Nonlinear Ultrasonic and Vibro-Acoustical Techniques for Nondestructive Evaluation (eBook)

Tribikram Kundu is a Professor in the Department of Civil Engineering and Engineering Mechanics at the University of Arizona.  Dr. Kundu has made significant and original contributions in both basic and applied research in nondestructive testing (NDT) and structural health monitoring (SHM) by ultrasonic and electromagnetic techniques. His fundamental research interests are monitoring the health of existing and new structures by ultrasonic and other NDT techniques. His research requires knowledge of elastic wave propogation in multi-layered solids, fracture mechanics, computational mechanic, geo- and biomechanics. He has collaborated extensively with international and U.S. scientists. He has spent 28 months in the Department of Biology, J.W. Goethe University, Frankfurt, Germany, first as an Alexander von Humboldt Fellow and then as a Humboldt Research Prize winner. He is a Fellow of the Acoustical Society of America.

Contents 8
Contributors 10
1 Fundamentals of Nonlinear Acoustical Techniques and Sideband Peak Count 14
1.1 Introduction 14
1.2 Mechanics of Higher Harmonic Generation for Bulk Waves 17
1.2.1 Nonlinear Wave Equations 17
1.2.2 Acoustic Nonlinear Parameters for Longitudinal Waves 20
1.2.3 Acoustic Nonlinear Parameter for Transverse Waves 22
1.2.4 Use of Nonlinear Bulk Waves for Nondestructive Evaluation 25
1.2.4.1 Nonlinear Acoustic Parameter Measurement 25
1.2.4.2 Specimens and Experimental Setup 26
1.3 Higher Harmonic Generation for Guided Waves 29
1.3.1 Acoustic Nonlinear Parameter for Surface Wave Propagation 29
1.3.2 NDE Application Potential of Nonlinear Surface Waves 32
1.3.3 Nonlinear Lamb Waves 34
1.3.3.1 Phase Matched Lamb Wave Modes 36
1.3.4 NDE Applications of Nonlinear Lamb Waves 37
1.3.4.1 Example 1: Detection of Thermal Fatigue in Composites by Second Harmonic Lamb Waves 37
1.3.4.2 Example 2: Assessment of Thermal Fatigue in Pipes by Nonlinear Guided Waves 43
1.4 Higher Harmonic Generation by Different Types of Material Nonlinearity 52
1.5 Acoustoelastic Technique 55
1.6 Nonlinear Resonance Techniques 58
1.7 Pump Wave and Probe Wave-Based Techniques 62
1.7.1 Nonlinear Wave Modulation Spectroscopy (NWMS) 62
1.7.1.1 Mathematical Proof of the Side Band Generation 63
1.7.1.2 Experimental Configuration 65
1.7.2 Dynamic Acoustoelastic Test (DAET) 66
1.7.3 Pump Wave After-Effect Monitoring Through Coda Wave Interferometry 69
1.8 Subharmonic Phased Array for Crack Evaluation (SPACE) 70
1.9 Collinear and Non–Collinear Wave Mixing Techniques 71
1.9.1 Collinear Wave Mixing Technique 71
1.9.2 Non-Collinear Wave Mixing Technique 72
1.10 Recent Advances of Wave Modulation Techniques 73
1.10.1 Finding Optimal Combinations of Probing and Pumping Frequencies 74
1.10.2 Sideband Peak Count (SPC) Technique 75
1.10.2.1 Crack Detection in Aluminum Plate Specimens 84
1.10.2.2 Crack Detection in Aircraft Fitting-Lugs 88
1.10.2.3 Crack Localization in Aluminum Plate Specimens 90
1.11 Concluding Remarks 94
References 95
2 Nonlinear Resonant Ultrasound Spectroscopy: Assessing Global Damage 102
2.1 Introduction and Motivation 102
2.2 Nonlinearity in General: Background 103
2.3 Nonlinear Resonance Techniques: History 106
2.3.1 Complication: Rate Dependence 107
2.3.2 Complication: Hysteresis 110
