E-Book, Englisch, Band 227, 305 Seiten, eBook
Detect - Assess - Avoid
E-Book, Englisch, Band 227, 305 Seiten, eBook
Reihe: Solid Mechanics and Its Applications
ISBN: 978-3-319-32534-7
Verlag: Springer International Publishing
Format: PDF
Kopierschutz: Wasserzeichen (»Systemvoraussetzungen)
The target group includes graduate students, researchers at universities and practicing engineers.
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Professional/practitioner
Autoren/Hrsg.
Weitere Infos & Material
1;Preface;6
2;Contents;8
3;Symbols;15
4;1 Designing Components and Structures According to Strength Criteria;20
4.1;1.1 Loads on Components and Structures;21
4.2;1.2 Stresses and Stress States in Components and Structures;24
4.2.1;1.2.1 Plane Stress State;25
4.2.2;1.2.2 Spatial Stress State;25
4.2.3;1.2.3 Principal Stresses;25
4.2.4;1.2.4 Plane Stress State or Plane Strain State;27
4.3;1.3 Proof of Static Strength;28
4.3.1;1.3.1 Equivalent Stress;28
4.3.2;1.3.2 Allowable Stress;29
4.3.3;1.3.3 Proof of Strength—Operational Sequence;30
4.3.4;1.3.4 Taking Account of the Notch Effect;31
4.3.5;1.3.5 Stress Concentration Factors;32
4.3.6;1.3.6 Material Parameters and Safety Factors;32
4.4;1.4 Proof of Fatigue Strength;37
4.4.1;1.4.1 Effective and Allowable Stresses;37
4.4.2;1.4.2 Material Parameters;38
4.4.3;1.4.3 Surface and Size Coefficients;40
4.4.4;1.4.4 Proof of Fatigue Strength with Notched Components;42
4.5;1.5 Proof of Structural Durability;42
4.6;1.6 Other Proofs;43
4.7;1.7 Limits of Classic Component Design;43
4.8;References;44
5;2 Damages Caused by Crack Growth;45
5.1;2.1 Crack Initiation and Crack Growth;47
5.2;2.2 Stable and Unstable Crack Growth;49
5.3;2.3 Damage Analysis/Fracture Surface Analysis;50
5.4;2.4 Fatigue Crack Growth in an ICE Wheel Tire;54
5.5;2.5 Crack Growth in a Press Frame;55
5.6;2.6 Fatigue Crack Growth in the Fastener Body of an Internal High-Pressure Metal Forming Machine;57
5.7;2.7 Fracture of the Drive Shaft of a Vintage Car;57
5.8;2.8 Other Damage Events;57
5.9;2.9 Basic Crack Paths and Crack Shapes in Components and Structures;59
5.9.1;2.9.1 Crack Paths of Basic Stress States;60
5.9.2;2.9.2 Crack Paths and Crack Shapes in Shafts;61
5.9.3;2.9.3 Systematizing Crack Types in Components and Structures;63
5.10;2.10 Crack Detection Using Non-destructive Testing Methods;67
5.11;References;69
6;3 Fundamentals of Fracture Mechanics;72
6.1;3.1 Cracks and Crack Modes;72
6.1.1;3.1.1 Mode I;73
6.1.2;3.1.2 Mode II;74
6.1.3;3.1.3 Mode III;74
6.1.4;3.1.4 Mixed Mode;74
6.2;3.2 Stress Distributions at Cracks;75
6.2.1;3.2.1 Solving Crack Problems with Elasticity Theory;75
6.2.2;3.2.2 Stress Distributions for Plane Crack Problems;76
6.2.2.1;3.2.2.1 Stress Distributions in Mode I;78
6.2.2.2;3.2.2.2 Stress Distributions for Plane Mixed-Mode Loading;78
6.2.3;3.2.3 Stress Distributions for Spatial Crack Problems;81
6.2.3.1;3.2.3.1 Stress Distributions in Cartesian Coordinates;81
6.2.3.2;3.2.3.2 Stress Distributions in Cylindrical Coordinates;81
6.3;3.3 Displacement Fields Near the Crack;83
6.4;3.4 Stress Intensity Factors;84
6.4.1;3.4.1 Stress Intensity Factors for Crack Modes I, II and III;84
6.4.1.1;3.4.1.1 Definition of the Stress Intensity Factors KI, KII, KIII;84
6.4.1.2;3.4.1.2 Dimension and Unit of Stress Intensity Factors;85
