Photoelasticity
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photoelasticity
(¦fōd·ō′i′las′tis·əd·ē)
(optics) An experimental technique for the measurement of stresses and strains in material objects by means of the phenomenon of mechanical birefringence. photoelastic effect
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Photoelasticity
An experimental technique for the measurement of stresses and strains in material objects by means of the phenomenon of mechanical birefringence. Photoelasticity is especially useful for the study of objects with irregular boundaries and stress concentrations, such as pieces of machinery with notches or curves, structural components with slits or holes, and materials with cracks. The method provides a visual means of observing overall stress characteristics of an object by means of light patterns projected on a screen or photographic film. Photoelasticity is generally used to study objects stressed in two planar directions (biaxial), but with refinements it can be used for objects stressed in three spatial directions (triaxial). See also Birefringence.
When a stressed model is subjected to monochromatic polarized light in a polariscope the birefringence of the model causes the light to emerge refracted into two orthogonal planes. Because the velocities of light propagation are different in each direction, there occurs a phase shifting of the light waves.
When the waves are recombined with the polariscope, regions of stress where the wave phases cancel appear black, and regions of stress where the wave phases combine appear light. Therefore, in models of complex stress distribution, light and dark fringe patterns (isochromatic fringes) are projected from the model. These fringes are related to the stresses. See also Polarized light.
When white light is used in place of monochromatic light, the relative retardation of the model causes the fringes to appear in colors of the spectrum. White light is often used for demonstration, and monochromatic light is used for precise measurements. See also Stress and strain.
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Photoelasticity
Photoelasticity is an experimental method to determine the stress distribution in a material. The method is mostly used in cases where mathematical methods become quite cumbersome. Unlike the analytical methods of stress determination, photoelasticity gives a fairly accurate picture of stress distribution, even around abrupt discontinuities in a material. The method is an important tool for determining critical stress points in a material, and is used for determining stress concentration in irregular geometries.
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History
The photoelastic phenomena was first described by the scottish physicist David Brewster[1] .[2] Photoelasticity developed at the beginning of the twentieth century with the works of E.G.Coker and L.N.G Filon of University of London. Their book Treatise on Photoelasticity published in 1930 by the Cambridge Press became a standard text on the subject. Between 1930 and 1940 many other books in Russian, German and French appeared on the subject.
At the same time much development occurred in the field. Great improvements were achieved in the technique and the equipment was simplified. With the improvement in technology the scope of photoelasticity was extended to three dimensional state of stress. Many practical problems were solved using photoelasticity, and it soon became popular. A number of photoelastic laboratories were established in educational institutions and industries.
With the advent of digital polariscope using LEDs, continuous monitoring of structures under load became possible. This led to the development of dynamic photoelasticity. Dynamic photoelasticity has contributed greatly to the study of complex phenomena of fracture of materials.
Principles
The method is based on the property of birefringence exhibited by certain transparent materials. Birefringence is a property where a ray of light passing through a birefringent material experiences two refractive indices. The property of birefringence (or double refraction) is exhibited by many optical crystals. But photoelastic materials exhibit the property of birefringence only on the application of stress, and the magnitude of the refractive indices at each point in the material is directly related to the state of stress at that point. Thus, the first task is to develop a model made of such materials. The model has a similar geometry to that of the structure on which stress analysis is to be performed, ensuring that the stress in the model is similar to the stress in the structure.
When a ray of plane polarised light is passed through a photoelastic material, it gets resolved along the two principal stress directions and each of these components experiences different refractive indices. The difference in the refractive indices leads to a relative phase retardation between the two component waves. The magnitude of the relative retardation is given by the stress optic law:
where R is the induced retardation, C is the stress optic coefficient, t is the specimen thickness, σ11 is the first principal stress, and σ22 is the second principal stress.
The two waves are then brought together in a polariscope. The phenomena of optical interference takes place, and a fringe pattern is revealed, which depends on relative retardation. By studying the fringe pattern one can determine the state of stress at various points in the material.
Isoclinics and isochromatics
Isoclinics are the locus of the points in the specimen along which the principal stresses are in the same direction.
Isochromatics are the locus of the points along which the difference in the first and second principal stress remains the same. Thus they are the lines which join the points with equal maximum shear stress magnitude.
Two-dimensional photoelasticity
Photoelasticity can be applied both to three dimensional and two dimensional state of stress. But the application of photoelasticty to the three dimensional state of stress is more involved as compared to the state of two dimensional / plane stress system. So the present section deals with application of photoelasticity in investigation of a plane stress system. This condition is achieved when the thickness of the prototype is much smaller as compared to dimensions in the plane. Thus one is only concerned with stresses acting parallel to the plane of the model, as other stress components are zero.
The experimental setup varies from experiment to experiment. The two basic kinds of setup used are plane polariscope and circular polariscope.
Plane polariscope
The setup consists of two linear polarizers and a light source. The light source can either emit monochromatic light or white light depending upon the experiment. First the light is passed through the first polarizer which converts the light into plane polarized light. The apparatus is set up in such a way that this plane polarized light then passes through the stressed specimen. This light then follows, at each point of the specimen, the direction of principal stress at that point. The light is then made to pass through the analyzer and we finally get the fringe pattern.
The fringe pattern in a plane polariscope setup consists of both the isochromatics and the isoclinics. The isoclinics change with the orientation of the polariscope while there is no change in the isochromatics.
The same device functions as a plane polariscoe when quarter wave plates are taken aside or rotated so their axes parallel to polarization axes
Circular polariscope
In a circular polariscope setup two quarter-wave plates are added to the experimental setup of the plane polariscope. The first quarter-wave plate is placed in between the polariser and the specimen and the second quarter-wave plate is placed between the specimen and the analyser. The effect of adding the quarter-wave plates is that we get circularly polarised light.
The basic advantage of a circular polariscope over a plane polariscope is that in a circular polariscope setup we only get the isochromatics and not the isoclinics. This eliminates the problem of differentiating between the isoclinics and the isochromatics.
Applications
Photoelasticity has been used for a variety of stress analyses and even for routine use in design, particularly before the advent of numerical methods, such as for instance finite elements or boundary elements.[3]
Photoelasticity can successfully be used to investigate the highly localized stress state within masonry[4][5] or in proximity of a rigid line inclusion (stiffener) embedded in an elastic medium.[6] In the former case, the problem is nonlinear due to the contacts between bricks, while in the latter case the elastic solution is singular, so that numerical methods may fail to provide correct results. These can be obtained through photoelastic techniques.
See also
References
- ^ D. Brewster, Experiments on the depolarization of light as exhibited by various mineral, animal and vegetable bodies with a reference of the phenomena to the general principle of polarization, Phil. Tras. 1815, pp.29-53.
- ^ D. Brewster, On the communication of the structure of doubly-refracting crystals to glass, murite of soda, flour spar, and other substances by mechanical compression and dilation, Phil. Tras. 1816, pp.156-178.
- ^ Frocht, M.M., 1965. Photoelasticity. J. Wiley and Sons, London
- ^ D. Bigoni and G. Noselli, Localized stress percolation through dry masonry walls. Part I - Experiments. European Journal of Mechanics A/Solids, 2010, 29, 291-298.
- ^ D. Bigoni and G. Noselli, Localized stress percolation through dry masonry walls. Part II - Modelling. European Journal of Mechanics A/Solids, 2010, 29, 299-307.
- ^ G. Noselli, F. Dal Corso and D. Bigoni, The stress intensity near a stiffener disclosed by photoelasticity. International Journal of Fracture, 2010, 166, 91–103.
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