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Cesar & Federico Sciammarella, University of Illinois, USA Cesar A Sciammarella is Adjunct Professor in the Department of Mechanical Engineering, University of Illinois, USA. In the past he has worked as a consultant for companies including: General Motors, Goodyear, Honeywell Corporation, Rand Corporation, Rockwell International, Sundstran, Uniroyal Tires, IBM, Tryodyne, Samsung, Case Corporation. A renowned experimentalist, his research currently focuses on developing techniques in solid mechanics and he has spoken at many conferences and published prolifically in journals which include Strain; Optical Engineering; SEM Conference on Experimental Mechanics and Journal of Strain Analysis for Engineering Design. Federico Sciammarella is Assistant Professor in the Department of Mechanical Engineering, University of Illinois. His research interests centre upon using optical methods for characterization of materials and structures including failure analysis. Over the past five years he has written multiple journal and conference research papers.
Preface xix
Foreword xxi
1 Continuum Mechanics - Historical Background 1
1.1 Definition of the Concept of Stress 4
1.2 Transformation of Coordinates 5
1.3 Stress Tensor Representation 6
1.4 Principal Stresses 8
1.5 Principal Stresses in Two Dimensions 10
1.6 The Equations of Equilibrium 11
1.7 Strain Tensor 13
1.8 Stress - Strain Relations 15
1.9 Equations of Compatibility 18
References 19
2 Theoretical Stress Analysis - Basic Formulation of Continuum Mechanics. Theory of Elasticity 21
2.1 Introduction 21
2.2 Fundamental Assumptions 21
2.3 General Problem 22
2.4 St. Venant's Principle 25
2.5 Plane Stress, Plane Strain 28
2.6 Plane Stress Solution of a Simply Supported Beam with a Uniform Load 30
2.7 Solutions in Plane Strain and in Plane Stress 33
2.8 The Plane Problem in Polar Coordinates 35
2.9 Thick Wall Cylinders 36
References 39
3 Strain Gages - Introduction to Electrical Strain Gages 41
3.1 Strain Measurements - Point Methods 41
3.2 Electrical Strain Gages 42
3.3 Basics of Electrical Strain Gages 43
3.4 Gage Factor 45
3.5 Basic Characteristics of Electrical Strain Gages 48
3.6 Errors Due to the Transverse Sensitivity 54
3.7 Errors Due to Misalignment of Strain Gages 58
3.8 Reinforcing Effect of the Gage 60
3.9 Effect of the Resistance to Ground 61
3.10 Linearity of the Gages. Hysteresis 63
3.11 Maximum Deformations 64
3.12 Stability in Time 64
3.13 Heat Generation and Dissipation 64
3.14 Effect of External Ambient Pressure 65
3.15 Dynamic Effects 67
References 71
4 Strain Gages Instrumentation - TheWheatstone Bridge 75
4.1 Introduction 75
References 109
5 Strain Gage Rosettes: Selection, Application and Data Reduction 111
5.1 Introduction 111
5.2 Errors, Corrections, and Limitations for Rosettes 119
5.3 Applications of Gages to Load Cells 119
References 121
6 Optical Methods - Introduction 123
6.1 Historical Perspective and Overview 123
6.2 Fundamental Basic Definitions of Optics 127
6.3 The Electromagnetic Theory of Light 128
6.4 Properties of Polarized Light 137
6.5 The Jones Vector Representation 138
6.6 Light Intensity 141
6.7 Refraction of the Light 141
6.8 Geometrical Optics. Lenses and Mirrors 146
References 154
7 Optical Methods - Interference and Diffraction of Light 155
7.1 Connecting Light Interference with Basic Optical Concepts 155
7.2 Light Sources 155
7.3 Interference 161
7.4 Interferometers 166
7.5 Diffraction of the Light 171
References 181
8 Optical Methods - Fourier Transform 183
8.1 Introduction 183
8.2 Simple Properties 185
8.3 Transition to Two Dimensions 187
8.4 Special Functions 188
8.5 Applications to Diffraction Problems 191
