defects in crystals. Since dislocation motion is relatively easier in metals and alloys, these mechanisms typically work best for metallic materials. We need to keep in mind that very often the strength of ceramics in tension and at low temperatures is dictated by the level of porosity (presence of small holes).

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  Rheology V1

  Theory and Applications

  • Frederick Eirich(Author)
  • 2012(Publication Date)
  • Academic Press

    (Publisher)

  Interactions between Dislocations 184 141 142 J. M. BURGERS AND W. G. BURGERS 1. Stress Fields Connected with Dislocations 184 a. Application of the Theory of Elasticity 184 b. Atomic Picture 185 c. Strain Energy Connected with Dislocations 186 d. Forces on Dislocations 187 2. Interference between Dislocations 189 a. Forces between Dislocations 189 b. Crossing of Dislocation Lines 191 3. Networks of Dislocation Lines in Crystals 191 a. Dislocation Lines in the Virginal State of a Lattice . . 191 b. Influence of an Increase of Temperature 195 c. Displacement of Sets of Dislocation Lines under the Influence of Ex-ternal Stresses 197 d. Grain-Boundary Energy 197 Nomenclature 199 I. General Considerations 1. INTRODUCTION The term Dislocations is used to denote certain types of structural defects in crystal lattices. These structural defects are connected with features of growth and it is probable that a crystal lattice cannot grow continuously from a vapor or from a solution with low degree of supersaturation in reasonable times unless some particular types of defects are present from the beginning. From the rheological point of view Dislocations are important because they play a fundamental part in the plastic behavior of a crystal. It is the presence of suitable movable Dislocations which makes possible the oc-currence of plastic deformation, with stresses much below the shear modu-lus. A study of the Dislocations provides a microscopic picture of what is happening and gives a basis for estimating the magnitude of the forces involved. To this should be added that the plastic deformation process itself often increases the number of Dislocations. Furthermore, it has been found that foreign atoms may collect in the lines which characterize the course of Dislocations; this influences their behavior while at the same time it has furnished a method for rendering Dislocations visible.

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  Mechanical Properties Of Metals

  Atomistic and Fractal Continuum Approaches

  • C W Lung, Norman H March(Authors)
  • 1999(Publication Date)
  • World Scientific

    (Publisher)

  Chapter 3 Introduction to Extended Defects and Mechanical Strength Dislocation theory relates the plastic properties of crystals to atomic struc-ture. Dislocations are more complicated than most other lattice defects. It is not easy to work with real laws of interatomic force, derived from quantum mechanics (see Chaps. 6-8). The strain field of a dislocation has a long range part, and this part can be discussed rigorously from simple elasticity theory. The amount of work on applications of the theory to the understanding of the structure-sensitive properties of crystals greatly exceeds that on the pure theory itself. The topic is vast, and it will not be possible to give a compre-hensive description in one chapter. We will limit ourselves to an overview for those who already have some textbook knowledge of dislocation theory (see, for example, Rosenberg, 1992). We will concentrate our attention on disloca-tion mobility and fracture. Much of what follows is based on the writings by Lothe (1992) and Cottrell (1964): see also Hull and Bacon (1984). 3.1. Some Basic Theory of Crystal Dislocations 3.1.1. Dislocations and Slip — Slip line. One part of the crystal slides as a unit across a neighbouring part along the slip direction lying in the surface of slip. The line of intersection of this surface with the outer surface of the crystal is called a slip line. — Schmid's law. Slip begins on a given plane and direction when shear stress resolved on that plane and direction reaches a critical value. — Dislocation. The boundary line between a slipped and an unslipped area is called a dislocation line. A dislocation line can never end within a crystal; it must form a closed ring or end at a free surface or be joined to other dislocation lines (Fig. 3.1). 43 44 Mechanical Properties of Metals Fig. 3.1. A loop C enclosing a surface A.

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  Preferred Orientation in Deformed Metal and Rocks

  An introduction to Modern Texture Analysis

  • Hans Rudolf Wenk(Author)
  • 2013(Publication Date)
  • Academic Press

    (Publisher)

  8 Dislocations and Microstructures D. J. Barber Physics Department University of Essex Wivenhoe Park, Colchester, Essex, England 1. Introduction Early work on Dislocations, well represented in conferences of the 1950s (e.g., Shockley et al. } 1952; Fisher et al, 1957), was concerned with experimental verifica-tion of the ideas (Orowan, 1934; Polanyi, 1934; Taylor, 1934) that Dislocations— line defects in crystals, should not only occur, but must play a central role in the plastic deformation of solids. Much of the work was on single crystals of non-metals. The advent of the transmission electron microscopy (TEM) method of studying crystal defects, the ease with which most metals could be electrothinned for TEM (see Section 6.3), and the importance of metals and their processing to manu-facturing industry subsequently changed the balance of our knowledge about mate-rials. More recently, the interest of earth scientists in the micromechanisms of deformation and recovery of rocks has led to increased research on Dislocations in minerals and nonmetals (e.g., see Christie and Ardell, 1976). TEM has extended the meaning of * microstructure from the limit of optical resolu-tion (— 1 μτή) to features in crystalline solids at the 10-nm level, which is approxi-mately the distance between Dislocations in heavily deformed metals (being of the same order as the radius of the strain field around a dislocation and hence a measure of the interaction distance). High-resolution TEM (resolution limit —0.15 nm) could be said to have produced an overlap between the terms microstructure and crystal structure. In general, however, we take microstructure to extend from the description of small numbers of individual defects in a crystal or grain, at one limit, to polycrystalline and often multiphase aggregates of grains, often with associated po-rosity, cracks, etc., at the other.

