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Fracture Mechanics: Fundamentals and Applications » (3rd Edition)

Book cover image of Fracture Mechanics: Fundamentals and Applications by T. L. Anderson

Authors: T. L. Anderson
ISBN-13: 9780849316562, ISBN-10: 0849316561
Format: Hardcover
Publisher: Taylor & Francis, Inc.
Date Published: June 2005
Edition: 3rd Edition

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Author Biography: T. L. Anderson

Book Synopsis

With its combination of practicality, readability, and rigor that is characteristic of any truly authoritative reference and text, Fracture Mechanics: Fundamentals and Applications quickly established itself as the most comprehensive guide to fracture mechanics available. It has been adopted by more than 100 universities and embraced by thousands of professional engineers worldwide. Now in its third edition, the book continues to raise the bar in both scope and coverage. It encompasses theory and applications, linear and nonlinear fracture mechanics, solid mechanics, and materials science with a unified, balanced, and in-depth approach.

Reflecting the many advances made in the decade since the previous edition came about, this indispensable Third Edition now includes:

  • A new chapter on environmental cracking
  • Expanded coverage of weight functions
  • New material on toughness test methods
  • New problems at the end of the book
  • New material on the failure assessment diagram (FAD) method
  • Expanded and updated coverage of crack closure and variable-amplitude fatigue
  • Updated solutions manual

    In addition to these enhancements, Fracture Mechanics: Fundamentals and Applications, Third Edition also includes detailed mathematical derivations in appendices at the end of applicable chapters; recent developments in laboratory testing, application to structures, and computational methods; coverage of micromechanisms of fracture; and more than 400 illustrations. This reference continues to be a necessity on the desk of anyone involved with fracture mechanics.