2.4 Demonstration: Nonlinearity Correlates with Damage 110
2.5 Conclusions 112
References 112
3 Modeling and Numerical Simulations in Nonlinear Acoustics Used for Damage Detection 115
3.1 Introduction 115
3.2 Nonlinear Elastic Wave Propagation Problem Formulation 120
3.3 Numerical Models for Wave Propagation in Nonlinear Media 127
3.3.1 Nonlinear Media Models 129
3.3.1.1 The Finite Element Method for Wave Propagation in Nonlinear Media 130
3.3.1.2 The Local Interaction Simulation Approach for Wave Propagation in Nonlinear Media 133
3.3.2 Nonlinear Damage Models 135
3.3.3 Models Implemented Within the Finite Element Method Framework 137
3.3.3.1 Activation/Deactivation Method 137
3.3.3.2 Penalty Method 139
3.3.4 Models Within the Local Interaction Simulation Approach Framework 140
3.3.4.1 Spring Model 140
3.3.4.2 Coulomb Friction Model 143
3.4 Discussion and Conclusions 144
References 146
4 Structural Damage Detection Based on Nonlinear Acoustics: Application Examples 150
4.1 Introduction 150
4.2 Theoretical Background 151
4.3 Experimental Examples 155
4.3.1 Overview 155
4.3.2 Glass 157
4.3.3 Aluminium 158
4.3.4 Composite Laminates 165
4.3.4.1 Local Defect Resonance 168
4.3.4.2 Vibro-Acoustic Modulation-Based Damage Imaging 172
4.3.4.3 Triple Correlation for Damage Detection in Composite Structures 174
4.3.5 Composite Sandwich Panels 176
4.3.5.1 Chiral Core Sandwich Panel 176
4.3.5.2 Foam Core Sandwich Panel 179
4.4 Final Remarks 181
References 182
5 Nonlinear and Hysteretic Constitutive Models for Wave Propagation in Solid Media with Cracks and Contacts 186
5.1 Introduction 186
5.2 Multiscale Approach and Three Contact Regimes 188
5.3 Brief History of the Mechanical Contact Problem 190
5.4 Normal Load–Displacement Relationship for Contact Between Rough Surfaces 191
5.5 Reduced Elastic Friction Principle 195
5.6 Method of Memory Diagrams for Partial Slip 199
5.6.1 Case of Constant Compression 200
5.6.2 Case of Overloading 201
5.6.3 Memory Diagrams for Arbitrary Loading Histories 204
5.6.3.1 Case YY 205
5.6.3.2 Case YN 207
5.6.3.3 Case N 208
5.6.4 Retrieving Physical Characteristics from Memory Diagram 210
5.6.5 Numerical Implementation and Examples 212
5.6.6 Summary of the Method of Memory Diagrams 215
5.7 Complete Contact Model Accounting for Three Contact Regimes 217
5.7.1 Partial Slip and Total Sliding Displacement Components 217
5.7.1.1 Contact Loss 218
5.7.1.2 Total Sliding 219
5.7.1.3 Partial Slip 219
5.7.2 Numerical Example 220
5.8 Finite Element Simulations Using the Developed Contact Model 223
5.8.1 General Remarks 223
5.8.2 Numerical Implementation of the Constitutive Crack Model 224
5.8.3 Test Sample Geometry and Physical Parameters 225
5.8.4 Nonlinear Hysteretic Tangential Behavior of Horizontal Crack 226
5.8.5 Nonlinear Normal and Tangential Behavior of Inclined Crack 229
5.9 Conclusions 233
References 234
6 Nonlinear Ultrasonic Techniques for Material Characterization 236
6.1 Time Harmonic Wave Motion in Elastic Solids with Quadratic Nonlinearity 236
6.1.1 Governing Equations 236
6.1.2 One-Dimensional Wave Propagation 240
6.1.3 Nonlinear Wave Mixing 243
6.1.3.1 Mixing of Two Collinear Longitudinal Plane Waves 245
6.1.3.2 Mixing of Two Collinear Transverse Plane Waves 246
6.1.3.3 Mixing of Collinear Longitudinal and Transverse Plane Waves 246
