Abstract
Using the theory of the unitary system of retarders, it is shown that two seemingly different theories of photoelasticity (Sampson’s phenomenological theory and Dally and Prabhakaran’s stress-proportioning concept) are identical if the heterogeneous nature of the composites is respected. It is also shown that the optical isoclinic parameter can be accurately predicted even if the initial birefringence is present in the unloaded specimen.
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Abbreviations
- E i :
-
component of the light vector
- E io :
-
component of light vector at the point of entrance
- \(2\Delta _i\) :
-
phase retardation (rad)
- \(2\Delta _{res}\) :
-
residual phase retardation
- α:
-
azimuth of the direction of polarization in the fiber and axis y
- θ:
-
azimuth of the direction of polarization in the fiber and matrix
- ξi :
-
azimuth of the direction of polarization and fiber
- M i :
-
coefficient of the matrix
- \(G(\Delta _i )\) :
-
phase matrix
- S(β):
-
rotation matrix
- \(\omega _i\) :
-
azimuth of the principal directions of Poincare’s equivalent system and axis x
- n :
-
number of fibers traversed by the light
- f l ,f t ,f lt :
-
fundamental photoelastic constants (Ref. 2)
References
Pih, H. andKnight, C. E., “Photoelastic Analysis of Anisotropic Fiber Reinforced Composites,”J. of Comp. Mat.,3,94 (1969).
Sampson, R. C., “A Stress-Optic Law for Photoelastic Analysis of Orthotropic Composites,”Experimental Mechanics,10 (5),210–215 (1970).
Dally, J. W., andPrabhakaran, R., “Photo-orthotropic-elasticity,”Experimental Mechanics,11 (8),346–356 (1971).
Bert, C. W., “Theory of Photoelasticity for Birefringent Filamentary Composites,”Fibre Science and Technology,5,165–171 (1972).
Pipes, R. B. andDalley, J. W., “On the Fiber-Reinforced Birefringent Composite Materials,”Experimental Mechanics,13 (8),348–349 (1973).
Jones, R. C., “A New Calculus for the Treatment of Optical Systems I,” J. of Opt. Soc. of Am., 488 (July, 1941).
Aben, H. K., “Optical Phenomena in Photoelastic Models by the Rotation of Principal Axes,”Experimental Mechanics,6 (1),13–22 (1966).
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Cernosek, J. On photoelastic response of composites. Experimental Mechanics 15, 354–357 (1975). https://doi.org/10.1007/BF02318876
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DOI: https://doi.org/10.1007/BF02318876