6.4.2;3.4.2 Stress Intensity Factors for Basic Crack Problems;85
6.4.2.1;3.4.2.1 Griffith Crack in an Infinitely Extended Plate;85
6.4.2.2;3.4.2.2 Circular Crack in an Infinitely Extended Body Under Tensile Loading;86
6.4.2.3;3.4.2.3 Internal Crack in a Finitely Extended Plate;86
6.4.2.4;3.4.2.4 Edge Crack in a Semi-infinitely and Finitely Extended Plate Under Tensile Loading;87
6.4.2.5;3.4.2.5 Inclined Internal Crack in an Infinitely Extended Plate Under Uniaxial Loading;88
6.4.2.6;3.4.2.6 Semi-elliptical Surface Crack in a Tensile-Loaded Component;89
6.4.2.7;3.4.2.7 Semi-circular Edge Crack in a Component;90
6.4.2.8;3.4.2.8 Notch Crack Problems;92
6.4.2.9;3.4.2.9 Interpolation Formula for Mode I Stress Intensity Factors;94
6.4.2.10;3.4.2.10 Interpolation Formulae for Mode II and Mode III Stress Intensity Factors;94
6.4.3;3.4.3 Superposition of Stress Intensity Factors, Equivalent Stress Intensity Factors;94
6.4.3.1;3.4.3.1 Superposition of Stress Intensity Factors;96
6.4.3.2;3.4.3.2 Equivalent Stress Intensity Factor with Plane Mixed-Mode Loading;97
6.4.3.3;3.4.3.3 Equivalent Stress Intensity Factor with Spatial Mixed-Mode Loading;98
6.5;3.5 Local Plasticity at the Crack Tip;101
6.5.1;3.5.1 Estimating the Plastic Zone;101
6.5.2;3.5.2 Crack Length Correction;104
6.5.3;3.5.3 Significance of the Plastic Zone in Fatigue Crack Propagation;105
6.6;3.6 Energy Release Rate and the J-Integral;105
6.6.1;3.6.1 Energy Release Rate;105
6.6.2;3.6.2 J-Integral;106
6.7;3.7 Determining the Stress Intensity Factors and Other Fracture-Mechanical Quantities;107
6.7.1;3.7.1 Determining the Stress Intensity Factors from the Stress Field in the Vicinity of the Crack;108
6.7.2;3.7.2 Determining the Stress Intensity Factors from the Displacement Field in the Vicinity of the Crack;109
6.7.3;3.7.3 Determining Fracture-Mechanical Quantities with the J-Integral;109
6.7.4;3.7.4 Determining Fracture-Mechanical Quantities with the Crack Closure Integral;110
6.8;3.8 Concepts for Predicting Unstable Crack Growth;112
6.8.1;3.8.1 K-Concept for Mode I;113
6.8.2;3.8.2 K-Concept for Mode II, Mode III and Mixed Mode Loadings;113
6.8.2.1;3.8.2.1 K-Concept for Mode II;114
6.8.2.2;3.8.2.2 K-Concept for Mode III;114
6.8.2.3;3.8.2.3 K-Concept for Plane Mixed Mode;115
6.8.2.4;3.8.2.4 K-Concept for Spatial Mixed Mode;116
6.8.3;3.8.3 Criterion of Energy Release Rate;119
6.8.4;3.8.4 J-Criterion;119
6.9;3.9 Fracture Toughness;120
6.10;3.10 Assessing Components with Cracks Using Fracture-Mechanical Methods;120
6.10.1;3.10.1 Fracture-Mechanical Proof—Operational Sequence;120
6.10.2;3.10.2 Applying the Fracture Criterion and the Fracture-Mechanical Analysis to Mode I Crack Problems;122
6.10.3;3.10.3 Applying the Fracture Criterion and the Fracture-Mechanical Analysis to Mode II, Mode III and Mixed Mode Problems;124
6.11;3.11 Combining Strength Calculation and Fracture Mechanics;125
6.12;References;128
7;4 Fatigue Crack Growth Under Cyclic Loading with Constant Amplitude;130
7.1;4.1 Relation Between Component Loading and Cyclic Stress Intensity;131
7.1.1;4.1.1 Stress Fields with Time-Varying Mode I Loading;132
7.1.2;4.1.2 Cyclic Stress Intensity Factor for Mode I;132
7.1.3;4.1.3 R-ratio;133
7.1.4;4.1.4 Crack Propagation Process;134
