Thermally Activated Mechanisms in Crystal Plasticity

Transcription

1 PERGAMON MATERIALS SERIES Thermally Activated Mechanisms in Crystal Plasticity by D. Caillard CEMES/CNRS-BP4347, F Toulouse Cedex J. L. Martin IPMC/EPFL-CH 1015 Lausanne 2003 PERGAMON An Imprint of Elsevier Amsterdam - Boston - London - New York - Oxford - Paris San Diego - San Francisco - Singapore - Sydney - Tokyo

2 Contents Series Preface Preface Reader's Guide v vii ix CHAPTER 1 INTRODUCTION 1.1. Scope and Outline Thermal Activation Theory: A Summary 5 References 8 CHAPTER 2 EXPERIMENTAL CHARACTERIZATION OF DISLOCATION MECHANISMS 2.1. Transient Mechanical Tests Strain-Rate Jump Experiments Stress Relaxation Tests Creep Tests Interpretation of Repeated Stress Relaxation Tests General Considerations Activation Volume and Microstructural Parameters Interpretation of Repeated Creep Tests Experimental Assessments Transition Between Monotonic and Transient Tests Examples of Repeated Creep Tests Results of Stress Relaxation Series Results of Creep Series and Comparison with Stress Relaxations Stress Reduction Experiments Conclusions About Transient Mechanical Tests Deformation Experiments in the Electron Microscope Some Key Technical Points Quantitative Information Provided by In Situ Experiments Reliability of In Situ Experiments in TEM In Situ Synchrotron X-ray Topography Observation of Slip Traces at the Specimen Surface Conclusion About the Characterization of Dislocation Mechanisms 51 References 51 xi

3 xii Contents CHAPTER 3 INTERACTIONS BETWEEN DISLOCATIONS AND SMALL-SIZE OBSTACLES 3.1. Thermally Activated Glide Across Fixed Small-size Obstacles The Rectangular Force-Distance Profile The Parabolic Force-Distance Profile The Cottrell-Bilby Potential (Cottrell and Bilby, 1949) Dislocations Interacting with Mobile Solute Atoms Long-Range Elastic Interactions Static Ageing, Dynamic Strain Ageing and the Portevin-Lechatelier Effect Diffusion-Controlled Glide Comparison with Experiments The Forest Mechanism Dislocations-Solute Atoms Interactions Domain 2: Thermally Activated Motion Across Fixed Obstacles Domain 3: Stress Instabilities and PLC Effect Domain 4: Glide Controlled by Solute-Diffusion 80 References 81 CHAPTER 4 FRICTIONAL FORCES IN METALS 4.1. Dislocation Core Structures and Peierls Potentials Kink-Pair Mechanism Principles \ Several Peierls Potentials and Associated Peierls Stresses Energy of an Isolated Kink Dorn and Rajnak Calculation (Smooth Potentials) Line Tension Approximation Abrupt Potential Energy of a Critical Bulge (High Stress Approximation) Dorn and Rajnak Calculation (1964) Line Tension Approximation Abrupt Potential Energy of a Critical Kink-Pair (Low Stress Approximation: Coulomb Elastic Interaction) Transition Between High Stress and Low Stress Regimes Properties of Dislocations Gliding by the Kink-Pair Mechanism 109

4 Contents xiii 4.3. Thermally Activated Core Transformations Transformations into a Higher Energy Core Structure Transformation into a Lower Energy Core Structure Sessile-Glissile Transformations in Series (Locking-Unlocking Mechanism) Transition Between the Locking-Unlocking and the Kink-Pair Mechanism Properties of Dislocations Gliding by the Locking-Unlocking Mechanism Conclusions 121 References 122 CHAPTER 5 DISLOCATION CROSS-SLIP 5.1. Modelling Cross-slip Elementary Mechanisms The Fleischer Model (1959) The Washburn Model (1965) The Schoeck, Seeger, Wolf model The Friedel-Escaig Cross-slip Mechanism Constriction Energy Escaig's Description of Cross-slip (1968) The Activation Energy for Cross-slip The Activation Volume Orientation Effects Refinements in the Activation Energy Estimation Experimental Assessments of Escaig's Modelling The Bonneville-Escaig Technique Experimental Observations of Cross-slip TEM Observations Optical Slip Trace Observations Peculiar Features of the Deformation Curves The Activation Parameters Experimental Study of Orientation Effects Atomistic Modelling of Dislocation Cross-slip Discussion and Conclusions Who is Closer to the Truth? Cross-slip and Stage III in FCC Metals 154 References 155

5 xiv Contents CHAPTER 6 EXPERIMENTAL STUDIES OF PEIERLS-NABARRO-TYPE FRICTION FORCES IN METALS AND ALLOYS 6.1. Prismatic Slip in HCP Metals Prismatic Slip in Titanium Prismatic Slip in Zirconium Prismatic Slip in Magnesium Prismatic Slip in Beryllium Conclusions on Prismatic Slip in HCP Metals Glide on Non-Close-Packed Planes in FCC Metals {110} Slip {100} Slip in Aluminium Creep Test Results Results of Constant Strain-Rate Tests Features of Dislocations in (001) Origin of Non-Octahedral Glide in Aluminium Glide^on Non-Close-Packed Planes in Copper Stress-Strain curves Microstructural Features Critical Stress for Non-Octahedral Glide Modelling of Non-Octahedral Glide in FCC Metals Possible Mechanisms {001} Glide in Aluminium and the Kink-Pair Mechanism Modelling {110} Glide in Aluminium Non-Octahedral Glide in Copper Comparison of FCC Metals ' The Relevance of Slip on Non-Close-Packed Planes in Close-Packed Metals Optimum Conditions for Unconventional Slip in Aluminium Non-Conventional Glide as a Rate Controlling Process Low-Temperature Plasticity of BCC Metals Mechanical Properties Iron and Iron Alloys Niobium Other BCC Metals Microstructural Observations Interpretations Conclusions on the Low-Temperature Plasticity of BCC Metals 220

