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Techniques for Non-Birefringent Objects: Coherent Shearing Interferometry and Caustics

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Photomechanics

Part of the book series: Topics in Applied Physics ((TAP,volume 77))

Abstract

Shearing interferometric techniques that can provide information about the stress or deformation states of non-birefringent transparent materials and opaque specularly reflective materials are described. Two types of coherent shearing interferometers that provide full-field information about the gradients of the stress state of an object are discussed. These techniques have recently found use in stress analysis, especially in experimental fracture mechanics studies. In addition, a simpler technique called the method of caustics which is also applicable to non-birefringent materials is described in brief. This technique does not provide full-field information but has been of historical interest in experimental fracture mechanics. Examples of application of all three techniques are given.

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References

  1. J. W. Dally, W. F. Riley: Experimental Stress Analysis, McGraw-Hill, New York (1991)

    Google Scholar 

  2. R. Jones, C. Wykes: Holographic and Speckle Interferometry, Cambridge Univ. Press., London (1983)

    Google Scholar 

  3. A. J. Durelli, V. J. Parks: Moiré Analysis of Strain, Prentice-Hall, Englewood Cliffs, NJ (1970)

    Google Scholar 

  4. D. Malacara: Optical Shop Testing, Wiley, New York (1992)

    Google Scholar 

  5. L. H. Tanner: Some Laser Interferometers for Use in Fluid Mechanics, J. Sci. Instrum. 42, 834 (1965)

    Article  ADS  Google Scholar 

  6. P. K. Rastogi: Holographic Interferometry-Principles and Methods, Springer, Berlin, Heidelberg (1984)

    Google Scholar 

  7. D. Post, B. Han, P. Ifju: High-Sensitivity Moiré: Experimental Analysis for Mechanics and Materials, Springer, Berlin, Heidelberg (1994)

    Google Scholar 

  8. Y. Y. Hung: Measurement of Slopes of Structural Deflections by Speckle-Shearing Interferometry, Exp. Mech. 17, 281 (1974)

    Article  MathSciNet  Google Scholar 

  9. W. J. Bates: A Wavefront Shearing Interferometer, Proc. Phys. Soc. 59, 196 (1947)

    Google Scholar 

  10. A. J. Rosakis: Two Optical Techniques Sensitive to Gradients of Optical Path Difference, in J. S. Epstein (Ed.): Experimental Techniques in Fracture, VCH, Weinheim (1993) p. 327

    Google Scholar 

  11. S. P. Timoshenko, J. N. Goodier: Theory of Elasticity, McGraw-Hill, New York (1970)

    MATH  Google Scholar 

  12. J. Beinert, J. F. Kalthoff: Experimental Determination of Dynamic Stress-Intensity Factors by Shadow Patterns, in G. Sih (Ed.): Mechanics of Fracture 7, Nijhoff, Hingham, MA (1981) p. 281

    Google Scholar 

  13. M. V. R. K. Murty: The Use of a Single Plane Parallel Plate as a Lateral Shearing Interferometer with a Visible Gas Laser Source, Appl. Opt. 3, 531 (1964)

    Article  ADS  Google Scholar 

  14. J. D. Briers: Prism Shearing Interferometry, Opt. Technol. 1, 196 (1969)

    Article  Google Scholar 

  15. P. H. Lee, G. A. Woolsey: Versatile Polarization Interferometers, Appl. Opt. 20, 3514 (1981)

    Article  ADS  Google Scholar 

  16. V. Ronchi: Forty Years of History of a Grating Interferometer, Appl. Opt. 3, 437 (1964)

    Article  ADS  Google Scholar 

  17. J. C. Wyant: Double Frequency Grating Lateral Shear Interferometer, Appl. Opt. 12, 2057 (1973)

    Article  ADS  Google Scholar 

  18. K. Patorski: Talbot Interferometry with Increased Shear, Appl. Opt. 24, 4448 (1985)

    Article  ADS  Google Scholar 

  19. P. Hariharan, W. H. Steel, J. C. Wyant: Double Grating Interferometer with Variable Lateral Shear, Opt. Commun. 11, 317 (1974)

    Article  ADS  Google Scholar 

  20. H. V. Tippur, S. Krishnaswamy, A. J. Rosakis: Optical Mapping of Crack Tip Deformations Using the Methods of Transmission and Reflection Coherent Gradient Sensing: a Study of Crack Tip K-dominance, Int. J. Fract. 52, 91 (1991)

    ADS  Google Scholar 

  21. H. S. Lee, S. Krishnaswamy: A Compact Polariscope and Shearing Interferometer for Mapping Stress Fields in Bimaterial Systems, Exp. Mech. 36, 404 (1996)

    Article  Google Scholar 

  22. H. A. Bruck, A. J. Rosakis: On the Sensitivity of Coherent Gradient Sensing. Part 1. A Theoretical Investigation of Accuracy in Fracture-Mechanics Applications, Opt. Lasers Eng. 17, 83–101, 1992; Part.2. An Experimental Investigation of Accuracy In Fracture-Mechanics Applications, Opt. Lasers Eng. 18, 25 (1993)

    Article  Google Scholar 

  23. H. V. Tippur: Coherent Gradient Sensing — A Fourier Optics Analysis and Applications to Fracture, Appl. Opt. 31, 4428 (1992)

    Article  ADS  Google Scholar 

  24. E. Hecht, A. Zajac: Optics, Addison-Wesley, Reading, MA (1974)

    Google Scholar 

  25. J. A. Lock, J. H. Andrews: Optical Caustics in Natural Phenomena, Am. J. Phys. 60, 397–407 (1992)

    Article  ADS  Google Scholar 

  26. G. B. Airy: On the Intensity of Light in the Neighbourhood of a Caustic, Trans. Cambridge Philos. Soc. 6, 379, (1838)