7.1.5;4.1.5 Stress Field with Time-Varying Mode II, Mode III and Mixed-Mode Loading;134
7.1.6;4.1.6 Cyclic Stress Intensity Factor for Mode II;135
7.1.7;4.1.7 Cyclic Stress Intensity Factor for Mode III;136
7.1.8;4.1.8 Two-Dimensional Mixed-Mode Loading;136
7.1.9;4.1.9 Three-Dimensional Mixed-Mode Loading;136
7.2;4.2 Relationship Between Crack Growth Rate and the Cyclic Stress Intensity Factor;137
7.2.1;4.2.1 Limits of Fatigue Crack Propagation for Mode I;139
7.2.2;4.2.2 Factors Influencing the Crack Growth Curve;139
7.2.3;4.2.3 Crack Closure Behavior During Fatigue Crack Growth;140
7.2.3.1;4.2.3.1 Plasticity-Induced Crack Closure;141
7.2.3.2;4.2.3.2 Roughness-Induced Crack Closure;141
7.2.3.3;4.2.3.3 Oxide-Induced Crack Closure;142
7.2.3.4;4.2.3.4 Fluid-Induced Crack Closure;143
7.2.3.5;4.2.3.5 Determining the Crack Opening Stress Intensity Factor;143
7.2.4;4.2.4 Threshold Value and Threshold Value Behavior;144
7.2.4.1;4.2.4.1 Threshold Value Behavior on the Basis of Crack Closure;145
7.2.4.2;4.2.4.2 Two-Criteria Approach to Threshold Value Behavior;146
7.3;4.3 Crack Propagation Concepts for Mode I;149
7.3.1;4.3.1 Paris Law;150
7.3.2;4.3.2 Erdogan/Ratwani Law;150
7.3.3;4.3.3 Forman/Mettu Equation;151
7.3.4;4.3.4 Comparison of the Crack Propagation Equations;152
7.3.5;4.3.5 Determining Residual Lifetime;154
7.4;4.4 Crack Growth Under Mode II, Mode III and Mixed-Mode Loading;157
7.4.1;4.4.1 Crack Growth Under Mode II Loading on the Initial Crack;157
7.4.2;4.4.2 Crack Growth Under Mode III Loading on the Initial Crack;159
7.4.3;4.4.3 Crack Growth Under Two-Dimensional Mixed-Mode Loading;159
7.4.4;4.4.4 Crack Growth Under Three-Dimensional Mixed-Mode Loading;160
7.5;4.5 Procedure for Assessing Fatigue Crack Growth;161
7.5.1;4.5.1 Fracture-Mechanical Assessment of Fatigue Crack Growth;162
7.5.2;4.5.2 Determining the Crack Length at Which Fatigue Crack Growth Is Possible;163
7.5.3;4.5.3 Safety Against the Occurrence of Fatigue Crack Growth;164
7.5.4;4.5.4 Area of Fatigue Crack Growth;164
7.5.5;4.5.5 Defining Inspection Intervals;165
7.6;4.6 Combination of Fatigue Strength Calculation and Fracture Mechanics;166
7.7;References;167
8;5 Experimental Determination of Fracture-Mechanical Material Parameters;169
8.1;5.1 Critical Stress Intensity Factor and Fracture Toughness;169
8.1.1;5.1.1 Determining Fracture Toughness According to ASTM E 399;170
8.1.1.1;5.1.1.1 Test Specimens and Sampling;170
8.1.1.2;5.1.1.2 Minimum Specimen Dimensions;172
8.1.1.3;5.1.1.3 Starter Notch and Initial Fatigue Crack;173
8.1.2;5.1.2 Testing Methods for Determining the Fracture Toughness;174
8.1.3;5.1.3 KIC or KQ?—Assessment of the Tests;174
8.1.3.1;5.1.3.1 Finding KQ and KIC Values in Force-Displacement Diagrams;174
8.1.3.2;5.1.3.2 Crack Length Measurement;175
8.1.3.3;5.1.3.3 Validity of the KIC Test;177
8.2;5.2 Threshold Values and Crack Growth Curves;177
8.2.1;5.2.1 Determining Threshold Values and Crack Growth Curves Acc. to ASTM E 647;177
8.2.1.1;5.2.1.1 Test Specimens and Specimen Dimensions;178
8.2.1.2;5.2.1.2 Starter Notch and Precracking;179
8.2.1.3;5.2.1.3 Testing Methods for Determining the Fatigue Crack Growth Curve;180
8.2.2;5.2.2 Methods of Determining the Threshold Value;181
8.2.2.1;5.2.2.1 Tests with a Constant Stress Ratio;182