6.1.4 Rayleigh Surface Waves 247
6.1.5 Lamb Waves 250
6.1.5.1 Solution for the Secondary Field 250
6.1.5.2 Some Properties of the Secondary Lamb Wave Modes 253
6.2 Measurement Techniques for Nonlinear Ultrasound and Their Applications 256
6.2.1 Through-Transmission of Bulk Waves 256
6.2.2 Collinear Wave Mixing 258
6.2.3 Rayleigh Surface Waves 262
6.2.4 Lamb Waves 268
6.3 Summary 269
References 270
7 Second-Harmonic Generation at Contacting Interfaces 273
7.1 Nonlinear Spring-Type Interface Model for Contacting Rough Surfaces 273
7.2 Second-Harmonic Generation by Plane Longitudinal Wave at Normal Incidence 277
7.2.1 Time-Domain Formulation 277
7.2.2 Perturbation Analysis 279
7.2.3 Frequency-Domain Analysis 282
7.2.4 Note on the Power-Law Stiffness–Pressure Relation 287
7.3 Second-Harmonic Generation by Plane Shear Wave at Normal Incidence 288
7.4 Second-Harmonic Generation by Plane Longitudinal Wave at Oblique Incidence 291
7.4.1 Formulation 291
7.4.2 Linear Response 293
7.4.3 Quadratic Nonlinear Response 297
7.5 Experimental Aspects 301
7.5.1 Quantitative Evaluation of the Second-Harmonic Amplitude 301
7.5.2 Comparison with the Prediction Based on the Nonlinear Spring-Type Interface Model 305
7.5.3 Other Experimental Investigations 307
References 308
8 Nonlinear Acoustic Response of Damage Applied for Diagnostic Imaging 310
8.1 Introduction 310
8.2 CAN Mechanisms and Nonlinear Vibration Spectra of Fractured Defects 312
8.3 Nonlinear Spectra of Damage and Defect–Selective Imaging 315
8.3.1 Nonlinear Imaging Via Laser Scanning Vibrometry 319
8.3.2 Nonlinear Air-Coupled Emission (NACE) 321
8.4 Local Defect Resonance: Concept, Simulations, and Experimental Evidence 325
8.4.1 LDR Concept and FEM Simulation 326
8.4.2 LDR Experimental Evidence and Study 328
8.5 Resonant Nonlinearity of Defects 331
8.5.1 LDR: Enhanced “Classical” Nonlinear Effects 331
8.5.2 Superharmonic Resonances 334
8.5.3 Combination Frequency Resonance 336
8.5.4 Parametric and Subharmonic Resonances 337
8.6 Resonant Nonlinear Defect-Selective Imaging 340
8.6.1 Contact Activation of Damage 340
8.6.2 Noncontact Nonlinear Imaging of Damage 345
8.7 Conclusions 350
References 351
9 Nonlinear Guided Waves and Thermal Stresses 353
9.1 Nonlinear Guided Waves in Isotropic Plates and Rods (Analytical Method) 353
9.1.1 Introduction 353
9.1.2 Nonlinear Strain Energy Expression 355
9.1.3 Nonlinear Equation of Motion for a Waveguide 356
9.1.4 Waveguide Mode Orthogonality 359
9.1.5 Complex Reciprocity Relation 360
9.1.6 Nonlinear Lamb Waves 362
9.1.6.1 Statement of the Problem 362
9.1.7 Solution to Nonlinear Problem 363
9.1.7.1 Forced Solution to Guided Waves 363
9.1.7.2 Perturbation 364
9.1.7.3 Solution 364
9.1.8 Condition for the Absence of Antisymmetric Modes 365
9.1.9 Application to First-Order Nonlinearity 366
9.1.10 A Representative Simulation Confirmation: Nonlinear SAFE Analysis in Plates 368
9.1.11 Application to Higher-Order Harmonics 370
9.1.12 Experimental Confirmation 372
9.1.13 Conclusions 374
9.1.14 Nonlinearity in Rods 374
9.1.15 Solution to the Nonlinear Problem 377
9.1.16 Analysis of Solution 378
9.1.17 Conclusions 382
9.2 Nonlinear Waves in Waveguides of Arbitrary Cross-Sections (Semi-Analytical Computational Method) 383
9.2.1 Introduction 383
9.2.2 Waves in Nonlinear Elastic Regime: Internal Resonance 383