8.6 Diffraction Patterns of Gratings 193
8.7 Angular Spectrum 195
8.8 Utilization of the FT in the Analysis of Diffraction Gratings 199
References 205
9 Optical Methods - Computer Vision 207
9.1 Introduction 207
9.2 Study of Lens Systems 208
9.3 Lens System, Coordinate Axis and Basic Layout 210
9.4 Diffraction Effect on Images 211
9.5 Analysis of the Derived Pupil Equations for Coherent Illumination 216
9.6 Imaging with Incoherent Illumination 217
9.7 Digital Cameras 230
9.8 Illumination Systems 242
9.9 Imaging Processing Systems 245
9.10 Getting High Quality Images 246
References 249
10 Optical Methods - Discrete Fourier Transform 251
10.1 Extension to Two Dimensions 253
10.2 The Whittaker-Shannon Theorem 257
10.3 General Representation of the Signals Subjected to Analysis 261
10.4 Computation of the Phase of the Fringes 271
10.5 Fringe Patterns Singularities 276
10.6 Extension of the Fringes beyond Boundaries 279
References 283
11 Photoelasticity - Introduction 285
11.1 Introduction 285
11.2 Derivation of the Fundamental Equations 286
11.3 Wave Plates 291
11.4 Polarizers 293
11.5 Instrument Matrices 294
11.6 Polariscopes 296
11.7 Artificial Birefringence 304
11.8 Polariscopes 307
11.9 Equations of the Intensities of the Plane Polariscope and the Circular Polariscope for a Stressed Plate 309
References 311
12 Photoelasticity Applications 313
12.1 Calibration Procedures of a Photoelastic Material 313
12.2 Interpretation of the Fringe Patterns 319
12.3 Determination of the Fringe Order 319
12.4 Relationship between Retardation Changes of Path and Sign of the Stress Differences 327
12.5 Isoclinics and Lines of Principal Stress Trajectories 328
12.6 Utilization of White Light in Photoelasticity 333
12.7 Determination of the Sign of the Boundary Stresses 338
12.8 Phase Stepping Techniques 342
12.9 RGB Photoelasticity 343
12.10 Reflection Photoelasticity 355
12.11 Full Field Analysis 364
12.12 Three Dimensional Analysis 366
12.13 Integrated Photoelasticity 375
12.14 Dynamic Photoelasticity 380
References 383
13 Techniques that Measure Displacements 387
13.1 Introduction 387
13.2 Formation of Moir¿e Patterns. One Dimensional Case 388
13.3 Formation of Moir¿e Patterns. Two Dimensional Case 390
13.4 Relationship of the Displacement Vector and the Strain Tensor Components 393
13.5 Properties of the Moire Fringes (Isothetic Lines) 395
13.6 Sections of the Surface of Projected Displacements 396
13.7 Singular Points and Singular Lines 401
13.8 Digital Moir¿e 402
13.9 Equipment Required to Apply the Moir¿e Method for Displacement and Strain Determination Utilizing Incoherent Illumination 412
13.10 Strain Analysis at the Sub-Micrometer Scale 419
13.11 Three Dimensional Moir¿e 424
13.12 Dynamic Moir¿e 426
References 432
14 Moir¿e Method. Coherent Ilumination 435
14.1 Introduction 435
14.2 Moir¿e Interferometry 435
14.3 Optical Developments to Obtain Displacement, Contours and Strain Information 439
14.4 Determination of All the Components of the Displacement Vector 3-D Interferometric Moir¿e 446
14.5 Application of Moir¿e Interferometry to High Temperature Fracture Analysis 451
References 456
15 Shadow Moir¿e & Projection Moir¿e - The Basic Relationships 459
15.1 Introduction 459
15.2 Basic Equation of Shadow Moir¿e 460
15.3 Basic Differential Geometry Properties of Surfaces 461
15.4 Connection between Differential Geometry and Moir¿e 463
15.5 Projective Geometry and Projection Moir¿e 467
15.6 Epipolar Model of the Two Projectors and One Camera System 469
15.7 Approaches to Extend the Moir¿e Method to More General Conditions of Projection and Observation 471
15.8 Summary of the Chapter 482
References 482
