《Virtual testing and predictive modeling: for fatigue and fracture mechanic...
《Virtual testing and predictive modeling: for fatigue and fracture mechanics allowables》虚拟测试和预测模型：疲劳与断裂力学
编者：
Bahram Farahmand
TASS – Americas, a subsidiary of TASS Inc.
出版社：Springer
出版时间：2009年
目录
1 Virtual Testing and Its Application in Aerospace Structural
Parts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Bahram Farahmand
1.1 Introduction to the Virtual Testing . . . . . . . . . . . . . . . . 2
1.2 Virtual Testing Theory and Fracture Toughness . . . . . . . . . 2
1.3 The Extended Griffith Theory and Fracture Toughness . . . . . 3
1.4 Extension of Farahmand’s Theory to Fatigue Crack
GrowthRateData . . . . . . . . . . . . . . . . . . . . . . . . 6
1.4.1 The Accelerated Region and Fracture Toughness . . . . 6
1.4.2 The Paris Constants, C and n . . . . . . . . . . . . . . 7
1.4.3 TheThresholdValue (Region I) . . . . . . . . . . . . 8
1.4.4 The da/dN Versus ΔK from Virtual Testing
AgainstTestData . . . . . . . . . . . . . . . . . . . . 9
1.5 Application of Virtual Testing in Aerospace Industry:
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.5.1 Background . . . . . . . . . . . . . . . . . . . . . . . 13
1.5.2 Manufacturing Process and Plastic Deformation
ofCOPVLiner . . . . . . . . . . . . . . . . . . . . . 14
1.5.3 Generating Fracture Allowables of Inconel 718
of COPV Liner Through Virtual Testing Technique . . 16
1.5.4 Generating Fracture Allowables of 6061-T6
Aluminum Tank Through Virtual Testing Technique . . 20
1.6 Summary andFutureWork . . . . . . . . . . . . . . . . . . . . 22
Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2 Tools for Assessing the Damage Tolerance of Primary
Structural Components . . . . . . . . . . . . . . . . . . . . . . . . 29
R. Jones and D. Peng
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.2 An Equivalent Block Method for Predicting Fatigue
CrackGrowth . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.3 Fatigue Crack Growth under Variable Amplitude Loading . . . 33
2.3.1 Fatigue Crack Growth in an F/A-18 Aircraft Bulkhead 36
xi
xii Contents
2.3.2 Crack Growth in Mil Annealed Ti–6AL–4V
under a Fighter Spectrum . . . . . . . . . . . . . . . . 38
2.4 A Virtual Engineering Approach for Predicting the S–N
Curves for 7050-T7451 . . . . . . . . . . . . . . . . . . . . . . 40
2.4.1 Computing the Endurance Limit . . . . . . . . . . . . 41
2.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
Appendix: Formulae for Computing the Crack Opening Stress . . . . . 43
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3 Cohesive Technology Applied to the Modeling
and Simulation of Fatigue Failure . . . . . . . . . . . . . . . . . . . 47
Spandan Maiti
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.2.1 Models for the Prediction of Threshold Fatigue
CrackBehavior . . . . . . . . . . . . . . . . . . . . . 49
3.2.2 Models for the Prediction of Fatigue Crack
Propagation . . . . . . . . . . . . . . . . . . . . . . . 50
3.3 Cohesive Modeling Technique . . . . . . . . . . . . . . . . . . 51
3.3.1 Reversible Cohesive Model . . . . . . . . . . . . . . . 53
3.3.2 A Bilinear Cohesive Law . . . . . . . . . . . . . . . . 54
3.3.3 A Cohesive Model Suitable for Fatigue Failure . . . . 56
3.3.4 Incorporation of Threshold Behavior . . . . . . . . . . 58
3.3.5 FiniteElement Implementation . . . . . . . . . . . . . 59
3.4 SimulationResults . . . . . . . . . . . . . . . . . . . . . . . . 61
3.4.1 ParisCurveSimulation . . . . . . . . . . . . . . . . . 61
3.4.2 Prediction of Threshold Limit of Fatigue Crack Growth 65
3.4.3 Effect of on theThresholdLimit . . . . . . . . . . . . 66
3.4.4 Effect of Load Ratio R on Fatigue Crack Threshold . . 68
3.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4 Fatigue Damage Map as a Virtual Tool for Fatigue
Damage Tolerance . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
Chris A. Rodopoulos
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.2 The Basic Understanding of Fatigue Damage . . . . . . . . . . 74
4.2.1 Development of Fatigue Cracks and Fatigue
Damage Stages . . . . . . . . . . . . . . . . . . . . . 74
4.2.2 Stage II Fatigue Cracking . . . . . . . . . . . . . . . . 77
4.2.3 Stage I Fatigue Cracking . . . . . . . . . . . . . . . . 78