9.2.3 Nonlinear Semi-Analytical Algorithm 387
9.2.4 Application: Railroad Track 389
9.2.4.1 Nonresonant Combination 391
9.2.4.2 Resonant Combination 393
9.2.5 Application: Viscoelastic Isotropic Plate 394
9.2.6 Application: Anisotropic Elastic Composite Laminate 396
9.2.7 Application: Reinforced Concrete Slab 399
9.2.8 Conclusions 402
9.3 Nonlinear Waves in Constrained Solids Under Temperature Fluctuations (Thermal Stress Case) 403
9.3.1 Introduction 403
9.3.2 Model 403
9.3.2.1 Interatomic Potential 404
9.3.2.2 Potential Energy for Constrained Thermal Expansion 405
9.3.2.3 Nonlinear Wave Equation for Constrained Thermal Expansion 409
9.3.2.4 Solution of the Nonlinear Wave Equation: Second-Harmonic Wave Generation for Constrained Thermal Expansion 414
9.3.3 Experimental Validation: Nonlinear Waves in a Steel Block under Constrained Thermal Expansion 415
9.3.4 Conclusions 420
A.1 Appendix 421
References 422
10 Subharmonic Phased Array for Crack Evaluation (SPACE) 426
10.1 Introduction 426
10.2 Theory of Subharmonic Generation at Closed Cracks 427
10.2.1 Historical Context 427
10.2.2 Analytical Theory [14, 15, 20] 428
10.2.3 Numerical Theory [14, 34, 35] 435
10.3 Principle of SPACE 439
10.4 Experiments 443
10.4.1 Open and Closed Fatigue Cracks [5, 6] 443
10.4.2 Dependence of a Fatigue Crack on Crack Closure Stress [5, 6] 444
10.4.3 Fatigue Crack Growth Monitoring [41, 42] 447
10.4.4 Closed Cracks Generated in Manufacturing Process [45] 450
10.4.5 Stress Corrosion Crack (SCC) Extending from a Deep Fatigue Precrack [47] 455
10.4.6 SCC Formed in a Weld Under Realistic Conditions [40] 458
10.4.7 SPACE Using Surface Acoustic Wave (SAW) [51, 52] 466
10.5 Conclusions 472
References 474
11 A Unified Treatment of Nonlinear Viscoelasticity and Non-equilibrium Dynamics 477
11.1 Introduction 477
11.2 Physical Modeling 478
11.2.1 Nonlinear Elastodynamics 479
11.2.2 Internal-Variable Model of Slow Dynamics 480
11.2.3 Viscoelasticity 481
11.3 Numerical Modeling 483
11.3.1 Numerical Strategy 484
11.3.2 Finite-Volume Method 485
11.4 Numerical Experiments 485
11.4.1 Dynamic Acoustoelasticity 486
11.4.2 Resonance Curves 486
11.5 Conclusion 488
References 490
12 Cement-Based Material Characterization Using Nonlinear Single-Impact Resonant Acoustic Spectroscopy (NSIRAS) 493
12.1 Introduction 493
12.2 Background 496
12.3 Signal Processing for Single-Impact Vibration 499
12.3.1 Sliding Window 499
12.3.2 Time Domain Fitting 500
12.4 Damage Quantification from a Single-Impact Response 502
12.5 Sources of Variability and Systematic Errors 504
12.5.1 Errors in Nonlinear Parameter Estimation 505
12.5.2 Effect of Test Configuration 506
12.5.3 Double-Hump Effect 507
12.5.4 Environmental Factors: Internal Moisture and Temperature 509
12.5.5 Material Conditioning 509
12.6 Concluding Remarks 510
References 511
13 Dynamic Acousto-Elastic Testing 515
13.1 Introduction 515
13.1.1 Inspirations and Principles of Dynamic Acousto-Elastic Testing 515
13.1.2 Comparison with Other Methods 518
13.2 Experimental Setups 518
13.2.1 Low-Frequency Pump Wave: Quasi-Homogeneous and Quasi-Static Requirements 519
13.2.2 Ultrasonic Probe Wave: Type, Amplitude, Position, and Orientation 520
13.2.3 Clock Synchronization and Phase Noise 521
13.2.4 DAET with Stationary Pump Wave 523
13.2.5 DAET with Propagative Pump Wave 524
13.3 Signal Analysis 525
