Strengthening mechanisms in crystal plasticity

The strengthening of metals by a variety of means has been of interest over much of history. However, the elucidation of the actual mechanisms involved in the processes of alloying and work hardening, and the related processes of metals as a scientific pursuit, has become possible only through the parallel developments in dislocation theory and in definitive experimental tools of electron microscopy and X-ray diffraction. The important developments over the past several decades in the mechanistic understanding of the often complex processes of interaction of dislocations with each other, with solute atoms and with precipitates during plastic flow have largely remained scattered in the professional literature. This has made it difficult for students and professionals to have ready access to this subject as a whole. While there are some excellent reviews of certain aspects of the subject, there is presently no single comprehensive coverage available of the central mechanisms and their modelling. The present book on Strengthening Mechanisms in Crystal Plasticity provides such a coverage in a generally transparent and readily understandable form. It is intended as an advanced text for graduate students in materials science and mechanical engineering. The central processes of strengthening that are presented are modeled by dislocation mechanics in detail and the results are compared extensively with the best available experimental information. The form of the coverage is intended to inspire students or professional practitioners in the field to develop their own models of similar or related phenomena and, finally, engage in more advanced computational simulations, guided by the book.

Author Notes

Ali S. Argon is Quention Berg Professor Emeritus in the Department of Mechanical Engineering at Massachusetts Institute of Technology.

