Photoelasticity for Designers

International Series of Monographs in Mechanical Engineering

1st Edition - January 1, 1969
Author: R. B. Heywood
Editors: D. J. Silverleaf, G. Blackburn
Language: English
eBook ISBN:
9 7 8 - 1 - 4 8 3 1 - 5 1 9 5 - 3

Photoelasticity for Designers covers the fundamental principles and techniques of photoelasticity, with an emphasis on its value as an aid to engineering design. This book is… Read more

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Photoelasticity for Designers covers the fundamental principles and techniques of photoelasticity, with an emphasis on its value as an aid to engineering design. This book is divided into 12 chapters, and begins with an introduction to the essential optical effects necessary for an understanding of the photoelastic phenomena. The next chapters describe the concept and features of polariscopes; the characterization of photoelastic materials; the formulation and testing of two-dimensional models of photoelasticity; and the application of model stresses to prototypes for the analysis of stresses occurring in the plane of the model, effectively of uniform thickness. These topics are followed by a discussion of the frozen stress technique and a comparison of the various materials that can be used for models in the technique. The ending chapters deal with the principles and application of the birefringent coating and distorted model techniques. This book will prove useful to photoelasticians, design engineers, and students.

Preface

Definitions

List of Symbols

Conversion Table

Multiplying Factors

1 Behavior of Light in Plane Polariscope

1.1. Nature of Light

1.2. Polaroid Polarizers

1.3. Polarization by Reflection or Refraction

1.4. Nicol Prism

1.5. Simple Polariscope

1.6. Determination of Polarization Axis

1.7. Effect of Stressed Transparent Model in Plane Polariscope

1.8. Stress- and Strain-Optical Coefficients Expressed in Terms of Relative Retardation

1.9. Derivation of Stress-Optical Coefficient

1.10. Fringe-Stress and Fringe-Strain Coefficients Expressed in Terms of the Fringe Order

1.11. The Brewster Unit

1.12. Three-Dimensional Effects

1.13. Summary of Photoelastic Effect

1.14. Effect of Plastic Strain

1.15. Comparison of Fringe-Stress and Strain Coefficients

1.16. Analysis by Light Vectors

1.17. Intensity of Light Emerging from Polariscope

1.18. Photoelastic Effect Using White Light

1.19. Isoclinics

1.20. Lines of Principal Stress

2 Behavior of Light in Circular Polariscope

2.1. Circularly Polarized Light

2.2. Polariscope Arrangements

2.3. Features of the Circular Polariscope

2.4. White Light in Circular Polariscope

2.5. λ/4 plates

2.6. Effect of a Stressed Model in Circular Polariscope

2.7. Compensators

3 Polariscopes

3.1. Diffusion Polariscope

3.2. Lens Polariscope

3.3. Parallel Light

3.4. Length of Polariscope

3.5. Two Lenses in System

3.6. Comparison of Diffusion and Lens-Type Polariscopes

3.7. Reflection Polariscopes

3.8. Examination of Fringes

3.9. Quality of Lenses for Polariscopes

3.10. Light Source

3.11. Photography

3.12. Camera

4 Photoelastic Materials

4.1. History

4.2. Measurement of Fringe-Stress and Strain Coefficients

4.3. Values of the Fringe-Stress and Strain Coefficients

4.4. Mechanical Properties

4.5. Choice of Material

4.6. Materials Available

4.7. Epoxy Resins

4.8. Catalin 61 893

4.9. Catalin 800 and Marblette

4.10. Columbia Resin CR 39

4.11. Celluloid

4.12. Gelatin

4.13. Polycarbonate

4.14. Urethane Rubber

4.15. Temperature Effects on the Fringe-Stress and Strain Coefficients

4.16. Effect of Creep on the Fringe-Stress and Strain Coefficients

4.17. Photoelastic Dispersion

4.18. Time-Edge Effects

4.19. Effect of Various Liquids on Plastics