13.3.1 Analysis of the Pump: Calculation of Strain/Stress Produced by the Pump Wave That is Experienced by the Probe Wave 525
13.3.2 Analysis of the Probe: Determination of the Change of Travel Time of the Probe Wave 526
13.3.3 Investigating the Relation Between the Change of Wave-Speed of the Probe and the Magnitude of the Pump Stress/Strain 529
13.3.4 Alternative Measures of Acoustic Nonlinearity 530
13.4 Observations in Different Materials 532
13.4.1 Liquids 533
13.4.1.1 Non-Bubbly Liquid 534
13.4.1.2 Liquid with Suspension of Gas MicroBubbles 534
13.4.1.3 Water-Saturated Glass Beads 535
13.4.2 Solids 535
13.4.2.1 Undamaged Homogeneous Solids 535
13.4.2.2 Damaged Homogeneous Solids 536
13.4.2.3 Rocks, Cementitious, and Granular Materials 538
13.5 Conclusions 548
References 549
14 Time Reversal Techniques 553
14.1 What Is Time Reversal? 553
14.1.1 Pebble on a Pond 553
14.1.2 Time Reversal in a Bounded Medium 554
14.1.3 Characteristics of Time Reversal 557
14.1.4 Methods of Time Reversal 558
14.1.5 Benefits and Limitations of Time Reversal 565
14.1.6 Applications of Time Reversal 566
14.2 Time Reversal for Locating Damage 568
14.2.1 Nonlinear Signatures of Defects 568
14.2.2 Time Reversal of Nonlinear Features Detected Remotely (Standard Time Reversal) 569
14.2.3 Focusing Elastic Wave Energy for Localized Nonlinear Inspection (Reciprocal Time Reversal) 572
14.2.4 Surficial and Depth Imaging with Time Reversal 576
14.2.5 Three-Dimensional Time Reversal Focusing 577
14.3 Conclusion 581
References 582
15 Nonlocal and Coda Wave Quantification of Damage Precursors in Composite from Nonlinear Ultrasonic Response 588
15.1 Introduction 589
15.1.1 Bottom-Up Multiscale Predictive Failure Models 591
15.1.2 Unifying Bottom-Up and Top-Down Approaches 592
15.2 Theoretical Development for Quantitative Ultrasonic Image Correlation: High-Frequency Method 594
15.2.1 Nonlocal Approach and Micromorphic Kernel Function 594
15.2.2 Fundamental Equation of Motion with Nonlocal Parameters 596
15.2.3 The Eigenvalue Problem 597
15.3 Damage State Quantification Process 599
15.3.1 Incremental Damage State and Its Relation with Nonlocal Parameters 599
15.3.2 Understanding Material Signature Using Scanning Acoustic Microscope 600
15.3.3 Identification of Nonlocal Parameter from Scanning Acoustic Microscope Data 603
15.3.4 Nonlocal Damage Entropy: Precursor Quantification Process Using Scanning Acoustic Microscope and Quantitative Ultrasonic Image Correlation 605
15.3.5 Damage State Quantification from Evaluation of Stiffness Degradation 607
15.4 Coda Wave Interferometry: Low-Frequency Method 608
15.4.1 Background 608
15.4.2 Mathematical Treatment of Coda Wave for Damage Quantification 609
15.4.2.1 Stretching Technique with Cross-Correlation 609
15.4.2.2 Taylor Series Expansion Theory 611
15.4.2.3 Application of Coda Wave Interferometry for Precursor Quantification in Composites 611
15.5 Experimental Design 612
15.5.1 Materials and Specimen Preparation [136, 137] 612
15.5.2 Tensile Test 613
15.5.3 Fatigue Testing 614
15.5.4 Pitch-Catch Ultrasonic Lamb Wave Experiment 616
15.6 Results and Discussion 616
15.6.1 Probability Distribution of Quasi-Longitudinal Wave Velocity 616
15.6.2 Precursor Damage Quantification Using Coda Wave Interferometry 617
15.6.3 Precursor Damage Quantification Using Nonlocal-Continuum Physics 620