4.2.4 Stage III Fatigue Cracks . . . . . . . . . . . . . . . . . 84
4.3 Fatigue Damage Map the Basic Rationale – The
Navarro–de los Rios Model . . . . . . . . . . . . . . . . . . . 85
4.3.1 Fatigue Damage Map – Defining the Stages of
FatigueDamage . . . . . . . . . . . . . . . . . . . . . 89
Contents xiii
4.3.2 Fatigue Damage Map – Defining the
Propagation Rate of Fatigue Stages . . . . . . . . . . . 97
4.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
5 Predicting Creep and Creep/Fatigue Crack Initiation and
Growth for Virtual Testing and Life Assessment of Components . . 105
K.M. Nikbin
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
5.1.1 Background to Life Assessment Codes . . . . . . . . . 106
5.1.2 CreepAnalysis ofUncrackedBodies . . . . . . . . . . 107
5.1.3 Physical Models Describing Creep . . . . . . . . . . . 108
5.1.4 ComplexStressCreep . . . . . . . . . . . . . . . . . . 110
5.1.5 Influence of Fatigue in Uncracked Bodies . . . . . . . 112
5.2 Fracture Mechanics Parameters in Creep and Fatigue . . . . . . 113
5.2.1 Creep Parameter C∗ Integral . . . . . . . . . . . . . . 114
5.3 Predictive Models in High-Temperature Fracture Mechanics . . 116
5.3.1 Derivation of K and C∗ . . . . . . . . . . . . . . . . . 116
5.3.2 Example of CCG Correlation with K and C∗ . . . . . . 117
5.3.3 Modelling Steady-State Creep Crack Growth Rate . . . 118
5.3.4 Transient Creep Crack Growth Modelling . . . . . . . 121
5.3.5 Predictions of Initiation Times ti Prior Onset of
Steady Creep Crack Growth . . . . . . . . . . . . . . 124
5.3.6 Consideration of Crack Tip Angle in the
NSW Model . . . . . . . . . . . . . . . . . . . . . . . 125
5.3.7 The New NSW-MOD Model . . . . . . . . . . . . . . 126
5.3.8 FiniteElementFramework . . . . . . . . . . . . . . . 127
5.3.9 Damage Accumulation at the Crack Tip . . . . . . . . 128
5.3.10 ElevatedTemperatureCyclicCrackGrowth . . . . . . 130
5.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
5.5 Nomenclatures and Abbreviations . . . . . . . . . . . . . . . . 133
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
6 Computational Approach Toward Advanced Composite
Material Qualification and Structural Certification . . . . . . . . . 137
Frank Abdi, J. Surdenas, Nasir Munir, Jerry Housner,
and Raju Keshavanarayana
6.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
6.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
6.2.1 FAA Durability and Damage Tolerance
CertificationStrategy . . . . . . . . . . . . . . . . . . 138
6.2.2 Damage Categories and Comparison of
Analysis Methods and Test Results . . . . . . . . . . . 139
6.2.3 FAA Building-Block Approach . . . . . . . . . . . . . 148
6.2.4 Test Reduction Process . . . . . . . . . . . . . . . . . 151
xiv Contents
6.3 Computational Process for Implementing
Building-BlockVerification . . . . . . . . . . . . . . . . . . . 153
6.3.1 Multiple Failure Criteria . . . . . . . . . . . . . . . . 154
6.3.2 Micro- and Macro-Composite Mechanics Analysis . . 156
6.3.3 Progressive Failure Micro-Mechanical Analysis . . . . 157
6.3.4 Calibration of Composite Constitutive Properties . . . 158
6.3.5 CompositeMaterialValidation . . . . . . . . . . . . . 159
6.3.6 Material Uncertainty Analyzer (MUA) . . . . . . . . . 161
6.4 EstablishA- andB-BasisAllowables . . . . . . . . . . . . . . 163
6.4.1 Combining Limited Test Data with Progressive
Failure and Probabilistic Analysis . . . . . . . . . . . 164
6.4.2 Examples of Allowable Generation for
Unnotched and Notched Composite Specimens . . . . 166
6.5 Certification byAnalysisExample . . . . . . . . . . . . . . . . 171
6.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
7 Modeling ofMultiscale Fatigue Crack Growth: Nano/Micro
and Micro/Macro Transitions . . . . . . . . . . . . . . . . . . . . . 187
G.C. Sih
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
7.2 Scale Implications Associated with Size Effects . . . . . . . . . 190
7.2.1 Physical Laws Change with Size and Time . . . . . . . 190
7.2.2 Surface-to-Volume Ratio as a Controlling Parameter . . 191
7.2.3 Strength and Toughness: Nano, Micro and Macro . . . 192
7.3 FormInvariant ofTwo-ParameterCrackGrowthRelation . . . . 193
7.4 Dual-Scale Fatigue Crack Growth Rate Models . . . . . . . . . 194
