Experimental Mechanics of Solids

  • ID: 2180797
  • Book
  • 776 Pages
  • John Wiley and Sons Ltd
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Experimental solid mechanics is the study of materials to determine their physical properties. This study might include performing a stress analysis or measuring the extent of displacement, shape, strain and stress which a material suffers under controlled conditions. In the last few years there have been remarkable developments in experimental techniques that measure shape, displacement and strains and these sorts of experiments are increasingly conducted using computational techniques.

Experimental Mechanics of Solids is a comprehensive introduction to the topics, technologies and methods of experimental mechanics of solids. It begins by establishing the fundamentals of continuum mechanics, explaining key areas such as the equations used, stresses and strains, and two and three dimensional problems. Having laid down the foundations of the topic, the book then moves on to look at specific techniques and technologies with emphasis on the most recent developments such as optics and image processing. Most of the current computational methods, as well as practical ones, are included to ensure that the book provides information essential to the reader in practical or research applications.

Key features:

- Presents widely used and accepted methodologies that are based on research and development work of the lead author
- Systematically works through the topics and theories of experimental mechanics including detailed treatments of the Moire, Speckle and holographic optical methods
- Includes illustrations and diagrams to illuminate the topic clearly for the reader
- Provides a comprehensive introduction to the topic, and also acts as a quick reference guide
- Accompanied by a website <a href="[external URL] hosting problems and solutions.

This comprehensive book forms an invaluable resource for graduate students and is also a point of reference for researchers and practitioners in structural and materials engineering.
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About the Authors xvii

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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The book is highly recommended as a textbook in courses of experimental mechanics and can be used as a basis on which the researcher, the student and the practitioner can develop their ideas and promote research and applications of the experimental methods in engineering problems. The connection and interrelation of the various optical techniques is astonishing.   (Wiley Experimental Techniques journal, 2012)

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