15.6.4 Precursor Damage Indication from SAW Velocity Profiles 621
15.6.5 Damage Characterization Using Optical Microcopy: Verification 622
15.6.6 Damage Characterization Using Scanning Electron Microscope (SEM) 623
15.6.7 Damage Characterization from Scanning Acoustic Microscopy 624
15.7 Conclusions 624
References 625
16 Anharmonic Interactions of Probing Ultrasonic Waves with Applied Loads Including Applications Suitable for Structural Health Monitoring 632
16.1 Introduction 632
16.2 Basic Theoretical Background and Modeling 635
16.3 Experimental Set-Up and Monitoring Schemes 643
16.4 Monitoring of Stress and Strain with Acoustic Waves 649
16.5 Related Applications of the Developed Monitoring Scheme 659
References 662
17 Noncontact Nonlinear Ultrasonic Wave Modulation for Fatigue Crack and Delamination Detection 665
17.1 Introduction 665
17.2 Noncontact Ultrasonic Generation and Measurement 667
17.2.1 Electromagnetic Acoustic Transducer (EMAT) 668
17.2.2 Air-Coupled Transducer (ACT) 668
17.2.3 Laser-Based Ultrasonic Generation 670
17.2.4 Laser-Based Ultrasonic Measurement 670
17.2.5 Laser Ultrasonic Scanning System 672
17.2.6 Different Scanning Strategies 672
17.3 Basic Principle of Nonlinear Ultrasonic Modulation 674
17.3.1 Nonlinear Ultrasonic Modulation 674
17.3.2 Necessary Conditions for Nonlinear Ultrasonic Modulation 675
17.3.3 Controlling of the Inputs for Nonlinear Ultrasonic Modulation 677
17.4 Damage Detection Techniques Using Noncontact Nonlinear Ultrasonic Modulation 679
17.4.1 Sequential Outlier Analysis Technique 680
17.4.2 Spatial Comparison Technique 680
17.4.3 Sideband Peak Count Technique 681
17.4.4 State Space Attractor Technique 684
17.5 Applications Using ACT-Based Measurement Systems 687
17.5.1 Fatigue Crack Detection in Plates 687
17.5.2 Fatigue Crack Detection in Rotating Shafts 689
17.6 Applications Using Laser-Based Measurement Systems 691
17.6.1 Fatigue Crack Detection on Plates 691
17.6.2 Delamination/Debonding Detection on Wind Turbine Blades 694
17.7 Discussions 697
17.8 Conclusions 698
References 698
18 Characterizing Fatigue Cracks Using Active Sensor Networks 702
18.1 Introduction 702
18.2 Guided Waves in Plate-like Structures 704
18.2.1 Fundamentals of Lamb Waves 704
18.2.2 Linear Features of Lamb Waves for Identification of Gross Damage 706
18.2.3 Nonlinear Features of Lamb Waves for Characterization of Undersized Damage 708
18.3 Modeling of Nonlinear Attributes of Lamb Waves 709
18.3.1 Modeling Nonlinearities in an Elastic Medium 710
18.3.1.1 Intact Medium 710
18.3.1.2 Fatigued Medium 711
18.3.1.3 Contact Acoustic Nonlinearity (CAN) 712
18.3.2 Modeling Nonlinear Lamb Waves 713
18.3.3 Realization in Finite Element Method 717
18.3.4 Simulation Results and Experimental Validation 720
18.3.4.1 RANP vs. Wave Propagation 720
18.3.4.2 RANP vs. Sensing Path Offset 722
18.3.4.3 Dependence on Angle of Incidence and Wave Propagation Distance 725
18.4 System Development for Implementation 726
18.4.1 Decentralized Standard Sensing 727
18.4.2 Development of a Modularized In Situ Diagnostic System 729
18.5 Characterization of Multiple Fatigue Cracks in Aluminum Plates 729
18.5.1 Experimental Investigation 731
18.5.2 Signal Processing and Imaging 733
18.5.3 Results and Discussions 736
18.6 Conclusions 737
References 740
Index 743