    ADS  Google Scholar 

  27. A. A. Cayley: A Memoir Upon Caustics, Philos. Trans. R. Soc. 147, 273, (1857)

    Article  Google Scholar 

  28. P. Manogg: Anwendung der Schattenoptik zur Untersuchung des Zerreissvor-ganges von Platten, Dissertation, University of Freiburg, Germany (1964)

    Google Scholar 

  29. P. S. Theocaris: Elastic Stress Intensity Factors Evaluated by Caustics, in G. C. Sih (Ed.): Mechanics of Fracture 7, 189, Nijhoff, Hingham, MA (1981)

    Google Scholar 

  30. J. F. Kalthoff: Shadow Optical Method of Caustics, in A. S. Kobayashi (Ed.): Handbook on Experimental Mechanics, McGraw-Hill, New York (1987), Chap. 9, p. 430

    Google Scholar 

  31. A. J. Rosakis, C. C. Ma, L. B. Freund: Analysis of the Optical Shadow Spot Method for a Tensile Crack in a Power-Law Hardening Material, J. Appl. Mech. 50, 777 (1983)

    Article  Google Scholar 

  32. P. S. Theocaris: Multicusp Caustics Formed from Reflections of Warped Surfaces, Appl. Opt. 27, 780 (1988)

    Article  ADS  Google Scholar 

  33. H. P. Rossmanith: The Caustic Approach to Rayleigh-Waves and their Interaction with Surface Irregularities, Opt. Lasers Eng. 14, 115 (1990)

    Article  Google Scholar 

  34. H. W. Liepmann, A. Roshko: Elements of Gas Dynamics, Wiley, New York (1957)

    Google Scholar 

  35. G. Dacosta, R. Escalona: Time Evolution of the Caustics of a Laser Heated Liquid Film, Appl. Opt. 29, 1023 (1990)

    Article  ADS  Google Scholar 

  36. S. Mahaut, D. K. Lewis, G. Quentin, M. Debilly: Visualization of Internal Caustics in Cylindrical Liquid Cavities with a Pulsed Schlieren System, J. Phys. IV, Paris, 4, 741 (1994)

    Google Scholar 

  37. A. Joets, R. Ribotta: Caustics and Symmetries in Optical Imaging: The Example of Convective Flow Visualization, J. Phys. I, Paris, 4, 1013 (1994)

    Google Scholar 

  38. M. V. Berry, A. N. Wilson: Black-and-White Fringes and the Colors of Caustics, Appl. Opt. 33, 4714 (1994)

    Article  ADS  Google Scholar 

  39. H. S. Lee: Quasi-static Subinterfacial Crack Propagation, Ph.D. thesis, Northwestern University, Chicago, IL (1998)

    Google Scholar 

  40. J. R. Rice: Elastic Fracture Mechanics Concepts for Interfacial Cracks, J. Appl. Mech. 55, 418 (1988)

    Article  Google Scholar 

  41. K. Hellan: Introduction to Fracture Mechanics, McGraw-Hill, New York (1985)

    Google Scholar 

  42. P. S. Theocaris, C. Stassinakis: Experimental Solution of the Problem of a Curvilinear Crack in Bonded-Dissimilar Materials, Int. J. Fract. 13, 13 (1977)

    Article  Google Scholar 

  43. K. Ravi-Chandar, W. G. Knauss: On the Characterization of Transient Stress Fields Near the Tip of a Crack, J. Appl. Mech. 54, 72 (1987)

    Article  Google Scholar 

  44. A. J. Rosakis, J. Duffy, L. B. Freund: The Determination of the Dynamic Fracture Toughness of AISI 4340 Steel by the Shadow Spot Method, J. Mech. Phys. Solids 34, 443 (1984)

    Article  Google Scholar 

  45. S. Krishnaswamy, A. J. Rosakis: On the Extent of Dominance of the Asymptotic Elastodynamic Crack-Tip Fields; Part 1: an Experimental Study Using Bifocal Caustics, J. Appl. Mech. 58, 87 (1990)

    Article  Google Scholar 

  46. H. Nigam, A. Shukla: Comparison of the Techniques of Transmitted Caustics and Photoelasticity as Applied to Fracture, Exp. Mech. 28, 123 (1988)

    Article  Google Scholar 

  47. S. Krishnaswamy, H. V. Tippur, A. J. Rosakis: Measurement of Transient Crack-Tip Deformation Field Using the Method of Coherent Gradient Sensing, J. Mech. Phys. Solids 40, 339 (1992)

    Article  ADS  Google Scholar 

  48. J. Lambros, A. J. Rosakis: Dynamic Decohesion of Bimaterials — Experimental-Observations and Failure Criteria, Int. J. Solids Struct. 32, 2677 (1997)

    Article  Google Scholar 

  49. R. P. Singh, J. Lambros, A. Shukla, A. J. Rosakis: Investigation of the Mechanics of Intersonic Crack Propagation along a Bimaterial Interface Using Coherent Gradient Sensing and Photoelasticity, Proc. R. Soc. London A 453, 2649 (1997)

    Article  ADS  Google Scholar 

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© 2000 Springer-Verlag Berlin Heidelberg

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Krishnaswamy, S. (2000). Techniques for Non-Birefringent Objects: Coherent Shearing Interferometry and Caustics. In: Rastogi, P.K. (eds) Photomechanics. Topics in Applied Physics, vol 77. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48800-6_9

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  • DOI: https://doi.org/10.1007/3-540-48800-6_9

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