Fundamentals of Strength: Principles, Experiments, and Applications of an Internal State Variable Constitutive Formulation (The Minerals, Metals & Materials Series)

This second edition updates and expands on the class-tested first edition text, augmenting discussion of dynamic strain aging and austenitic stainless steels and adding a section on analysis of nickel-base superalloys that shows how the mechanical threshold stress (MTS) model, an internal state variable constitutive formulation, can be used to de-convolute synergistic effects. The new edition retains a clear and rigorous presentation of the theory, mechanistic basis, and application of the MTS model. Students are introduced to critical competencies such as crystal structure, dislocations, thermodynamics of slip, dislocation-obstacle interactions, deformation kinetics, and hardening through dislocation accumulation. The model described in this volume facilitates readers' understanding of integrated computational materials engineering (ICME), presenting context for the transition between length scales characterizing the mesoscale (mechanistic) and the macroscopic. Presenting readers a model buttressed by detailed examples and applications, the textbook is ideal for students, practitioners, and materials researchers. The new edition: Maximizes reader understanding of the mechanical threshold stress (MTS) model using data, examples, and applications Connects deformation in metals to structure and defects, including data and analyses of more than 20 pure metals and alloys Reinforces concepts with exercises and tools for estimating influence of temperature and strain rate on deformation Foreword to the Second Edition 6 Preface to the First Edition 8 Preface to the Second Edition 10 Acknowledgment 11 How to Use This Textbook 13 Contents 16 About the Author 22 Symbols 23 Chapter 1: Measuring the Strength of Metals 28 1.1 How Is Strength Measured? 28 1.2 The Tensile Test 30 1.3 Stress in a Test Specimen 32 1.4 Strain in a Test Specimen 33 1.5 The Elastic Stress Versus Strain Curve 33 1.6 The Elastic Modulus 34 1.7 Lateral Strains and Poisson ́s Ratio 36 1.8 Defining Strength 37 1.9 Stress-Strain Curve 38 1.10 The True Stress-True Strain Conversion 43 1.11 Example Tension Tests 45 1.12 Accounting for Strain Measurement Errors 49 1.13 Formation of a Neck in a Tensile Specimen 52 1.14 Strain Rate 54 1.15 Summary 56 Exercises 56 References 61 Chapter 2: Structure and Bonding 62 2.1 Forces and Resultant Energies Associated with an Ionic Bond 62 2.2 Elastic Straining and the Force Versus Separation Diagram 65 2.3 Crystal Structure 66 2.4 Plastic Deformation 69 2.5 Dislocations 72 2.6 Summary 77 Exercises 78 References 80 Chapter 3: Contributions to Strength 81 3.1 Strength of a Single Crystal 81 3.2 The Peierls Stress 86 3.3 The Importance of Available Slip Systems and Geometry of HCP Metals 88 3.4 Contributions from Grain Boundaries 90 3.5 Contributions from Impurity Atoms 93 3.6 Contributions from Stored Dislocations 95 3.7 Contributions from Precipitates 98 3.8 Summary 98 Exercises 99 References 102 Chapter 4: Dislocation-Obstacle Interactions 103 4.1 A Simple Dislocation/Obstacle Profile 103 4.2 Thermal Energy-Boltzmann ́s Equation 105 4.3 The Implication of 0 K 106 4.4 Addition of a Second Obstacle to a Slip Plane 106 4.5 Kinetics 108 4.6 Analysis of Experimental Data 110 4.7 Multiple Obstacles 114 4.8 Kinetics of Hardening 115 4.9 Summary 116 Exercises 117 References 119 Chapter 5: A Constitutive Law for Metal Deformation 121 5.1 Constitutive Laws in Engineering Design and Materials Processing 121 5.2 Simple Hardening Models 126 5.3 State Variables 129 5.4 Defining a State Variable in Metal Deformation 130 5.5 The Mechanical Threshold Stress Model 131 5.5.1 Example Material and Constitutive Law 133 5.6 Common Deviations from Model Behavior 136 5.7 Summary 139 Exercises 140 References 142 Chapter 6: Further MTS Model Developments 144 6.1 Removing the Temperature Dependence of the Shear Modulus 144 6.2 Introducing a More Descriptive Obstacle Profile 148 6.3 Dealing with Multiple Obstacles 150 6.4 Defining the Activation Volume in the Presence of Multiple Obstacles Populations 157 6.5 The Evolution Equation 159 6.6 Adiabatic Deformation 160 6.7 Summary 163 Exercises 164 References 167 Chapter 7: Data Analysis: Deriving MTS Model Parameters 168 7.1 A Hypothetical Alloy 168 7.2 Pure Fosium 169 7.3 Hardening in Pure Fosium 172 7.4 Yield Stress Kinetics in Unstrained FoLLyalloy 172 7.5 Hardening in FoLLyalloy 175 7.6 Evaluating the Stored Dislocation Obstacle Population 177 7.7 Deriving the Evolution Equation 185 7.8 The Constitutive Law for FoLLyalloy 187 7.9 Summary 189 Exercises 189 Chapter 8: Application of MTS Model to