List of Symbols	p. xv
1 Structure of Crystalline Solids and the "Defect State"	p. 1
1.1 Overview	p. 1
1.2 Principal Crystal Structures of Interest	p. 2
1.3 Small-Strain Elasticity in Crystals	p. 4
1.3.1 Hooke's Law	p. 4
1.3.2 Orthorhombic Crystals	p. 9
1.3.3 Hexagonal Crystals	p. 9
1.3.4 Cubic Crystals	p. 10
1.3.5 Isotropic Materials	p. 10
1.3.6 Temperature and Strain Dependence of Elastic Response	p. 11
1.4 Inelastic Deformation and the Role of Crystal Defects	p. 13
1.5 Vacancies and Interstitials	p. 14
1.6 Line Properties of Dislocations	p. 17
1.6.1 Topology and Stress Fields of Dislocations	p. 17
1.6.2 Line Energies of Dislocations	p. 20
1.7 Planar Faults	p. 22
References	p. 25
Appendix Dislocation Stress Fields in a Finite Cylinder	p. 26
2 Kinematics and Kinetics of Crystal Plasticity	p. 27
2.1 Overview	p. 27
2.2 Kinematics of Inelastic Deformation	p. 27
2.2.1 Plasticity Resulting from Shear Transformations	p. 27
2.2.2 Plasticity Resulting from Dislocation Glide	p. 29
2.2.3 Lattice Rotations Accompanying Slip	p. 31
2.3 Flexure and Motion of Dislocations under Stress	p. 33
2.3.1 Interaction of a Dislocation Line with an External Stress	p. 33
2.3.2 Interaction Energies of Dislocations with Stresses External to Them	p. 35
2.3.3 Interaction of a Dislocation with Free Surfaces and Inhomogeneities	p. 36
2.3.4 Line Tension of a Dislocation	p. 37
2.3.5 Uniformly Moving Dislocations and The Dislocation Mass	p. 39
2.3.6 The Basic Differential Equation for a Moving Dislocation Line	p. 40
2.3.7 The Multiplication of Dislocation Line Length	p. 41
2.4 The Mechanical Threshold of Deformation	p. 44
2.5 Elements of Thermally Activated Deformation	p. 45
2.5.1 General Principles	p. 45
2.5.2 Principal Activation Parameters for Crystal Plasticity	p. 49
2.6 Selection of Slip Systems in Specific Crystal Structures	p. 52
2.7 Dislocations in Close-packed Structures	p. 54
2.7.1 Dissociation of Perfect Dislocations in FCC	p. 54
2.7.2 The Thompson Tetrahedron and Other Partial Dislocations	p. 57
2.7.3 The Burgers Vector/Material Displacement Rule	p. 59
2.7.4 Dislocation Reactions and Sessile Locks	p. 60
2.8 Plastic Deformation by Shear Transformations	p. 62
2.8.1 Types of Transformation	p. 62
2.8.2 Deformation Twinning	p. 62
2.8.3 Stress-induced Martensitic Transformations	p. 64
2.8.4 Kinking	p. 66
References	p. 68
3 Overview of Strengthening Mechanisms	p. 70
3.1 Introduction	p. 70
3.2 The Continuum Plasticity Approach to Strengthening Compared with the Dislocation Mechanics Approach	p. 70
3.3 The Lattice Resistance	p. 73
3.4 Solid-solution Strengthening	p. 73
3.5 Precipitation Strengthening	p. 74
3.6 Strengthening by Strain Hardening	p. 76
3.7 Phenomena Associated with Strengthening mechanisms	p. 77
References	p. 77
4 The Lattice Resistance	p. 78
4.1 Overview	p. 78
4.2 Model of a Dislocation in a Discrete Lattice	p. 78
4.2.1 The Peierls-Nabarro Model of an Edge Dislocation-Updated	p. 78
4.2.2 The Stress to Move the Dislocation	p. 81
4.3 Inception of Plastic Deformation	p. 85
4.3.1 HCP and FCC Metals	p. 85
4.3.2 BCC Metals	p. 87
4.4 Structure of the Cores of Screw Dislocations in BCC Metals	p. 89
4.5 Temperature and Strain Rate Dependence of the Lattice Resistance in BCC Metals	p. 94
4.5.1 The Nature of Thermal Assistance over a Lattice Energy Barrier	p. 94
4.5.2 Lattice Potentials	p. 98
4.5.3 Shapes and Energies of Geometrical Kinks	p. 99
4.5.4 Double-kink Energy in Regime I	p. 101
4.5.5 Double-kink Energy in Regime II	p. 102
4.6 The Plastic Strain Rate in BCC Metals	p. 104
4.6.1 The Preexponential Factor and the Net Shear Rate	p. 104
4.6.2 Temperature and Strain Rate Dependence of the Plastic Resistance	p. 106
4.6.3 Comparison of Theory with Experiments on BCC Transition Metals	p. 108
4.7 The Lattice Resistance of Silicon	p. 114
4.7.1 Dislocations in Silicon	p. 114
4.7.2 Dislocation Mobility in Silicon	p. 118
4.7.3 Models of the Dislocation Core Structure in Silicon	p. 119
4.7.4 Model of Dislocation Motion	p. 123
4.7.5 Comparison of Models with Experiments	p. 128
4.8 The Phonon Drag	p. 132
References	p. 133
5 Solid-solution Strengthening	p. 136
5.1 Overview	p. 136
5.2 Forms of Interaction of Solute Atoms with Dislocations in FCC Metals	p. 136
5.2.1 Overview	p. 136
5.2.2 The Size Misfit Interaction	p. 137
5.2.3 The Modulus Misfit Interaction	p. 139
5.2.4 Combined Size and Modulus Misfit Interactions	p. 141
5.3 Forms of Sampling of the Solute Field by a Dislocation in an FCC Metal	p. 145
5.4 The Solid-solution Resistance of FCC Alloys	p. 149
5.4.1 The Athermal Resistance	p. 149
5.4.2 Thermally Assisted Advance of a Dislocation in a Field of Solute Atoms in an FCC Metal	p. 151
5.5 Comparison of Solid-solution-strengthening Models for FCC Metals with Experiments	p. 153
5.5.1 Overview of Experimental Information	p. 153
5.5.2 Peak Solute Interaction Forces	p. 155
5.5.3 Dependence of Flow Stress on Solute Concentration	p. 156