6 Contents xv 6.4. The Importance of Friction Forces in Metals and Alloys 220 References 221 CHAPTER 7 THE PEIERLS-NABARRO MECHANISM IN COVALENT CRYSTALS 7.1. Dislocation Core Structures and Peierls-Nabarro Friction Forces Dislocation Velocities High Kink Mobility (Metal-Like Model of Suzuki et al., 1995) Low Kink Mobility: Case of Undissociated Dislocations Point-Obstacle Model of Celli et al. (1963) Kink Diffusion Model of Hirth and Lothe (1982) Low Kink Mobility: Case of Dissociated Dislocations Experimental Results on Dislocation Velocities Mobility as a Function of Character Elemental Semiconductors (Si) Compound Semiconductors Velocity as a Function of Stress Velocity as a Function of Temperature Regimes of Dislocation Movements Velocity Enhancement Under Irradiation Experiments at Very High Stresses Conclusions 275 References 276 CHAPTER 8 DISLOCATION CLIMB 8.1. Introduction: Basic Mechanisms ; Definition of Climb Mechanical Forces for Pure Climb Diffusion of Point Defects Jog-Point Defect Interactions Jog-Vacancy Interactions Jog-Interstitial Interactions Summary Vacancy Emission Climb Mechanism High Jog Density Climbing Dislocations with a Small Average Curvature Growth or Shrinking of Small Prismatic Dislocation Loops Low Jog Density No Pipe Diffusion 293

7 xvi Contents The Role of Pipe Diffusion Jog-Pair Nucleations Stress Dependence of the Climb Velocity Conclusion on the Vacancy-Emission Climb Mechanism Vacancy or Interstitial-Absorption Climb Mechanism High Jog Density (e.g. Curved Dislocations) Low Jog Density (e.g. Polygonal Dislocations) Growth and Shrinking of Prismatic Loops During Annealing Experimental Studies of Climb Processes Pure Climb-Plasticity Climb in HCP Magnesium and Beryllium Climb in Intermetallic Alloys Climb in Quasicrystals Growth and Shrinking of Loops During Annealing Shrinking of Vacancy Loops in Thin Foils Competitive Loop Growth in Bulk Materials Growth of Loops Under High Defect Supersaturations Conclusions on the Loop-Annealing Experiments Irradiation-Induced Creep Conclusion 318 References 318 CHAPTER 9 DISLOCATION MULTIPLICATION, EXHAUSTION AND WORK-HARDENING 9.1. Dislocation Multiplication Models of Sources i Observed Dislocation Sources Glide Sources with One Pinning Point Closed Loop Multiplication Open Loop Multiplication Multiplication Processes in Covalent Materials General Features Three Dimensional Mesoscopic Simulations of Dislocation Multiplication Testing the Proper Multiplication Laws Conclusions About Dislocation Multiplication in Covalent Crystals Mobile Dislocation Exhaustion Cell Formation 343

8 Contents xvii Exhaustion Through Lock Formation in Ni 3 Al Impurity or Solute Pinning (Cottrell Effect) Exhaustion with Annihilation Work-Hardening Versus Work-Softening Conclusions About Dislocation Multiplication, Exhaustion and Subsequent Work-Hardening Dislocation Multiplication at Surfaces Dislocation Generation at Crack Tips Dislocation Nucleation at a Solid Free Surface Conclusion on Dislocation Multiplication at Free Surfaces 358 References 358 CHAPTER 10 MECHANICAL BEHAVIOUR OF SOME ORDERED INTERMETALLIC COMPOUNDS Ni 3 Al and Ll 2 Compounds General Considerations Dislocation Cores Technical Difficulties Bound to Dislocation Core Characterization in Ni 3 Al Data About Fault Energies Cube Glide Dislocation Cores Dislocation Mobility Octahedral Glide General Considerations Microscopic Aspect of {111} Glide Complete Versus Incomplete KWL Understanding the Mechanical Properties of Ni 3 Al compounds Definition of the Yield Stress Temperature Variations of the Yield Stress and Work-hardening Rate Yield Stress Peak Temperature (Single Crystals) Yield Stress Peak Temperature (Polycrystals) Conclusion About the Peak Temperature for the Yield Stress The Temperature of the Work-hardening Peak in Single Crystals The Temperature of the Work-hardening Peak in Polycrystals 394

9 xviii Contents Conclusions About the Peak in Work-Hardening The Role of Different Fault Energies Strength and Dislocation Density ~ Values of Dislocation Densities in Ni 3 Al Dislocation Densities and Mechanical parameters Stress Anomalies in other Intermetallics Other LI 2 Crystals B2 Alloys Deformation Mechanisms in p CuZn FeAl Compounds Conclusion on Strength Anomalies in Ordered intermetallics Creep behaviour of Ni 3 Al Compounds Conclusions J 411 References 411 CONCLUSION 417 GLOSSARY OF SYMBOLS 419 INDEX 425