High Sensitivity Moiré

1 Introduction.- 1.1 Our Subject.- 1.2 Scope and Style.- 1.3 History.- 1.4 Comment on Exercises.- 1.5 References.- I.- 2 Elements of Optics.- 2.1 The Nature of Light.- • More Details.- • Metallic Reflection.- • Dielectric Reflection.- • Refraction.- 2.2 Optical Elements.- • Light Sources.- • Wedges, Prisms, Mirrors.- • Partial Mirrors.- • Antireflection Coatings.- • Lenses.- • Laser-beam Expander, Spatial Filter, Optical Fibers.- • Parabolic Mirrors.- 2.3 Coherent Superposition.- • Pure Two-beam Interference.- • Conservation of Energy.- • Impure Two-beam Interference.- • Fringe Patterns and Walls of Interference.- • Warped Wave Fronts.- • The Camera.- • Two-beam Interferometers.- • Derivation of the Interference Equations.- • Interference with Broad Spectrum Light.- 2.4 Superposition of Incoherent Light Waves.- 2.5 Diffraction Gratings and Diffraction.- • Wave Fronts and Optical Path Lengths.- • Equivalency and Virtual Gratings.- • Self-imaging of Gratings.- 2.6 References.- 2.7 Key Relationships.- 2.8 Exercises.- 3 Geometric Moiré.- 3.1 Basic Features of Moiré.- • Gratings, Fringes, Visibility.- • Intensity Distribution.- • Multiplicative and Additive Intensities.- • Pure Rotation and Extension.- • Moiré Fringes as Parametric Curves.- • Fringe Vectors.- • Amplification by Moire.- • Fringe Sharpening and Multiplication.- • Circular Gratings.- 3.2 In-plane Displacements of a Deformed Body.- • Physical Concepts, Absolute Displacements.- • Practical Example, Relative Displacements.- • Mismatch Fringes (Carrier Fringes).- • Fringe Shifting.- 3.3 Out-of-plane Displacements.- • Shadow Moiré.- • Projection Moiré.- • Comparison.- 3.4 References.- 3.5 Key Relationships.- 3.6 Exercises.- 4 Moiré Interferometry.- 4.1 Introduction.- 4.2 A More Rigorous Explanation.- 4.3 Mathematical Analysis.- • Implications of the Analysis.- 4.4 The Virtual Reference Grating Concept.- 4.5 Theoretical Limit.- 4.6 Sensitivity and Resolution.- 4.7 Optical Systems for Moiré Interferometry.- • Alignment.- • Size of Field.- • Environmental Concerns: Air Currents.- • Vibrations, Optical Tables.- • Loading Fixtures.- • Two-beam Systems.- • Four-beam Systems.- • Achromatic Systems.- • Three-beam Interferometer.- • ±45° Gratings.- 4.8 Transmission Systems.- 4.9 Specimen Gratings.- • Replication.- • The Mold.- • Alignment of Specimen Gratings.- • Curved Surfaces.- • Zero-thickness Gratings and High-temperature Gratings.- 4.10 Fringe Counting.- • Sign of Fringe Gradient: Experimental Method.- 4.11 Strain Analysis.- 4.12 In-plane Rigid-body Rotations.- 4.13 Carrier Fringes.- 4.14 Fringe Vectors.- 4.15 Anomalies and Subtraction of Uniform Gradients.- 4.16 Two-body Problems, Bridges.- 4.17 Coping with the Initial Field.- 4.18 Optical Filtering.- 4.19 Sensitivity to Out-of-plane Motion.- • Black Holes and Out-of-Plane Slopes.- 4.20 Coping with Vibrations.- 4.21 Variations of Moiré Interferometry.- • Replication of Deformed Specimen Gratings.- • Replication for Thermal Strains.- • Moiré Fringe Multiplication.- • Multiplication by One.- 4.22 Mechanical Differentiation.- 4.23 Comments on Data Analysis.- 4.24 Shear Lag and the Thickness of Specimen Gratings.- 4.25 References.- 4.26 Key Relationships.- 4.27 Exercises.- 5 Microscopic Moiré Interferometry: Very High Sensitivity.- 5.1 Introduction.- • Scope and Summary.- 5.2 The Immersion Interferometer.- • Sensitivity in a Refractive Medium.- • Optical Configurations.- • Four-beam Immersion Interferometer.- 5.3 Optical/Digital Fringe Multiplication.- • Fringe Shifting.- • Fringe Sharpening and Multiplication: Physical Analysis.- • Mathematical Analysis.- • Implications of the Analyses.- 5.4 Shear Lag and Grating Thickness.- 5.5 References.- 5.6 Exercises.- 6 On the Limits of Moiré Interferometry.