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分享一本讲断裂力学的书：Fracture mechanics-fundamentals and applications
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在论坛里搜了一下，没有重复。这本书比较基础，讲的很全面。 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 Π-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 RCurve ....................................................................................................38 2.5.1 Reasons for the RCurve 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 Kand 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 Kand 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 JContour Integral .........................................................................................................107 3.2.1 Nonlinear Energy Release Rate ...............................................................................108 3.2.2 Jas a Path-Independent Line Integral .....................................................................110 3.2.3 Jas 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 Jand CTOD ...................................................................................120 3.4 Crack-Growth Resistance Curves ........................................................................................123 3.4.1 Stable and Unstable Crack Growth..........................................................................124 3.4.2 Computing Jfor 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 TStress..................................................................................................137 3.6.2 J-QTheory................................................................................................................140 3.6.2.1 The J-QToughness Locus.........................................................................142 3.6.2.2 Effect of Failure Mechanism on the J-QLocus.......................................................................................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 JContour Integral ...............................................................................156 A3.3 Jas 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 CtParameter ......................................................................................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 JIntegral .......................................................................................200 4.3.2.1 Constitutive Equations ..............................................................................200 4.3.2.2 Correspondence Principle..........................................................................200 4.3.2.3 Generalized JIntegral ...............................................................................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 KIc Testing ............................................................................................................................308 7.2.1 ASTM E 399 ............................................................................................................309 7.2.2 Shortcomings of E 399 and Similar Standards .......................................................312 7.3 K-RCurve Testing ................................................................................................................316 7.3.1 Specimen Design ......................................................................................................317 7.3.2 Experimental Measurement of K-RCurves .............................................................318 7.4 JTesting of Metals ...............................................................................................................320 7.4.1 The Basic Test Procedure and JIcMeasurements ....................................................320 7.4.2 J-RCurve Testing.....................................................................................................322 7.4.3 Critical JValues 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 KIaMeasurements .....................................................................................................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 Kand Jfor 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 KlcTesting .................................................................................................................362 8.1.4 JTesting....................................................................................................................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 KIfor 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 JEstimates.............................................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 JSolutions 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 ∆KValues....................................................................................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 JContour 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 ..........................................................................................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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