Copper and Nickel 192 8.1 Pure Copper 193 8.2 Follansbee and Kocks Experiments 194 8.3 Temperature-Dependent Stress-Strain Curves 200 8.4 Eleiche and Campbell Measurements in Torsion 204 8.5 Analysis of Deformation in Nickel 210 8.6 Predicted Stress-Strain Curves in Nickel and Comparison with Experiment 215 8.7 Application to Shock Deformed Nickel 217 8.8 Deformation in Nickel Plus Carbon Alloys 219 8.9 Monel 400-Analysis of Grain-Size Dependence 222 8.10 Copper-Aluminum Alloys 226 8.11 Summary 232 Exercises 233 References 234 Chapter 9: Application of MTS Model to BCC Metals and Alloys 236 9.1 Pure BCC Metals 237 9.2 Comparison with Campbell and Ferguson Measurements 245 9.3 Trends in the Activation Volume for Pure BCC Metals 248 9.4 Structure Evolution in BCC Pure Metals and Alloys 251 9.5 Analysis of the Constitutive Behavior of a Fictitious BCC Alloy-UfKonel 252 9.6 Analysis of the Constitutive Behavior of AISI 1018 Steel 256 9.7 Analysis of the Constitutive Behavior of Polycrystalline Vanadium 266 9.8 Deformation Twinning in Vanadium 272 9.9 Signature of Dynamic Strain Aging in Vanadium 275 9.10 Analysis of Deformation Behavior of Polycrystalline Niobium 278 9.11 Summary 286 Exercises 289 References 294 Chapter 10: Application of MTS Model to HCP Metals and Alloys 295 10.1 Pure Zinc 296 10.2 Kinetics of Yield in Pure Cadmium 301 10.3 Structure Evolution in Pure Cadmium 304 10.4 Pure Magnesium 308 10.5 Magnesium Alloy AZ31 311 10.6 Pure Zirconium 322 10.7 Structure Evolution in Zirconium 326 10.7.1 The Influence of Deformation Twinning on Hardening 329 10.8 Analysis of Deformation in Irradiated Zircaloy-2 332 10.9 Analysis of Deformation Behavior of Polycrystalline Titanium 339 10.9.1 Dynamic Strain Aging in Polycrystalline Titanium 350 10.10 Analysis of Deformation Behavior of Titanium Alloy Ti6Al-4V 353 10.11 Summary 359 Exercises 363 References 366 Chapter 11: Application of MTS Model to Austenitic Stainless Steels 369 11.1 Variation of Yield Stress with Temperature and Strain Rate in Annealed Materials 369 11.2 Nitrogen in Austenitic Stainless Steels 374 11.3 The Hammond and Sikka Study in 316 382 11.4 Modeling the Stress-Strain Curve 384 11.5 Dynamic Strain Aging in Austenitic Stainless Steels 387 11.6 Application of the Model to Irradiation-Damaged Material 391 11.7 Summary 394 Exercises 395 References 399 Chapter 12: Application of MTS Model to Nickel-Base Superalloys 401 12.1 Deformation in Nickel-Based Superalloys 401 12.2 Yield Stress Kinetics 403 12.3 Strain Hardening in Several Nickel-Base Superalloys 407 12.3.1 Strain Hardening in Inconel 600 409 12.3.2 Strain Hardening in Inconel 718 411 12.3.3 Yield Stress Kinetics and Strain Hardening in C-276 415 12.3.4 Yield Stress Kinetics and Strain Hardening in C-22 418 12.3.5 Potential Origins of High Hardening Rates 422 12.4 Signatures of Dynamic Strain Aging 423 12.5 Summary 425 Exercises 426 References 429 Chapter 13: A Model for Dynamic Strain Aging 432 13.1 Review of Signatures of DSA 432 13.2 Focusing on the Increased Stress Levels Accompanying DSA 437 13.3 Toward a Mechanistic Understanding 439 13.4 Model Predictions 443 13.5 Predicting the Stresses When DSA is Active 447 13.6 Summary 450 Appendix 13.A1 The Effect of an Incorrect Assumption on the Analysis Using Eq. 13.15 451 Appendix 13.A2 The Effect of DSA on the Stage II Hardening Rate 453 Exercises 456 References 456 Chapter 14: Application of MTS Model to the Strength of Heavily Deformed Metals 458 14.1 Complications Introduced at Large Deformations 458 14.2 Stress Dependence of the Normalized Activation Energy goε 459 14.3 Addition of Stage IV Hardening to the Evolution Law 463 14.4 Grain Refinement 466 14.5 Application to Large-Strain ECAP Processing of Copper 472 14.5.1 Using the Torsion Curve Rather Than the Compression Curve 474 14.6 Further Insight into the Strain Hardening at High Strains 480 14.7 A Large-Strain Constitutive Description of Nickel 485 14.8 Application to Large-Strain ECAP Processing of Nickel 489 14.9 Application to Large-Strain ECAP Processing of Austenitic Stainless Steel 493 14.10 Analysis of Fine-Grained Processed Tungsten 500 14.11 Summary 503 Exercises 504 References 507 Chapter 15: Summary and Status of Model Development 509 15.1 Analyzing the Temperature-Dependent Yield Stress 510 15.2 Stress Dependence of the Normalized Activation Energy goε 513 15.3 Evolution 513 15.4 Temperature and Strain-Rate Dependence of Evolution (Strain Hardening) 515 15.5 The Effects of Deformation Twinning 519 15.6 The Signature of Dynamic Strain Aging 522 15.7 Adding Insight to Deformation in Nickel-Base Superalloys 527 15.8 Adding Insight to Complex Processing Routes 527 15.9 Temperature Limits 533 15.10 Summary 536 References 538 Index 540