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 |  موضوع: كتاب Fracture Mechanics - Fundamentals and Applications السبت 23 فبراير 2019, 11:07 pm | |
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Fracture Mechanics - Fundamentals and Applications
T.L. Anderson, Ph.D.
ويتناول الموضوعات الأتية :
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 ?-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 562.7 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 1403.6.2.1 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 213Part 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 293Part 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 J
Ic 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 K
Ia 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 3738.3 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 47310.5.1 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 ?K 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 ?Keff 500
10.9 Damage Tolerance Methodology 501
Appendix 10: Application of The J Contour Integral to Cyclic Loading .504
A10.1 Definition of ?J 504
A10.2 Path Independence of ?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 53511.5 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 .
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