    • Table of Contents

    Part I
    Introduction 1
    Chapter 1
    History and Overview 3
    1.1 Why Structures Fail 3
    1.2 Historical Perspective 6
    1.2.1 Early Fracture Research 8
    1.2.2 The Liberty Ships 9
    1.2.3 Post-War Fracture Mechanics Research 10
    1.2.4 Fracture Mechanics from 1960 to 1980 10
    1.2.5 Fracture Mechanics from 1980 to the Present 12
    1.3 The Fracture Mechanics Approach to Design 12
    1.3.1 The Energy Criterion 12
    1.3.2 The Stress-Intensity Approach 14
    1.3.3 Time-Dependent Crack Growth and Damage Tolerance 15
    1.4 Effect of Material Properties on Fracture 16
    1.5 A Brief Review of Dimensional Analysis 18
    1.5.1 The Buckingham P-Theorem 18
    1.5.2 Dimensional Analysis in Fracture Mechanics 19
    References 21
    Part II
    Fundamental Concepts 23
    Chapter 2
    Linear Elastic Fracture Mechanics 25
    2.1 An Atomic View of Fracture 25
    2.2 Stress Concentration Effect of Flaws 27
    2.3 The Griffith Energy Balance 29
    2.3.1 Comparison with the Critical Stress Criterion 31
    2.3.2 Modified Griffith Equation 32
    2.4 The Energy Release Rate 34
    2.5 Instability and the R Curve 38
    2.5.1 Reasons for the R Curve Shape 39
    2.5.2 Load Control vs. Displacement Control 40
    2.5.3 Structures with Finite Compliance 41
    2.6 Stress Analysis of Cracks 42
    2.6.1 The Stress Intensity Factor 43
    2.6.2 Relationship between K and Global Behavior 45
    2.6.3 Effect of Finite Size 48
    2.6.4 Principle of Superposition 54
    2.6.5 Weight Functions 56
    2.7 Relationship between K and G 58
    2.8 Crack-Tip Plasticity 61
    2.8.1 The Irwin Approach 61
    2.8.2 The Strip-Yield Model 64
    2.8.3 Comparison of Plastic Zone Corrections 66
    2.8.4 Plastic Zone Shape 66
    2.9 K-Controlled Fracture 69
    2.10 Plane Strain Fracture: Fact vs. Fiction 72
    2.10.1 Crack-Tip Triaxiality 73
    2.10.2 Effect of Thickness on Apparent Fracture Toughness 75
    2.10.3 Plastic Zone Effects 78
    2.10.4 Implications for Cracks in Structures 79
    2.11 Mixed-Mode Fracture 80
    2.11.1 Propagation of an Angled Crack 81
    2.11.2 Equivalent Mode I Crack 83
    2.11.3 Biaxial Loading 84
    2.12 Interaction of Multiple Cracks 86
    2.12.1 Coplanar Cracks 86
    2.12.2 Parallel Cracks 86
    Appendix 2: Mathematical Foundations of Linear Elastic
    Fracture Mechanics 88
    A2.1 Plane Elasticity 88
    A2.1.1 Cartesian Coordinates 89
    A2.1.2 Polar Coordinates 90
    A2.2 Crack Growth Instability Analysis 91
    A2.3 Crack-Tip Stress Analysis 92
    A2.3.1 Generalized In-Plane Loading 92
    A2.3.2 The Westergaard Stress Function 95
    A2.4 Elliptical Integral of the Second Kind 100
    References 101
    Chapter 3
    Elastic-Plastic Fracture Mechanics 103
    3.1 Crack-Tip-Opening Displacement 103
    3.2 The J Contour Integral 107
    3.2.1 Nonlinear Energy Release Rate 108
    3.2.2 J as a Path-Independent Line Integral 110
    3.2.3 J as a Stress Intensity Parameter 111
    3.2.4 The Large Strain Zone 113
    3.2.5 Laboratory Measurement of J 114
    3.3 Relationships Between J and CTOD 120
    3.4 Crack-Growth Resistance Curves 123
    3.4.1 Stable and Unstable Crack Growth 124
    3.4.2 Computing J for a Growing Crack 126
    3.5 J-Controlled Fracture 128
    3.5.1 Stationary Cracks 128
    3.5.2 J-Controlled Crack Growth 131
    3.6 Crack-Tip Constraint Under Large-Scale Yielding 133
    3.6.1 The Elastic T Stress 137
    3.6.2 J-Q Theory 140
    3.6.2.1 The J-Q Toughness Locus 142
    3.6.2.2 Effect of Failure Mechanism
    on the J-Q Locus 144
    3.6.3 Scaling Model for Cleavage Fracture 145
    3.6.3.1 Failure Criterion 145
    3.6.3.2 Three-Dimensional Effects 147
    3.6.3.3 Application of the Model 148