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  Topics in the Theory of Solid Materials

  • J.M. Vail(Author)
  • 2018(Publication Date)
  • CRC Press

    (Publisher)

  Chapter 5 Dislocations 5.1 Introduction We now enter the realm of plastic deformation of a solid material. Plastic deformation is not elastic: when the stresses that cause the deformation are removed, the deformation does not disappear. For crystalline materials, plastic deformation is associated with the motion of a particular kind of crystal lattice defect called a dislocation. Although this type of defect can be described up to a point by the continuum theory of solids, and will be so described in this chapter, more detailed understanding requires atomistic considerations. A dislocation is essentially a linear or filamentary defect in a crystal. The variety of crystal structures that can exist, coupled with the topological variety associated with filamentary systems, leads to a huge variety of config-urations, motions, and physical effects. Beyond that, when one considers dynamical aggregates of Dislocations as they occur in materials, and the interactions of Dislocations with other crystal lattice defects such as point defects, interfaces and surfaces, the variety of concepts and phenomena burgeons much further. In this chapter we limit the discussion to introducing the basic terms and concepts by which Dislocations are described ( section 5.2 ), and to the application of continuum elasticity theory ( Chapter 1 ) to determine the equilibrium deformation field at some distance from a disloca-tion ( section 5.3 ). In section 5.4 we analyse an aspect of dislocation motion, and in section 5.5 we give some view of the range of topics not to be discussed here, as well as some comments on the textbook/monograph literature. 5.2 Description of Dislocations The textbook by the Weertmans (1964) gives an extraordinarily lucid intro-duction to the nature of Dislocations, and we follow their approach closely. We can think of creating a dislocation in a crystal through a process of plastic deformation that is illustrated in an extremely schematic 57

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  Materials Science and Engineering

  An Introduction

  • William D. Callister, Jr., David G. Rethwisch(Authors)
  • 2018(Publication Date)
  • Wiley

    (Publisher)

  Finally, the latter sections of this chapter are concerned with recovery and recrystallization—processes that occur in plastically deformed metals, normally at elevated temperatures—and, in addition, grain growth. 7.1 INTRODUCTION Early materials studies led to the computation of the theoretical strengths of perfect crystals, which were many times greater than those actually measured. During the 1930s it was theorized that this discrepancy in mechanical strengths could be explained by a type of linear crystalline defect that has come to be known as a dislocation. Not until the 1950s, however, was the existence of such dislocation defects established by direct ob- servation with the electron microscope. Since then, a theory of Dislocations has evolved that explains many of the physical and mechanical phenomena in metals [as well as crystalline ceramics (Section 12.10)]. Dislocations and Plastic Deformation With knowledge of the nature of Dislocations and the role they play in the plastic deformation process, we are able to understand the underlying mechanisms of the techniques that are used to strengthen and harden metals and their alloys. Thus, it becomes pos- sible to design and tailor the mechanical properties of materials—for example, the strength or toughness of a metal–matrix composite. • 181 182 • Chapter 7 / Dislocations and Strengthening Mechanisms Edge and screw are the two fundamental dislocation types. In an edge dislocation, local- ized lattice distortion exists along the end of an extra half-plane of atoms, which also defines the dislocation line (Figure 4.4). A screw dislocation may be thought of as result- ing from shear distortion; its dislocation line passes through the center of a spiral, atomic plane ramp (Figure 4.5). Many Dislocations in crystalline materials have both edge and screw components; these are mixed Dislocations (Figure 4.6). Plastic deformation corresponds to the motion of large numbers of Dislocations.

