Abstract
The use of holographic interferometry for stress analysis of nontransparent objects is limited by rigid-body displacements of the object. These displacements can alter the fringe patterns and often cause the fringes to disappear completely. A technique of compensation for this deterioration of the fringe pattern forreal-time holographic interferometry is described in this paper. It is especially designed to permit the accurate measurement of the out-of-plane component of strain near regions of stress concentration in plates that are subjected to in-plane loading. It is first shown that the fringes caused by a pure rigid-body displacement can be eliminated almost completely by translations of the hologram and rotation of the illumination wave. This procedure is first described when the displacement is known; then when it is unknown. A method to estimate the error made in the correction is presented.
In actual stress-analysis problems, the object is both rigidly displaced and strained. Assuming the rigid displacement is known and corrected as previously, the analysis is developed to relate the fringe pattern to the strain-related displacement. This analysis takes into account the optical modifications of the system that are necessary to achieve the rigid-body-displacement correction. When the rigid-body displacement is unknown, the method is shown still to be workable through the use of various symmetries and boundary conditions. Two sample interferograms are presented as illustrations. Quantitative treatment of data from one of these are presented in a companion paper.
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Abbreviations
- i's:
-
unit vectors, with directions as defined in text
- L :
-
distance between the object and the optical center of the viewing system
- l's :
-
optical distances from the center of the specimen to source of illumination
- N p :
-
fringe order related to point P
- O Z :
-
optical axis of the viewing system
- Oξ:
-
axis of rotation in the plane of the specimen
- r :
-
distance between the optical axis and a given point P on the object
- S :
-
distance between the center of the specimen and any point on its surface
- u r :
-
radial component of the displacement due to strains
- w :
-
out-of-plane component of the displacement due to strains
- α:
-
angle of rotation of the illumination beam
- δ o :
-
optical-path difference related to the point O
- δ p :
-
optical-path difference related to a point P
- ∈ δ :
-
error in optical-path difference due to improper correction of rotations
- ∈ N :
-
error in fringe order corresponding to E
- λ:
-
wavelength of the illuminating light
- ϕ:
-
angle of rotation of the specimen
- θ:
-
angular distance between a point P on the object and the optical axis
References
Champagne, E. B., “Proc. of the Soc. of Photo-optical Instrumentation Engineers-Dev. in Holography,” 133–144, Boston (1971).
Kersh, L. A., “Optical & Acoustical Holography,” 277–302, Plenum Press (1972).
Wales, S., “Visibility of Fringes in Holographic Interferometry of Diffusely Reflecting Surfaces,”Arkiv fur Fysik,40,299 (1970).
Vienot, J. Ch., et al, “Engineering Uses of Holography,” Cambridge University Press, 133 (1970).
Sollid, J. E., “Proc. of the Soc. of Photo-optical Instrumentation Engineers-Dev. in Holography,” 171–176, Boston (1971).
Sciammarella, C. A., andGilbert, J. A., Ap. Op.,12 (8),1951–1957 (1973).
DeLarminat, P. M., and Wei, R. P., “Normal Surface Displacement Around A Circular Hole by Reflection Holographic Interferometry,” submit. to Experimental Mechanics (SESA) (1975).
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deLarminat, P.M., Wei, R.P. A fringe-compensation technique for stress analysis by reflection holographic interferometry. Experimental Mechanics 16, 241–248 (1976). https://doi.org/10.1007/BF02321147
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DOI: https://doi.org/10.1007/BF02321147