7.4.1 Micro/MacroFormulation . . . . . . . . . . . . . . . 196
7.4.2 Nano/Micro Formulation . . . . . . . . . . . . . . . . 197
7.5 Micro/Macro Time-Dependent Physical Parameters . . . . . . . 198
7.5.1 Macroscopic Material Properties . . . . . . . . . . . . 198
7.5.2 Microscopic Material Properties . . . . . . . . . . . . 201
7.6 Nano/Micro Time-Dependent Physical Parameters . . . . . . . 204
7.6.1 Nanoscopic Material Properties . . . . . . . . . . . . . 205
7.6.2 Nanoscopic Fatigue Crack Growth Coefficient . . . . . 207
7.7 FatigueCrackGrowth andVelocityData . . . . . . . . . . . . 208
7.7.1 PredictedMicro/MacroResults . . . . . . . . . . . . . 209
7.7.2 Predicted Nano/Micro Results . . . . . . . . . . . . . 210
7.8 Validation of Nano/Micro/Macro Fatigue Crack
GrowthBehavior . . . . . . . . . . . . . . . . . . . . . . . . . 212
7.9 Implication of Multiscaling and Future Considerations . . . . . 214
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
8 Multiscale Modeling of Nanocomposite Materials . . . . . . . . . . 221
Gregory M. Odegard
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221
Contents xv
8.2 Computational Modeling Tools . . . . . . . . . . . . . . . . . 223
8.3 Equivalent-Continuum Models . . . . . . . . . . . . . . . . . . 224
8.3.1 RepresentativeVolumeElement . . . . . . . . . . . . 224
8.3.2 Equivalent Continuum . . . . . . . . . . . . . . . . . 227
8.3.3 Equivalence of Averaged Scalar Fields . . . . . . . . . 231
8.3.4 Kinematic Equivalence . . . . . . . . . . . . . . . . . 232
8.4 Equivalent-Continuum Modeling Strategies . . . . . . . . . . . 233
8.4.1 Crystalline and Highly Ordered Material Systems . . . 233
8.4.2 Fluctuation Methods . . . . . . . . . . . . . . . . . . 234
8.4.3 Static Deformation Methods . . . . . . . . . . . . . . 235
8.4.4 Dynamic Deformation Methods . . . . . . . . . . . . 236
8.5 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236
8.5.1 Silica Nanoparticle/Polymer Composites . . . . . . . . 236
8.5.2 Nanotube/Polymer Composites . . . . . . . . . . . . . 238
8.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 242
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
9 Predictive Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . 247
Michael Doyle
9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248
9.2 Nanocomposites . . . . . . . . . . . . . . . . . . . . . . . . . 251
9.2.1 Nanotechnology and Modeling . . . . . . . . . . . . . 253
9.2.2 Composites . . . . . . . . . . . . . . . . . . . . . . . 255
9.2.3 The InterfaceRegion . . . . . . . . . . . . . . . . . . 258
9.2.4 Functionalization of Interface Region . . . . . . . . . 259
9.2.5 Modeling Approaches . . . . . . . . . . . . . . . . . . 262
9.2.6 MethodDevelopments . . . . . . . . . . . . . . . . . 265
9.3 Multiscale Modeling . . . . . . . . . . . . . . . . . . . . . . . 266
9.4 Continuum Methods . . . . . . . . . . . . . . . . . . . . . . . 267
9.4.1 Predicting Material Properties from the
Top-Down Approach . . . . . . . . . . . . . . . . . . 267
9.4.2 Analytical Continuum Modeling . . . . . . . . . . . . 268
9.4.3 Computational Continuum Modeling . . . . . . . . . . 268
9.5 Materials Engineering Simulation Across Multi-Length
and Time Scales . . . . . . . . . . . . . . . . . . . . . . . . . 269
9.5.1 Predicting Material Properties from the
Bottom-Up Approach . . . . . . . . . . . . . . . . . . 269
9.5.2 Quantum Scale . . . . . . . . . . . . . . . . . . . . . 271
9.5.3 Molecular Scale . . . . . . . . . . . . . . . . . . . . . 272
9.5.4 Molecular Dynamics . . . . . . . . . . . . . . . . . . 274
9.6 Extension of Atomistic Ensemble Methods . . . . . . . . . . . 275
9.6.1 Combining the Top-Down and Bottom-Up
Approaches . . . . . . . . . . . . . . . . . . . . . . . 275
9.7 Future Improvement . . . . . . . . . . . . . . . . . . . . . . . 278
9.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281
xvi Contents
10 Multiscale Approach to Predicting the Mechanical
Behavior of Polymeric Melts . . . . . . . . . . . . . . . . . . . . . . 291
R.C. Picu
10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291
10.2 Single and Multiscale Modeling Methods: Limitations
and Tradeoffs . . . . . . . . . . . . . . . . . . . . . . . . . . . 293