4.20. Distribution of Surface Stresses in Notched Parts

4.21. Liquids Causing Damage to Plastics

4.22. Annealing

5 Two-Dimensional Models: Their Preparation and Testing

5.1. Making the Model

5.2. Machining of Plastics

5.3. Grinding and Polishing the Faces of Models

5.4. Loading Frames

5.5. Tension

5.6. Compression

5.7. Bending

5.8. Load Application and Measurement

5.9. Significance of Fringes

5.10. Thickness of Model

5.11. Boundary Stresses

5.12. Counting the Fringes

5.13. Self-Calibrating Models

6 Model Stresses Applied to Prototypes

6.1. Plane Stress and Plane Strain

6.2. Effect of Elastic Constants—Two-Dimensional

6.3. Effect of Elastic Constants—Three-Dimensional

6.4. Interpretation of Model Stresses to the Prototype

6.5. Notches

6.6. Comparison of Designs

6.7. St. Venant's Principle

7 Separation of Stresses within Two-Dimensional Model

7.1. When Separation Needs to be Undertaken

7.2. Transverse Stress Just Below Free Boundary

7.3. Principal Stresses On Axis of Symmetry

7.4. Separation of Principal Stresses by the Oblique Incidence Method

7.5. Frocht's Shear Difference Method

7.6. Lateral Extensometer

7.7. Filon's graphical method

7.8. Evaluation of Stress Sum from Laplace'S Equation

8 Frozen Stress Technique for Three-Dimensional Analysis

8.1. Three-Dimensional Techniques

8.2. Development and Theory of the Frozen Stress Method

8.3. Heat Treatment

8.4. Oven

8.5. Slicing the Model

8.6. Examination of Slice

8.7. Double Slice or Subslice Method of Examination

8.8. Post's Core Method of Examination at a Free Boundary

8.9. Examination of Slice by the Oblique Incidence Method

8.10. Immersion Fluid

8.11. Counting the Fringes

8.12. Determination of Fringe-Stress Coefficient

8.13. Distortion

8.14. Advantages of Distortion

8.15. Effect of Poisson's Ratio

Applications

8.16. Turbine Disk

8.17. Poppet Valve

8.18. Crankshaft

8.19. Gear Wheel

8.20. Dynamic Applications

8.21. Gravitational Fields

8.22. Quenching Stresses

9 Materials for Frozen Stress Analysis

9.1. General Comparison of Material Properties

9.2. Epoxy Resins

9.3. Catalin 61 893

9.4. Fosterite

9.5. Catalin 800 (Phenolic Resin)

9.6. Marco Resin SB 28C

9.7. Castolite

9.8. Columbia Resin CR 39

9.9. Kriston

9.10. Gelatin

10 Birefringent Coating Technique

10.1. Description of Method

10.2. Stress and Strain in the Prototype

10.3. Technique

10.4. Coating Errors

10.5. Fringe Multiplication

10.6. Techniques with Examination Parallel to Surface

10.7. The Photoelastic Strain Gauge

11 Improvement of Designs

11.1. Nature's Designs

11.2. Perfection in Design

11.3. Design Procedures

11.4. Streamline, Ideal or Neutral Fillets

11.5. Technique for Ascertaining the Ideal Contour

11.6. Improving the Shape of Fillets

11.7. Shape of Streamline Fillets

11.8. Size of Streamline Fillets

11.9. General Conclusions as to the Shape of Streamline Fillets

Examples of Streamline Fillets

11.10. Streamline Fillets in Flanged Parts

11.11. Streamline Fillets in Connecting Rods

11.12. Streamline Fillets in Loaded Projections

11.13. Streamline Fillets in Shouldered Shafts

11.14. Comparison of Fillet Shapes

11.15. Machining Considerations

11.16. Elliptical Fillets

11.17. Undercut Fillets

11.18. Removal of External Corners

12 New Distorted Model Technique for the Improvement of Designs

12.1. Outline

12.2. Basis of Method

12.3. Distortion at Stress Concentrations

12.4. General Distortion

12.5. Effect of Poisson's Ratio

12.6. Model Tests

Examples

12.7. Grooved Specimens

12.8. Shouldered Specimens

12.9. Holes

12.10. Miscellaneous Designs

12.11. Association of Distorted Model Technique with Photoelasticity

12.12. Three-Dimensional Models

Bibliography

Author Index

Subject Index