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On the effect of rotating secondary principal stresses in scattered-light photoelasticity

The concept of poincare's equivalent system is applied in order to develop the general scattered-light-photoelasticity equations

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Abstract

The lack of understanding of the effect of the rotation of secondary principal axes has been a severe limitation of the scattered-light method. The method of Poincare's equivalent system has been applied in order to develop a general formula for scattered-light intensity. Relationships among the orientation of eigenvectors and their phase retardation and stresses have been found. The method is illustrated by the solution of the problem of a circular rod loaded by a combination of torsion and axial load. An experimental procedure has also been suggested.

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Abbreviations

E i :

component of light vector

\(\sigma _{ij} \) :

component of stress tensor

U :

transformation unitary matrix

M i :

component of the transformation matrix

x, y, z :

referential coordinate axes

x o ,y o ,z :

referential coordinate axes at the point of entrance to the model

u, v :

eigenvectors

u o ,v o :

eigenvectors at the point of entrance to the model

2Δ:

phase retardation, deg

\(2\Delta _o \) :

phase retardation of the eigenvectors, deg

\(2\Delta _k \) :

phase retardation of the compensator, deg

I sc :

scattered-light intensity

I scc :

scattered-light intensity, incident light circularly polarized

ϕ:

angle of rotation of secondary principal axes, deg

R :

\(\frac{{d\phi }}{{d\Delta }}\)

\(\omega _1 ,\omega _2 \) :

angle of eigenvectors and axes of referential coordinate system, deg

\(\omega _1 ^* ,\omega _2 ^* \) :

angles of eigenvectors and secondary principal stresses, deg

\(\theta = \omega _1 + \omega _2 \) :

Poincare rotator angle, deg

α:

observation angle, deg

β:

angle of principal direction of the compensator and polarization of incident light, deg

γ:

angle of principal direction of the compensator and eigenvector, deg

\(\alpha _2 \) :

angle of eigenvector and the direction of observation, deg

References

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  2. Anderholt, R., McKinney, J. M., Ranson, W. F. andSwinson, W. F., “Effect of Rotating Secondary Principal Axes in Scattered-light Photelasticity,”Experimental Mechanics,10 (4),160–165 (1970).

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  3. Drucker, D. R. andMindlin, R. D., “Stress Analysis by Three-dimensional Photoelastic Methods,”J. Appl. Phys.,11,724 (1940).

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  4. 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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  5. Pipes, L. A., Applied Mathematics for Engineers and Physicist, McGraw-Hill, New York (1958).

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  6. Richartz, M. and Hsu, H. Y., “Analysis of Elliptical Polarization,” J. of Opt. Soc. of Am., 136 (Feb. 1949).

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  8. Jones, R. C., “A New Calculus for the Treatment of Optical Systems I,” J. of Opt. Soc. of Am.,488 (July 1941).

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Authors and Affiliations

  1. Solid Mechanics Center, Institute of Technology, Southern Methodist University, 75222, Dallas, TX

    Jan Cernosek (Associate Professor of Solid Mechanics)

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  1. Jan Cernosek
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Cernosek, J. On the effect of rotating secondary principal stresses in scattered-light photoelasticity. Experimental Mechanics 13, 273–279 (1973). https://doi.org/10.1007/BF02322723

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  • DOI: https://doi.org/10.1007/BF02322723

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