- 6.1 Introduction.- 6.2 Warped Wave Front Model.- 6.3 Fourier Wave Front Model.- 6.4 Strain Fields.- 6.5 Boundary Effects, Discontinuities.- 6.6 Spatial Resolution.- 6.7 Displacement Resolution.- 6.8 Strain and Gage Length.- • Strain Resolution.- 6.9 Dynamic Range.- 6.10 Absolute Accuracy.- 6.11 Summary.- 6.12 References.- II.- 7 Laminated Composites in Compression: Free-edge Effects.- 7.1 Introduction.- 7.2 In-plane Compression, Quasi-isotropic Specimen.- • Carrier Fringes.- 7.3 In-plane Compression, Cross-ply Specimen.- 7.4 Interlaminar Compression, Quasi-isotropic Specimen.- 7.5 Interlaminar Compression, Cross-ply Specimen.- • Out-of-plane Displacements.- • Normal Strains ex, Microscopic Study.- 7.6 References.- 7.7 Exercises.- 8 Thermal Stresses Near the Interface of a Bimaterial Joint.- 8.1 Introduction.- 8.2 The Experiments.- • Experimental Method.- • Relationships and Notation.- • Elevated Temperature Replication.- • Extracting the Coefficients of Expansion.- 8.3 Stress Analysis.- • ?y within the Interface Zone.- 8.4 Experiments by Microscopic Moiré Interferometry.- 8.5 Comments.- 8.6 References.- 8.7 Exercises.- 9 Textile Composites.- 9.1 Introduction.- 9.2 Woven Textile Composites.- • Data Reduction and Results.- 9.3 Braided Textile Composites.- 9.4 Open Hole Tension.- 9.5 Compact Moiré Interferometer.- 9.6 References.- 9.7 Exercises.- 10 Thermal Deformations in Electronic Packaging.- 10.1 Introduction.- 10.2 Grating Replication.- 10.3 Controlled-Collapse Chip Connection (C4).- • Ceramic Chip Carrier.- • Organic Chip Carrier.- 10.4 Solder Ball Connection.- 10.5 Low Temperature Application.- • Replication of Deformed Grating.- 10.6 Coefficient of Thermal Expansion.- 10.7 References.- 10.8 Exercises.- 11 Advanced Composites Studies.- 11.1 Introduction.- 11.2 Ceramic Composites.- • Delamination of Specimen Gratings.- 11.3 Creep.- 11.4 Metal-Matrix Composite.- 11.5 Residual Stresses.- 11.6 Thermal Strains, Residual Strains.- • Micromechanics:.- • Thermal Deformation of Boron/Aluminum.- 11.7 Simulation.- 11.8 Wavy Plies.- 11.9 References.- 11.10 Exercises.- 12 Metallurgy, Fracture, Dynamic Loading.- 12.1 Introduction.- 12.2 Metallurgy.- • Elastic-plastic Joint.- • Weld Defects.- • Micromechanics: Grain Deformations.- • Tube-plate Joints.- 12.3 Fracture.- • Plastic Wake, Damage Wake.- • The J Integral.- • Micromechanics: Crack Arrest.- • Interior Strains, Stress Freezing.- 12.4 Dynamic Moiré Interferometry.- • Equipment.- • Wave Propagation in a Composite Laminate.- 12.5 References.- 12.6 Exercises.- 13 Strain Standard for Calibration of Electrical Strain Gages.- 13.1 Introduction.- • The Calibration Factor.- 13.2 The Specimen Grating.- 13.3 Apparatus and Basic Procedure.- • The Interferometer.- • Experimental Procedure: Basic Description.- • The Optical System.- 13.4 Tuning the Optical System.- • Symmetry.- • Circulation.- • Specimen Plane.- • Collimation.- 13.5 Mechanical Systems.- • Method of Attachment.- • Fringe Shifting Device.- • Beam Deflection Device.- 13.6 Calibration of the Specimen Grating.- 13.7 Strain Gage Instrumentation.- 13.8 Systematic Errors, Uncertainties.- • Additional Considerations.- 13.9 The Experiment: Data Sequence, Computations and Results.- 13.10 Accuracy.- 13.11 Gage Factor Measurements.- 13.12 Future Refinements.- 13.13 References.- 13.14 Exercises.- Appendices.- A Shadow Moiré with Enhanced Sensitivity.- A.1 Introduction.- A.2 Shadow Moiré with O/DFM.- A.3 In-plane Geometric Moiré with O/DFM.- A.4 Reference.- B Submaster Grating Molds.- B.1 Introduction.- B.2 Production of Silicone Rubber Submasters.- B.3 Production of Epoxy Submasters.- B.4 Application of the Reflective Film.- B.5 References.- C Adhesives for Replication of Specimen Gratings.- C.1 Adhesives.- C.2 Addresses.