Dislocations and Plastic Deformation

Preface

Chapter 1. The Concept of Dislocation


1.1. Structural Defects


1.2. Deformation of Single Crystals


1.3. The critical Shear Stress


1.4. Lattice Defects


1.5. Dislocations in the Lattice


1.6. Burgers Vector


1.7. Conservation of the Burgers Vector


1.8. The Origin of Dislocations and Their Distribution in the Crystal

Chapter 2. Dislocations in an Elastic Continuum


2.1. Fundamentals of the Continuum Theory


2.2. The Definition of Dislocations in an Elastic Continuum


2.3. The Energy of Dislocations


2.4. Forces Acting on Dislocations


2.5. Properties of Individual Straight Dislocations


2.5.1. The Stress-Field and Energy of an Edge Dislocation


2.5.2. Energy and Stress-Field of a Screw Dislocation


2.5.3. Forces Acting on Straight Dislocations


2.5.4. The Interaction of Straight and Parallel Dislocations


2.5.5. Dislocation Dipoles


2.5.6. The Energy of Mixed Dislocations


2.5.7. The Interaction of Straight, Non-Parallel Dislocations


2.6. Dislocation Loops


2.7. The Effect of Dislocations on the Thermal Properties of Crystals


2.7.1. The Gibbs Potential of an Isotropic Body


2.8. The Line Tension of Dislocations


2.9. Boundary Condition Problems


2.10. The Motion of Dislocations in an Elastic Continuum


2.11. General Continuum Theory of Lattice Defects


2.11.1. Introduction


2.11.2. The General Deformation Tensor


2.11.3. Analogy between the Elastic and Magnetostatic Fields


2.11.4. The Solution of the Basic Equations of the General Continuum Theory (Isotropic Case)


2.11.5. The Dislocation Density Tensor


2.11.6. An Example of the Incompatibility Tensor


2.11.7. Summary of the Continuum Theory

Chapter 3. The Properties of Point Defects


3.1. Point Defects in Crystals


3.2. The Energy of Point Defects


3.3. The Continuum Model of Volume Defects


3.4. Volume Defects in Bodies with Free Surfaces


3.5. The Elastic Interactions of Point Defects with other Stress-Fields


3.5.1. The Interaction of the Dilatation Center with Other Stress-Fields; Size Effect


3.5.2. The Interaction of Inhomogeneities with Other Stress-Fields; Modulus Effect


3.6. The Interaction of Dislocations and Point Defects


3.6.1. Straight Edge Dislocations


3.6.2. Infinite Screw Dislocations

Chapter 4. Dislocations in Crystals


4.1. The Frenkel Model


4.2. Peierls Model


4.3. The Stress Necessary to Slip a Dislocation


4.4. Kinks on Dislocations


4.5. Glide Systems


4.6. Glide and Climb


4.7. Jogs on Dislocations


4.8. The Role of Dislocations in Crystal Growth

Chapter 5. Multiplication of Dislocations


5.1. Sources of Dislocations


5.2. The Geometry of the Frank-Read Source


5.3. Stress Required for the Operation of a Frank-Read Source


5.4. The Formation of Sources


5.5. Dynamic Multiplication

Chapter 6. Partial Dislocations


6.1. Stacking Faults in Close-packed Lattices


6.2. Generalization of the Burgers Circuit


6.3. Partial Dislocations in Fee Lattices


6.4. Extended Dislocations in Fee Lattices


6.5. Stacking Faults and Extended Dislocations in bcc Crystals


6.5.1. Splitting in the {110} Plane


6.5.2. Splitting in the {112} Plane


6.6. Reactions of Dislocations


6.7. Extended Fogs


6.8. Extended Dislocations in Ordered Alloys


6.9. The Formation of Dislocation Loops by Vacancy Condensation


6.10. The Energy of Stacking Faults

Chapter 7. Effect of Lattice Defects on the Physical Properties of Metals


7.1. Mechanical Properties of Pure Metals


7.1.1. Small Plastic Deformation of Single Crystals


7.1.2. Relation between the Macroscopic Deformation and the Motion of Dislocations


7.1.3. Flow Stress of Pure Metals


7.1.4. The Plastic Deformation of Polycrystalline Metals


7.1.5. Creep Phenomena


7.2. Theory of the Yield Stress of Solid Solutions


7.2.1. Introduction


7.2.2. Theoretical Principles


7.2.3. Theories of Mott and Nabarro


7.2.4. The Friedel Theory


7.2.5. The Schoeck-Seeger Theory


7.2.6. The Fleischer Theory


7.2.7. Temperature Dependence of the Yield Stress of Solid Solutions


7.2.8. Yield Point Phenomena


7.3. Theory of Precipitation (Dispersion)-Hardening


7.3.1. Introduction


7.3.2. Investigation of the Yield Stress


7.4. The effect of Lattice Defects on the Electrical Resistivity of Metals


7.4.1. Introduction


7.4.2. The Extraresistivity of the Lattice Defects


7.5. Increase of Defect Concentration during Plastic Deformation

Chapter 8. Work-Hardening


8.1. General Features


8.2. The Stress-Strain Curve of Fee Crystals


8.3. The "Forest" Theory of Work-Hardening


8.4. The "Jog" Theory of Work-Hardening


8.5. The "Meshlength" Theory of Hardening


8.5.1. Stage I of the Stress-Strain Curve


8.5.2. Stages II and III of the Stress-Strain Curve


8.6. The "Long-Range Stress" Theory of Hardening


8.6.1. Stage I of the Stress-Strain Curve


8.6.2. Stage II of the Stress-Strain Curve


8.6.3. Stage III of the Stress-Strain Curve


8.7. Stability of the Deformed State

Chapter 9. Effect of Heat-Treatment on the Defect Structure of Metals


9.1. Introduction


9.2. Processes during Heat-Treatment


9.3. Change of the Physical Properties during Heat-Treatment

Appendix A. Concepts and Notations of Crystal Geometry

A.l. Lattice Criterion, Unit Cell, Crystal Systems

A.2. Lattice Planes, Miller Indices

A.3. Lattice Vectors, Zone

Appendix B. Principles of the Theory of Elasticity

B.l. The Dilatation Tensor

B.2. The Stress Tensor

B.3. Equilibrium Conditions

B.4. The Relation between the Stress and Dilatation Tensors for Isotropic Bodies

B.5. Relations between the Elastic Constants

B.6. Equations of Motion and Equilibrium Conditions of Isotropic Bodies

B.7. The Equilibrium of an Elastic Body in the Case of Two-Dimensional Deformations

Appendix C. The Stress-Fields of Straight Edge and Screw Dislocations

C.l. Edge Dislocations

C.2. The Stress-Field of Screw Dislocations

References

Index

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