    3.6.4 Limitations of Two-Parameter Fracture Mechanics 149
    Appendix 3: Mathematical Foundations
    of Elastic-Plastic Fracture Mechanics 153
    A3.1 Determining CTOD from the Strip-Yield Model 153
    A3.2 The J Contour Integral 156
    A3.3 J as a Nonlinear Elastic Energy Release Rate 158
    A3.4 The HRR Singularity 159
    A3.5 Analysis of Stable Crack Growth
    in Small-Scale Yielding 162
    A3.5.1 The Rice-Drugan-Sham Analysis 162
    A3.5.2 Steady State Crack Growth 166
    A3.6 Notes on the Applicability of Deformation Plasticity
    to Crack Problems 168
    References 171
    Chapter 4
    Dynamic and Time-Dependent Fracture 173
    4.1 Dynamic Fracture and Crack Arrest 173
    4.1.1 Rapid Loading of a Stationary Crack 174
    4.1.2 Rapid Crack Propagation and Arrest 178
    4.1.2.1 Crack Speed 180
    4.1.2.2 Elastodynamic Crack-Tip Parameters 182
    4.1.2.3 Dynamic Toughness 184
    4.1.2.4 Crack Arrest 186
    4.1.3 Dynamic Contour Integrals 188
    4.2 Creep Crack Growth 189
    4.2.1 The C * Integral 191
    4.2.2 Short-Time vs. Long-Time Behavior 193
    4.2.2.1 The C t Parameter 195
    4.2.2.2 Primary Creep 196
    4.3 Viscoelastic Fracture Mechanics 196
    4.3.1 Linear Viscoelasticity 197
    4.3.2 The Viscoelastic J Integral 200
    4.3.2.1 Constitutive Equations 200
    4.3.2.2 Correspondence Principle 200
    4.3.2.3 Generalized J Integral 201
    4.3.2.4 Crack Initiation and Growth 202
    4.3.3 Transition from Linear to Nonlinear Behavior 204
    Appendix 4: Dynamic Fracture Analysis 206
    A4.1 Elastodynamic Crack Tip Fields 206
    A4.2 Derivation of the Generalized Energy
    Release Rate 209
    References 213
    Part III
    Material Behavior 217
    Chapter 5
    Fracture Mechanisms in Metals 219
    5.1 Ductile Fracture 219
    5.1.1 Void Nucleation 219
    5.1.2 Void Growth and Coalescence 222
    5.1.3 Ductile Crack Growth 231
    5.2 Cleavage 234
    5.2.1 Fractography 234
    5.2.2 Mechanisms of Cleavage Initiation 235
    5.2.3 Mathematical Models of Cleavage Fracture
    Toughness 238
    5.3 The Ductile-Brittle Transition 247
    5.4 Intergranular Fracture 249
    Appendix 5: Statistical Modeling of Cleavage Fracture 250
    A5.1 Weakest Link Fracture 250
    A5.2 Incorporating a Conditional Probability
    of Propagation 252
    References 254
    Chapter 6
    Fracture Mechanisms in Nonmetals 257
    6.1 Engineering Plastics 257
    6.1.1 Structure and Properties of Polymers 258
    6.1.1.1 Molecular Weight 258
    6.1.1.2 Molecular Structure 259
    6.1.1.3 Crystalline and Amorphous Polymers 259
    6.1.1.4 Viscoelastic Behavior 260
    6.1.1.5 Mechanical Analogs 263
    6.1.2 Yielding and Fracture in Polymers 265
    6.1.2.1 Chain Scission and Disentanglement 265
    6.1.2.2 Shear Yielding and Crazing 265
    6.1.2.3 Crack-Tip Behavior 267
    6.1.2.4 Rubber Toughening 268
    6.1.2.5 Fatigue 270
    6.1.3 Fiber-Reinforced Plastics 270
    6.1.3.1 Overview of Failure Mechanisms 271
    6.1.3.2 Delamination 272
    6.1.3.3 Compressive Failure 275
    6.1.3.4 Notch Strength 278
    6.1.3.5 Fatigue Damage 280
    6.2 Ceramics and Ceramic Composites 282
    6.2.1 Microcrack Toughening 285
    6.2.2 Transformation Toughening 286
    6.2.3 Ductile Phase Toughening 287
    6.2.4 Fiber and Whisker Toughening 288
    6.3 Concrete and Rock 291
    References 293
    Part IV
    Applications 297
    Chapter 7
    Fracture Toughness Testing of Metals 299
    7.1 General Considerations 299
    7.1.1 Specimen Configurations 299
    7.1.2 Specimen Orientation 301
    7.1.3 Fatigue Precracking 303
    7.1.4 Instrumentation 305
    7.1.5 Side Grooving 307
    7.2 K Ic Testing 308
    7.2.1 ASTM E 399 309
    7.2.2 Shortcomings of E 399 and Similar Standards 312
    7.3 K-R Curve Testing 316
    7.3.1 Specimen Design 317