16 Moir¿e Contouring Applications 485
16.1 Introduction 485
16.2 Basic Principles of Optical Contouring Measuring Devices 486
16.3 Contouring Methods that Utilize Projected Carriers 486
16.4 Parallax Determination in an Area 489
16.5 Mathematical Modeling of the Parallax Determination in an Area 490
16.6 Limitations of the Contouring Model 492
16.7 Applications of the Contouring Methods 494
16.8 Double Projector System with Slope and Depth-of-Focus Corrections 506
16.9 Sensitivity Limits for Contouring Methods 518
References 520
17 Reflection Moir¿e 523
17.1 Introduction 523
17.2 Incoherent Illumination. Derivation of the Fundamental Relationship 523
17.3 Interferometric Reflection Moir¿e 526
17.4 Analysis of the Sensitivity that can be Achieved with the Described Setups 530
17.5 Determination of the Deflection of Surfaces Using Reflection Moir¿e 531
17.6 Applications of the Reflection Moir¿e Method 532
17.7 Reflection Moir¿e Application - Analysis of a Shell 539
References 545
18 Speckle Patterns and Their Properties 547
18.1 Introduction 547
18.2 First Order Statistics 550
18.3 Three Dimensional Structure of Speckle Patterns 558
18.4 Sensor Effect on Speckle Statistics 560
18.5 Utilization of Speckles to Measure Displacements. Speckle Interferometry 562
18.6 Decorrelation Phenomena 564
18.7 Model for the Formation of the Interference Fringes 567
18.8 Integrated Regime. Metaspeckle 569
18.9 Sensitivity Vector 572
18.10 Speckle Techniques Set-Ups 573
18.11 Out-of-Plane Interferometer 576
18.12 Shear Interferometry (Shearography) 577
18.13 Contouring Interferometer 578
18.14 Double Viewing. Duffy Double Aperture Method 579
References 581
19 Speckle 2 583
19.1 Speckle Photography 583
19.2 Point-Wise Observation of the Speckle Field 584
19.3 Global View 585
19.4 Different Set-Ups for Speckle Photography 589
19.5 Applications of Speckle Interferometry 590
19.6 High Temperature Strain Measurement 593
19.7 Four Beam Interferometer Sensitive to in Plane Displacements 597
References 606
20 Digital Image Correlation (DIC) 607
20.1 Introduction 607
20.2 Process to Obtain the Displacement Information 608
20.3 Basic Formulation of the Problem 610
20.4 Introduction of Smoothing Functions to Solve the Optimization Problem 613
20.5 Determination of the Components of the Displacement Vector 618
20.6 Important Factors that Influence the Packages of DIC 619
20.7 Evaluation of the DIC Method 621
20.8 Double Viewing DIC. Stereo Vision 627
References 628
21 Holographic Interferometry 631
21.1 Holography 631
21.2 Basic Elements of the Holographic Process 632
21.3 Properties of Holograms 634
21.4 Set up to Record Holograms 636
21.5 Holographic Interferometry 641
21.6 Derivation of the Equation of the Sensitivity Vector 644
21.7 Measuring Displacements 646
21.8 Holographic Moir¿e 651
21.9 Lens Holography 658
21.10 Holographic Moir¿e. Real Time Observation 661
21.11 Displacement Analysis of Curved Surfaces 665
21.12 Holographic Contouring 669
21.13 Measurement of Displacements in 3D of Transparent Bodies 675
21.14 Fiber Optics Version of the Holographic Moir¿e System 675
References 677
22 Digital and Dynamic Holography 681
22.1 Digital Holography 681
22.2 Determination of Strains from 3D Holographic Moir¿e Interferograms 685
22.3 Introduction to Dynamic Holographic Interferometry 689
22.4 Vibration Analysis 693
22.5 Experimental Set up for Time Average Holography 695
22.6 Investigation on Fracture Behavior of Turbine Blades Under Self-Exciting Modes 700
22.7 Dynamic Holographic Interferometry. Impact Analysis. Wave Propagation 708
22.8 Applications of Dynamic Holographic Interferometry 712
References 721
Index 723
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