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  Dislocations

  International Series of Monographs on Solid State Physics

  • J. Friedel, R. Smoluchowski, Balak Das Kurmi, N. Kurti(Authors)
  • 2013(Publication Date)
  • Pergamon

    (Publisher)

  PART ONE General Properties of Dislocations This page intentionally left blank CHAPTER I DEFINITION AND EXAMPLES 1.1. PERFECT AND REAL CRYSTALS A perfect crystal is, of course, an assembly of atoms distributed periodic-ally in space. It can be built up from a unit cell, consisting usually of only a few atoms, by means of a set of translations b = «iai + w 2 a 2 + ma^; (1.1) wi, w 2 , ns can take on all integer values, positive and negative, and ai, a 2 , a3 are the three non-coplanar basis vectors of the Bravais lattice of the crystal. A real crystal differs from this perfect scheme by the defects it contains, which often strongly modify its properties: surface defects (the mere fact that it has a finite size); point defects (if it contains impurity atoms); volume defects (thermal motion, for example). The Dislocations are, similarly, linear defects, the nature of which will be specified; and if their study in crystals has only lately developed, it is, no doubt, because their more difficult geometry does not fit in our Cartesian framework. A simple case will first be analysed: the classical elastic medium, i.e. a continuous, homogeneous, and isotropic body. 1.2. CLASSICAL ELASTIC MEDIUM Consider for instance a cylinder of rubber assumed at rest (Fig. 1.1a): no internal stresses have been introduced during its fabrication, and it is not subjected to any external stresses. Cut it along a radial surface S, open the lips Si and S 2 of the cut (Fig. 1.1b) and introduce into the slit thus created a cylindrical segment of the same material, as shown by the shaded section in Fig. 1.1c. If the parts are stuck together along the surfaces Si and S 2 , the elastic material will be subjected to stresses, even when the external stresses are removed. These are called internal stresses. There is nothing special about the surfaces Si and S 2 . Clearly the stresses have cylindrical symmetry about the axis L.

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  Mechanical Properties of Engineered Materials

  • Wole Soboyejo(Author)
  • 2002(Publication Date)
  • CRC Press

    (Publisher)

  7 ________________________ Dislocations and Plastic Deformation 7.1 INTRODUCTION Let us begin this chapter by performing the following thought experiment. Imagine picking up a piece of copper tubing that can be bent easily, at least the first time you try to bend it. Now think about what really happens when you bend the piece of copper a few times. You will probably remember from past experience that it becomes progressively harder to bend the piece of copper tubing after each bend. However, you have probably never asked yourself why. Upon some reflection, you will probably come to the conclusion that the response of the copper must be associated with internal changes that occur in the metal during bending. In fact, the strength of the copper, and the progressive hardening of the copper, are associated with the movement of Dislocations, and their interactions with defects in the crystalline copper lattice. This is hard to imagine. However, it is the basis for crystalline plasticity in most metallic materials and their alloys. This chapter presents an overview of how dislocation motion and dislocation interactions contribute to plastic deformation in crystalline materials. We begin with a qualitative description of how individual dis-locations move, interact, and multiply. The contributions of individual Dislocations to bulk plastic strain are then considered within a simple con-177 178 Chapter 7 tinuum framework. This is followed by an introduction to the crystallogra-phy of slip in hexagonal and cubic materials. The role that Dislocations play in the deformation of single crystals and polycrystals is then explained. 7.2 DISLOCATION MOTION IN CRYSTALS As discussed in Chap. 6, Dislocations tend to glide on close-packed planes along close-packed directions. This is due to the relatively low lattice friction stresses in these directions, Eq. (6.8a) or (6.8b). Furthermore, the motion of Dislocations along a glide plane is commonly referred to as conservative motion.

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  Imperfections in Crystalline Solids

  • Wei Cai, William D. Nix(Authors)
  • 2016(Publication Date)
  • Cambridge University Press

    (Publisher)

  However, Chapters 8 (dislocation geometry), 11 (partial Dislocations) and 12 (dislocation core structure) have no corresponding chapters in Part II. This is because the geometry and atomistic core structure of Dislocations are much more complex than those of the point defects; the latter are mostly covered in Sections 4.1 and 4.2. At the same time, there is no chapter on “dislocation thermodynamics” that corresponds to Chapter 5 on point defect thermodynamics. This is because the energy of a dislocation line is so large that they should not exist if the crystal were in a truly thermodynamic equilibrium state. In comparison, a finite concentration of point defects should always exist at thermal equilib-rium. Therefore, when discussing Dislocations, we are necessarily dealing with non-equilibrium (perhaps meta-stable) states. For example, Dislocations are usually generated in great quantities during plastic deformation, which is a highly dissipative, non-equilibrium process. 8 Dislocation geometry The main purpose of this chapter is to introduce the geometrical properties of Dislocations, the rules governing dislocation reactions, and the directions of dislocation motion in response to applied stress. The goal is to develop an intuitive understanding of the basic behaviors of Dislocations without obtaining their stress field (which is the subject of the next chapter). We start with Section 8.1 on why Dislocations are necessary for plastic deformation of crystals. In Section 8.2 , we introduce Volterra Dislocations in an elastic continuum, and then describe the differences between them and Dislocations in a crystal. In Section 8.3 , we define the Burgers vector of a dislocation, and describe the geometric rule for Burgers vectors that must be satisfied when Dislocations react. Section 8.4 shows which direction a dislocation should move on its glide plane under an applied stress. It also introduces cross-slip and climb, as alternative modes of dislocation motion.

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