    7.3.2 Experimental Measurement of K-R Curves 318
    7.4 J Testing of Metals 320
    7.4.1 The Basic Test Procedure and JIc Measurements 320
    7.4.2 J-R Curve Testing 322
    7.4.3 Critical J Values for Unstable Fracture 324
    7.5 CTOD Testing 326
    7.6 Dynamic and Crack-Arrest Toughness 329
    7.6.1 Rapid Loading in Fracture Testing 329
    7.6.2 KIa Measurements 330
    7.7 Fracture Testing of Weldments 334
    7.7.1 Specimen Design and Fabrication 334
    7.7.2 Notch Location and Orientation 335
    7.7.3 Fatigue Precracking 337
    7.7.4 Posttest Analysis 337
    7.8 Testing and Analysis of Steels in the Ductile-Brittle Transition Region 338
    7.9 Qualitative Toughness Tests 340
    7.9.1 Charpy and Izod Impact Test 341
    7.9.2 Drop Weight Test 342
    7.9.3 Drop Weight Tear and Dynamic Tear Tests 344
    Appendix 7: Stress Intensity, Compliance, and Limit Load Solutions
    for Laboratory Specimens 344
    References 350
    Chapter 8
    Fracture Testing of Nonmetals 353
    8.1 Fracture Toughness Measurements in Engineering Plastics 353
    8.1.1 The Suitability of K and J for Polymers 353
    8.1.1.1 K-Controlled Fracture 354
    8.1.1.2 J-Controlled Fracture 357
    8.1.2 Precracking and Other Practical Matters 360
    8.1.3 Klc Testing 362
    8.1.4 J Testing 365
    8.1.5 Experimental Estimates of Time-Dependent Fracture Parameters 369
    8.1.6 Qualitative Fracture Tests on Plastics 371
    8.2 Interlaminar Toughness of Composites 373
    8.3 Ceramics 378
    8.3.1 Chevron-Notched Specimens 378
    8.3.2 Bend Specimens Precracked by Bridge Indentation 380
    References 382
    Chapter 9
    Application to Structures 385
    9.1 Linear Elastic Fracture Mechanics 385
    9.1.1 KI for Part-Through Cracks 387
    9.1.2 Influence Coefficients for Polynomial Stress Distributions 388
    9.1.3 Weight Functions for Arbitrary Loading 392
    9.1.4 Primary, Secondary, and Residual Stresses 394
    9.1.5 A Warning about LEFM 395
    9.2 The CTOD Design Curve 395
    9.3 Elastic-Plastic J-Integral Analysis 397
    9.3.1 The EPRI J-Estimation Procedure 398
    9.3.1.1 Theoretical Background 398
    9.3.1.2 Estimation Equations 399
    9.3.1.3 Comparison with Experimental J Estimates 401
    9.3.2 The Reference Stress Approach 403
    9.3.3 Ductile Instability Analysis 405
    9.3.4 Some Practical Considerations 408
    9.4 Failure Assessment Diagrams 410
    9.4.1 Original Concept 410
    9.4.2 J-Based FAD 412
    9.4.3 Approximations of the FAD Curve 415
    9.4.4 Estimating the Reference Stress 416
    9.4.5 Application to Welded Structures 423
    9.4.5.1 Incorporating Weld Residual Stresses 423
    9.4.5.2 Weld Misalignment 426
    9.4.5.3 Weld Strength Mismatch 427
    9.4.6 Primary vs. Secondary Stresses in the FAD Method 428
    9.4.7 Ductile-Tearing Analysis with the FAD 430
    9.4.8 Standardized FAD-Based Procedures 430
    9.5 Probabilistic Fracture Mechanics 432
    Appendix 9: Stress Intensity and Fully Plastic J Solutions
    for Selected Configurations 434
    References 449
    Chapter 10
    Fatigue Crack Propagation 451
    10.1 Similitude in Fatigue 451
    10.2 Empirical Fatigue Crack Growth Equations 453
    10.3 Crack Closure 457
    10.3.1 A Closer Look at Crack-Wedging Mechanisms 460
    10.3.2 Effects of Loading Variables on Closure 463
    10.4 The Fatigue Threshold 464
    10.4.1 The Closure Model for the Threshold 465
    10.4.2 A Two-Criterion Model 466
    10.4.3 Threshold Behavior in Inert Environments 470
    10.5 Variable Amplitude Loading and Retardation 473
    10.5.1 Linear Damage Model for Variable Amplitude Fatigue 474
    10.5.2 Reverse Plasticity at the Crack Tip 475
    10.5.3 The Effect of Overloads and Underloads 478
    10.5.4 Models for Retardation and Variable Amplitude Fatigue 484