10.2.1 Atomistic and Atomistic-Like Models . . . . . . . . . 293
10.2.2 Molecular Models . . . . . . . . . . . . . . . . . . . . 296
10.2.3 Continuum Models . . . . . . . . . . . . . . . . . . . 297
10.3 Two Information-PassingExamples . . . . . . . . . . . . . . . 298
10.3.1 General Strategy . . . . . . . . . . . . . . . . . . . . . 298
10.3.2 Calibration of Rheological Constitutive Models . . . . 299
10.3.3 Developing Coarse-Grained Models of
PolymericMelts . . . . . . . . . . . . . . . . . . . . . 306
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317
11 Prediction of Damage Propagation and Failure of
Composite Structures (Without Testing) . . . . . . . . . . . . . . . 321
G. Labeas
11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321
11.2 Basics of Progressive Damage Modelling methodology . . . . . 323
11.2.1 PDM–AnOverview . . . . . . . . . . . . . . . . . . 323
11.2.2 Multiscale Computational Model . . . . . . . . . . . . 324
11.2.3 Prediction of Local Failure at Different Scale Levels . . 329
11.2.4 Behaviour of Damaged Material . . . . . . . . . . . . 331
11.3 Buckling and Damage Interaction of Open-Hole
CompositePlates byPDM . . . . . . . . . . . . . . . . . . . . 334
11.3.1 Composite Panel with Circular Cut-Out . . . . . . . . 334
11.3.2 Computational Model for the Open-Hole Panel
Problem . . . . . . . . . . . . . . . . . . . . . . . . . 335
11.3.3 Interaction Effects Between Damage Failure
andPlateBuckling . . . . . . . . . . . . . . . . . . . 337
11.4 Implementation ofPDMinCompositeBolted Joints . . . . . . 339
11.4.1 DescriptionofCompositeBolted JointProblem . . . . 339
11.4.2 Damage Initiation and Progression Within the
Bolted Joint . . . . . . . . . . . . . . . . . . . . . . . 342
11.5 Implementation of PDM in Composite Bonded Repairs . . . . . 345
11.5.1 Description of the Composite Repair Patch Problem . . 345
11.5.2 Details of PDM Model for Composite Repair
PatchAnalysis . . . . . . . . . . . . . . . . . . . . . . 346
11.5.3 Effects of Composite Patch Geometry and
Material ontheSIF . . . . . . . . . . . . . . . . . . . 348
11.6 Multi-Scale Modeling of Tensile Behavior of Carbon
Nanotube-Reinforced Composites . . . . . . . . . . . . . . . . 350
11.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353
Contents xvii
12 Functional Nanostructured Polymer–Metal Interfaces . . . . . . . 357
Niranjan A. Malvadkar, Michael A. Ulizio, Jill Lowman,
and Melik C. Demirel
12.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357
12.2 Oblique-Angle Polymerization . . . . . . . . . . . . . . . . . . 358
12.2.1 Nanostructured Polymer growth . . . . . . . . . . . . 358
12.2.2 Control of Morphology and Topography . . . . . . . . 360
12.3 Metallization of Nanostructured Polymers . . . . . . . . . . . . 361
12.3.1 Electroless Metal Deposition . . . . . . . . . . . . . . 362
12.3.2 Vapor Phase Metal Deposition . . . . . . . . . . . . . 363
12.3.3 Nanoparticle Assembly . . . . . . . . . . . . . . . . . 364
12.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 366
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 368
13 Advanced Experimental Techniques
for Multiscale Modeling of Materials . . . . . . . . . . . . . . . . . 371
Reza S. Yassar and Hessam M.S. Ghassemi
13.1 AtomicForceMicroscopy (AFM) . . . . . . . . . . . . . . . . 372
13.1.1 Principles ofAFM . . . . . . . . . . . . . . . . . . . 372
13.1.2 AFMOperation . . . . . . . . . . . . . . . . . . . . . 374
13.1.3 Application ofAFM. . . . . . . . . . . . . . . . . . . 375
13.1.4 Modeling andSimulation . . . . . . . . . . . . . . . . 379
13.2 X-RayUltra-Microscopy . . . . . . . . . . . . . . . . . . . . . 382
13.2.1 Principles ofXuM. . . . . . . . . . . . . . . . . . . . 382
13.2.2 Phase Contrast and Absorption Contrast . . . . . . . . 384
13.2.3 3D Imaging and Multiscale Modeling Applications . . 385
13.3 In Situ Micro-Electro-Mechanical-Systems (MEMS) Introduction 388
13.3.1 Principle andDesignofMEMSDevices . . . . . . . . 389
13.3.2 Application of MEMS Devices for Materials Modeling 392
13.4 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . 395
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 396
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399
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