8.2.2.2;5.2.2.2 Tests with a Constant Maximum Stress Intensity;183
8.2.2.3;5.2.2.3 Tests with Increasing Cyclic Stress Intensity;183
8.2.3;5.2.3 Methods of Measuring Crack Length;184
8.2.3.1;5.2.3.1 Optical Methods;184
8.2.3.2;5.2.3.2 Current Potential Drop Method;185
8.2.3.3;5.2.3.3 Compliance Method;187
8.2.3.4;5.2.3.4 Crack Length Measurement on Fractured Specimens;187
8.2.4;5.2.4 Determining the Fatigue Crack Growth Rate;188
8.2.4.1;5.2.4.1 Secant Method;188
8.2.4.2;5.2.4.2 Incremental Polynomial Method;189
8.2.5;5.2.5 Evaluating the Threshold Value and Crack Growth Curve Tests;189
8.3;5.3 Material Parameters for Mode I Crack Growth;191
8.3.1;5.3.1 Fracture Toughnesses;191
8.3.1.1;5.3.1.1 Basic Dependencies of Fracture Toughnesses;191
8.3.1.2;5.3.1.2 Overview of the Fracture Toughnesses of Various Materials;191
8.3.1.3;5.3.1.3 Fracture Toughnesses for Selected Materials;191
8.3.2;5.3.2 Threshold Values of Fatigue Crack Growth;193
8.3.3;5.3.3 Fatigue Crack Growth Curves;193
8.3.3.1;5.3.3.1 Basic Course of the Crack Growth Curves for Selected Materials;194
8.3.3.2;5.3.3.2 Parameters for the Paris Equation;194
8.3.3.3;5.3.3.3 Parameters for the Forman/Mettu Equation;195
8.4;5.4 Material Parameters for Mode II and Mixed-Mode Loading;195
8.4.1;5.4.1 Mode II Loading;197
8.4.2;5.4.2 Two-Dimensional Mixed-Mode Loading;198
8.4.3;5.4.3 Three-Dimensional Mixed-Mode Loading;199
8.5;References;201
9;6 Fatigue Crack Growth Under Service Loads;203
9.1;6.1 Load Spectra and Cumulative Frequency Distribution;203
9.1.1;6.1.1 Determining Service Loads;204
9.1.2;6.1.2 Counting Methods;204
9.1.3;6.1.3 Standard Load Spectra;205
9.2;6.2 Interaction Effects;207
9.2.1;6.2.1 Overloads;207
9.2.1.1;6.2.1.1 Effect of Overloads on Fatigue Crack Growth;208
9.2.1.2;6.2.1.2 Quantifying Retardation Behavior;209
9.2.1.3;6.2.1.3 Factors Influencing the Retardation Effect;210
9.2.2;6.2.2 Underloads;212
9.2.3;6.2.3 Combinations of Underloads and Overloads;212
9.2.4;6.2.4 Overload Sequences;212
9.2.5;6.2.5 Block Loading;214
9.2.6;6.2.6 Service Loads;216
9.2.6.1;6.2.6.1 Effect of Service Loads;216
9.2.6.2;6.2.6.2 Implications of Reconstructing Load-Time Functions;217
9.2.6.3;6.2.6.3 Implications of Extrapolating Load-Time Functions;218
9.3;6.3 Crack Propagation Concepts for Variable Amplitude Loading;220
9.3.1;6.3.1 Global Analyses;220
9.3.2;6.3.2 Linear Damage Accumulation;221
9.3.3;6.3.3 Yield Zone Models;222
9.3.3.1;6.3.3.1 Wheeler Model;224
9.3.3.2;6.3.3.2 Gray/Gallagher Model;226
9.3.3.3;6.3.3.3 Willenborg Model;227
9.3.4;6.3.4 Crack Closure Models;229
9.3.5;6.3.5 Strip Yield Models;230
9.4;6.4 Mixed-Mode Loading;232
9.4.1;6.4.1 Crack Growth After a Change in the Loading Direction or in the Local Load at the Crack;233
9.4.2;6.4.2 Effect of Mixed-Mode Overloads on Fatigue Crack Growth;234
9.5;References;235
10;7 Simulations of Fatigue Crack Growth;238
10.1;7.1 Analytical Crack Growth Simulations;238
10.1.1;7.1.1 NASGRO and ESACRACK;239
10.1.2;7.1.2 AFGROW;240
10.2;7.2 Numerical Crack Growth Simulations;241
10.2.1;7.2.1 Basic Procedure with Finite Elements;241
10.2.2;7.2.2 Program System FRANC/FAM for Two-Dimensional Crack Propagation Simulations;244
10.2.3;7.2.3 Program System ADAPCRACK3D for Three-Dimensional Crack Propagation Simulations;245
