Book contents
- Frontmatter
- Contents
- Preface
- Note to the Reader
- 1 Stress and Strain
- 2 Elasticity
- 3 Tensile Testing
- 4 Other Tests of Plastic Behavior
- 5 Strain-Hardening of Metals
- 6 Plasticity Theory
- 7 Strain-Rate and Temperature Dependence of Flow Stress
- 8 Slip
- 9 Dislocation Geometry and Energy
- 10 Dislocation Mechanics
- 11 Mechanical Twinning and Martensitic Shear
- 12 Hardening Mechanisms in Metals
- 13 Ductility and Fracture
- 14 Fracture Mechanics
- 15 Viscoelasticity
- 16 Creep and Stress Rupture
- 17 Fatigue
- 18 Residual Stresses
- 19 Ceramics and Glasses
- 20 Polymers
- 21 Composites
- 22 Mechanical Working
- Appendix A Miller Indices
- Appendix B Stereographic Representation of Orientations
- Index
10 - Dislocation Mechanics
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- Preface
- Note to the Reader
- 1 Stress and Strain
- 2 Elasticity
- 3 Tensile Testing
- 4 Other Tests of Plastic Behavior
- 5 Strain-Hardening of Metals
- 6 Plasticity Theory
- 7 Strain-Rate and Temperature Dependence of Flow Stress
- 8 Slip
- 9 Dislocation Geometry and Energy
- 10 Dislocation Mechanics
- 11 Mechanical Twinning and Martensitic Shear
- 12 Hardening Mechanisms in Metals
- 13 Ductility and Fracture
- 14 Fracture Mechanics
- 15 Viscoelasticity
- 16 Creep and Stress Rupture
- 17 Fatigue
- 18 Residual Stresses
- 19 Ceramics and Glasses
- 20 Polymers
- 21 Composites
- 22 Mechanical Working
- Appendix A Miller Indices
- Appendix B Stereographic Representation of Orientations
- Index
Summary
Introduction
Once the concept of dislocations was accepted, there were three important questions to be answered.
When a single crystal is deformed, slip occurs with shear offsets of thousands of atom distances on relatively widely spaced planes, rather than uniformly throughout the crystal. See Figure 10.1. Why doesn't slip occur uniformly at an atomic scale?
Cold working increases the dislocation content of crystals even though dislocations must run out of the crystals. See Figures 10.2 and 10.3. Where do the additional dislocations come from?
The yield stress increases as the number of dislocations increases even though without any dislocations, the strength would be even higher. See Figure 10.4. Why does the yield stress increase with dislocation density?
Frank–Read sources
The first two of these questions can be answered in terms of the Frank–Read source, which generates dislocations. Suppose that there is a dislocation of finite length, AB, in a slip plane (Figure 10.5). The dislocation leaves the plane at A and B, but the end points are pinned at A and B. A shear stress, τ, acting on the plane will create a force that causes the dislocation to bow. This bowing is resisted by the line tension of the dislocation. As the shear stress is increased the dislocation will bow out until it spirals back on itself. The sections that touch annihilate each other, leaving a dislocation loop that can expand under the stress and a restored dislocation segment between the pinning points.
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- Chapter
- Information
- Mechanical Behavior of Materials , pp. 158 - 169Publisher: Cambridge University PressPrint publication year: 2005