    10.6 Growth of Short Cracks 488
    10.6.1 Microstructurally Short Cracks 491
    10.6.2 Mechanically Short Cracks 491
    10.7 Micromechanisms of Fatigue 491
    10.7.1 Fatigue in Region II 491
    10.7.2 Micromechanisms Near the Threshold 494
    10.7.3 Fatigue at High DK Values 495
    10.8 Fatigue Crack Growth Experiments 495
    10.8.1 Crack Growth Rate and Threshold Measurement 496
    10.8.2 Closure Measurements 498
    10.8.3 A Proposed Experimental Definition of DKeff 500
    10.9 Damage Tolerance Methodology 501
    Appendix 10: Application of The J Contour Integral to Cyclic Loading 504
    A10.1 Definition of D J 504
    A10.2 Path Independence of D J 506
    A10.3 Small-Scale Yielding Limit 507
    References 507
    Chapter 11
    Environmentally Assisted Cracking in Metals 511
    11.1 Corrosion Principles 511
    11.1.1 Electrochemical Reactions 511
    11.1.2 Corrosion Current and Polarization 514
    11.1.3 Electrode Potential and Passivity 514
    11.1.4 Cathodic Protection 515
    11.1.5 Types of Corrosion 516
    11.2 Environmental Cracking Overview 516
    11.2.1 Terminology and Classification of Cracking Mechanisms 516
    11.2.2 Occluded Chemistry of Cracks, Pits, and Crevices 517
    11.2.3 Crack Growth Rate vs. Applied Stress Intensity 518
    11.2.4 The Threshold for EAC 520
    11.2.5 Small Crack Effects 521
    11.2.6 Static, Cyclic, and Fluctuating Loads 523
    11.2.7 Cracking Morphology 523
    11.2.8 Life Prediction 523
    11.3 Stress Corrosion Cracking 525
    11.3.1 The Film Rupture Model 527
    11.3.2 Crack Growth Rate in Stage II 528
    11.3.3 Metallurgical Variables that Influence SCC 528
    11.3.4 Corrosion Product Wedging 529
    11.4 Hydrogen Embrittlement 529
    11.4.1 Cracking Mechanisms 530
    11.4.2 Variables that Affect Cracking Behavior 531
    11.4.2.1 Loading Rate and Load History 531
    11.4.2.2 Strength 533
    11.4.2.3 Amount of Available Hydrogen 535
    11.4.2.4 Temperature 535
    11.5 Corrosion Fatigue 538
    11.5.1 Time-Dependent and Cycle-Dependent Behavior 538
    11.5.2 Typical Data 541
    11.5.3 Mechanisms 543
    11.5.3.1 Film Rupture Models 544
    11.5.3.2 Hydrogen Environment Embrittlement 544
    11.5.3.3 Surface Films 544
    11.5.4 The Effect of Corrosion Product Wedging on Fatigue 544
    11.6 Experimental Methods 545
    11.6.1 Tests on Smooth Specimens 546
    11.6.2 Fracture Mechanics Test Methods 547
    References 552
    Chapter 12
    Computational Fracture Mechanics 553
    12.1 Overview of Numerical Methods 553
    12.1.1 The Finite Element Method 554
    12.1.2 The Boundary Integral Equation Method 556
    12.2 Traditional Methods in Computational Fracture Mechanics 558
    12.2.1 Stress and Displacement Matching 558
    12.2.2 Elemental Crack Advance 559
    12.2.3 Contour Integration 560
    12.2.4 Virtual Crack Extension: Stiffness Derivative Formulation 560
    12.2.5 Virtual Crack Extension: Continuum Approach 561
    12.3 The Energy Domain Integral 563
    12.3.1 Theoretical Background 563
    12.3.2 Generalization to Three Dimensions 566
    12.3.3 Finite Element Implementation 568
    12.4 Mesh Design 570
    12.5 Linear Elastic Convergence Study 577
    12.6 Analysis of Growing Cracks 585
    Appendix 12: Properties of Singularity Elements 587
    A12.1 Quadrilateral Element 587
    A12.2 Triangular Element 589
    References 590
    Chapter 13
    Practice Problems 593
    13.1 Chapter 1 593
    13.2 Chapter 2 593
    13.3 Chapter 3 596
    13.4 Chapter 4 598
    13.5 Chapter 5 599
    13.6 Chapter 6 600
    13.7 Chapter 7 600
    13.8 Chapter 8 603
    13.9 Chapter 9 605
    13.10 Chapter 10 607
    13.11 Chapter 11 608
    13.12 Chapter 12 609
    Index 611

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