10.3;7.3 Determining the Effect of Load Changes with Finite Element Analyses;247
10.4;References;250
11;8 Crack Initiation Under Cyclic Loading;253
11.1;8.1 Models for Describing Crack Initiation;254
11.1.1;8.1.1 Threshold Value Curve Concept;255
11.1.2;8.1.2 Theories of Critical Distances;257
11.1.3;8.1.3 Fatigue Crack Resistance Curve Concept;258
11.1.4;8.1.4 ?area Concept;260
11.2;8.2 Short Crack Growth;262
11.3;References;263
12;9 Practical Examples;265
12.1;9.1 Leak in a Pipeline;265
12.1.1;9.1.1 Stresses in the Pipe;265
12.1.2;9.1.2 Stress Intensity Factors for the Crack;267
12.1.3;9.1.3 Safety Against Unstable Crack Propagation;267
12.1.4;9.1.4 Crack Length at Which Unstable Crack Propagation Initiates;268
12.2;9.2 Investigating Fatigue Crack Growth in ICE Tires;268
12.2.1;9.2.1 Structure and Load of Rubber-Sprung Wheels;268
12.2.2;9.2.2 Numerical Stress Analysis;270
12.2.3;9.2.3 Damage Analysis of the Wheel Tire Fracture;271
12.2.4;9.2.4 Fracture-Mechanical Characterization of the Tire Material;272
12.2.5;9.2.5 Numerical Simulation of Fatigue Crack Growth;272
12.2.6;9.2.6 Experimental Simulation of Crack Growth;274
12.3;9.3 Simulation of Fatigue Crack Growth in a Press Frame;276
12.4;9.4 Preventing Crack Growth in a Piston;279
12.5;9.5 Investigating Crack Growth in an Aircraft Structure;281
12.6;9.6 Parameter Study of a Surface Crack in a Shaft Under Rotating Bending Load;284
12.6.1;9.6.1 Influence of the Cumulative Frequency Distribution;285
12.6.2;9.6.2 Influence of the Notch Effect and Press-Fit Stresses;287
12.6.3;9.6.3 Influence of the Initial Crack Depth and Geometry on Residual Life Simulation;288
12.7;9.7 Restoration of a Press;289
12.7.1;9.7.1 Modeling the Crack Geometry in the Sealing Cap;290
12.7.2;9.7.2 Stress Analysis for the Cap;290
12.7.3;9.7.3 Results of the FE Analyses for the Cracked Sealing Cap;291
12.7.4;9.7.4 Fracture-Mechanical Assessment of the FE Results;291
12.7.5;9.7.5 Consequences for Continued Machine Operation;292
12.8;9.8 Measures for Extending the Residual Life of Machines and Equipment;292
12.8.1;9.8.1 Continued Operation of a Machine or System After Crack Detection;293
12.8.1.1;9.8.1.1 Continued Operation with Regular Inspections;293
12.8.1.2;9.8.1.2 Continuous Operation Under Reduced Load;294
12.8.1.3;9.8.1.3 Extending Residual Life by Means of Targeted Restoration Measures;294
12.8.1.4;9.8.1.4 Exchanging the Damaged Component;295
12.8.2;9.8.2 Optimization Measures for a New Design;295
12.8.2.1;9.8.2.1 Limiting or Reducing Component Load;295
12.8.2.2;9.8.2.2 Reducing Local Stresses in the Component;295
12.8.2.3;9.8.2.3 Selecting a Material that Is Less Susceptible to Cracking;295
12.8.2.4;9.8.2.4 Preventing Manufacturing Defects;296
12.8.2.5;9.8.2.5 Optimization Potential;296
12.9;References;296
13;Index;298
Preface.- 1 Designing Components and Structures According to Strength Criteria.- 2 Damages Caused by Crack Growth.- 3 Fundamentals of Fracture Mechanics.- 4 Fatigue Crack Growth under Cyclic Loading with Constant Amplitude.- 5 Experimental Determination of Fracture-Mechanical Material Parameters.- 6 Fatigue Crack Growth under Service Loads.- 7 Simulations of Fatigue Crack Growth.- 8 Crack Initiation under Cyclic Loading.- 9 Practical Examples.- 10 Important Symbols.- Index.