5.5.4 Comparison of Temperature Dependence of CRSS between Experiments and Theoretical Models	p. 157
5.5.5 Summary of Solid-solution Strengthening of FCC Alloys	p. 159
5.5.6 The "Stress Equivalence" of the Solid-solution Resistance of FCC Alloys	p. 159
5.5.7 The Plateau Resistance	p. 163
5.6 Solid-solution Strengthening of BCC Metals by Substitutional Solute Atoms	p. 163
5.6.1 Overview of Phenomena	p. 163
5.6.2 Experimental Manifestations of BCC Solid-solution Alloy Systems	p. 165
5.7 Interactions of Solute Atoms with Screw Dislocations in BCC Metals	p. 166
5.7.1 Overview of Model of Interaction of Solute Atoms with Screw Dislocation Cores	p. 166
5.7.2 Interaction of Solute Atoms with Screw Dislocation Cores	p. 168
5.7.3 Binding Potential of Solutes to Screw Dislocation Cores	p. 170
5.8 The Shear Resistance	p. 172
5.8.1 The Athermal Resistance at the Plateau	p. 172
5.8.2 Resistance Governed by Kink Mobility	p. 173
5.8.3 Double-kink-nucleation-controlled Resistance	p. 177
5.8.4 Combination of Resistances	p. 180
5.8.5 The Strain Rate Dependence of the Flow Stress in the Plateau Range	p. 181
5.9 Comparison of Model Results with Experiments	p. 184
5.9.1 The Athermal Resistance at the Plateau	p. 184
5.9.2 Kink-mobility-controlled Plastic Resistance	p. 185
5.9.3 Double-kink-nucleation-controlled Resistance	p. 187
5.9.4 Strain Rate Dependence of the Flow Stress in the Plateau Region, and Activation Volumes	p. 189
References	p. 191
6 Precipitation Strengthening	p. 193
6.1 Overview	p. 193
6.2 Formation of Second Phases in the Form of Precipitate Particles, Heterogeneous Domains, or other Lattice Defect Clusters	p. 194
6.2.1 Discrete Precipitates	p. 194
6.2.2 Spinodal-decomposition Domains	p. 198
6.2.3 Defect Clusters and Nanovoids	p. 199
6.3 Sampling of Precipitates by Dislocations	p. 200
6.3.1 Precipitate Shapes and Sizes	p. 200
6.3.2 Two Forms of Interaction of Precipitates with Dislocations	p. 201
6.3.3 Statistics of Sampling Random Point Obstacles in a Plane	p. 202
6.3.4 Sampling Point Obstacles of Different Kinds	p. 207
6.3.5 Sampling Obstacles of Finite Width	p. 208
6.3.6 Precipitate Growth, Peak Aging, and Overaging	p. 212
6.3.7 Thermally Assisted Motion of Dislocations through a Field of Penetrable Obstacles	p. 213
6.4 Specific Mechanisms of Precipitation Strengthening	p. 219
6.4.1 Overview	p. 219
6.4.2 Chemical Strengthening, or Resistance to Interface Step Production in Shearing	p. 220
6.4.3 Stacking-fault Strengthening	p. 223
6.4.4 Atomic-order Strengthening	p. 235
6.4.5 Size Misfit Strengthening (Coherency Strengthening)	p. 247
6.4.6 Modulus Misfit Strengthening	p. 256
6.4.7 The Orowan Resistance and Dispersion Strengthening	p. 264
6.4.8 Strengthening by Spinodal-decomposition Microstructures	p. 267
6.4.9 Precipitate-like Obstacles	p. 271
References	p. 279
7 Strain Hardening	p. 283
7.1 Overview	p. 283
7.2 Features of Deformation	p. 284
7.2.1 Active Slip Systems in FCC Metals	p. 284
7.2.2 Stress-Strain Curves	p. 286
7.2.3 Slip Distributions	p. 292
7.2.4 Dislocation Microstructures	p. 294
7.3 Strain-hardening Models	p. 306
7.3.1 Overview	p. 306
7.3.2 Dislocation Intersections	p. 307
7.3.3 Stage I Strain Hardening	p. 312
7.3.4 Stage II Strain Hardening	p. 317
7.3.5 Ingredients of Stage III Hardening	p. 320
7.3.6 Components of Strain Hardening in Stage III	p. 325
7.3.7 Recovery Processes in Stage III	p. 330
7.3.8 Total Strain-hardening Rate in Stage III	p. 334
7.3.9 Strain Hardening in Stage IV	p. 336
7.3.10 Stage V Deformation with No Strain Hardening	p. 340
7.4 Strain Hardening in Other Crystal Structures	p. 340
References	p. 340
8 Deformation Instabilities, Polycrystals, Flow in Metals with Nanostructure, Superposition of Strengthening Mechanisms, and Transition to Continuum Plasticity	p. 344
8.1 Overview	p. 344
8.2 Yield Phenomena	p. 345
8.3 Balance between the Interplane and the Intraplane Resistances and the Mobile Dislocation Density	p. 349
8.4 The Portevin-Le Chatelier Effect and Jerky Flow	p. 351
8.5 Dynamic Overshoot at Low Temperatures	p. 355
8.6 Plastic Deformation in Polycrystals	p. 358
8.6.1 Plastic Resistance of Polycrystals	p. 358
8.6.2 Evolution of Deformation Textures	p. 360
8.7 Plastic Deformation in the Presence of Heterogeneities	p. 364
8.7.1 Geometrically Necessary Dislocations	p. 364
8.7.2 Rise in Flow Stress and Enhanced Strain-hardening-rate Effects of Geometrically Necessary Dislocations	p. 364
8.8 Grain Boundary Strengthening	p. 370
8.9 Plasticity in Metals with Nanoscale Microstructure	p. 376
8.10 Superposition of Deformation Resistances	p. 382
8.11 The Bauschinger Effect	p. 386
8.12 Phenomenological Continuum Plasticity	p. 388
8.12.1 Conditions of Plastic Flow in the Mathematical Theory of Plasticity	p. 388
8.12.2 Transition from Dislocation Mechanics to Continuum Mechanics	p. 389
References	p. 391
Author Index	p. 394
Subject Index	p. 399

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