Photoelasticity
Encyclopedia
Stress analysis
Stress analysis is an engineering discipline that determines the stress in materials and structures subjected to static or dynamic forces or loads. A stress analysis is required for the study and design of structures, e.g., tunnels, dams, mechanical parts, and structural frames among others, under...
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 serves as an important tool for determining the critical stress points in a material and is often used for determining stress concentration factors in irregular geometries.
History
The photoelastic phenomena was first described by the scottishScotland
Scotland is a country that is part of the United Kingdom. Occupying the northern third of the island of Great Britain, it shares a border with England to the south and is bounded by the North Sea to the east, the Atlantic Ocean to the north and west, and the North Channel and Irish Sea to the...
physicist
Physicist
A physicist is a scientist who studies or practices physics. Physicists study a wide range of physical phenomena in many branches of physics spanning all length scales: from sub-atomic particles of which all ordinary matter is made to the behavior of the material Universe as a whole...
David Brewster
David Brewster
Sir David Brewster KH PRSE FRS FSA FSSA MICE was a Scottish physicist, mathematician, astronomer, inventor, writer and university principal.-Early life:...
.
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
University of London
-20th century:Shortly after 6 Burlington Gardens was vacated, the University went through a period of rapid expansion. Bedford College, Royal Holloway and the London School of Economics all joined in 1900, Regent's Park College, which had affiliated in 1841 became an official divinity school of the...
. 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
Russian language
Russian is a Slavic language used primarily in Russia, Belarus, Uzbekistan, Kazakhstan, Tajikistan and Kyrgyzstan. It is an unofficial but widely spoken language in Ukraine, Moldova, Latvia, Turkmenistan and Estonia and, to a lesser extent, the other countries that were once constituent republics...
, German
German language
German is a West Germanic language, related to and classified alongside English and Dutch. With an estimated 90 – 98 million native speakers, German is one of the world's major languages and is the most widely-spoken first language in the European Union....
and French
French language
French is a Romance language spoken as a first language in France, the Romandy region in Switzerland, Wallonia and Brussels in Belgium, Monaco, the regions of Quebec and Acadia in Canada, and by various communities elsewhere. Second-language speakers of French are distributed throughout many parts...
appeared on the subject.
At the same time lot of development was made in field. Great improvements were achieved in the technique and the equipment was simplified. With the improvement in technology the scope of photoelasticity was also extended to three dimensional state of stress. Many practical problems were solved using photoelasticity and it soon became very popular. A number of photoelastic laboratories were then setup in both 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
Birefringence
Birefringence, or double refraction, is the decomposition of a ray of light into two rays when it passes through certain anisotropic materials, such as crystals of calcite or boron nitride. The effect was first described by the Danish scientist Rasmus Bartholin in 1669, who saw it in calcite...
, which is exhibited by certain transparent materials. Birefringence is a property by virtue of which a ray of light passing through a birefringent material experiences two refractive indices
Refractive index
In optics the refractive index or index of refraction of a substance or medium is a measure of the speed of light in that medium. It is expressed as a ratio of the speed of light in vacuum relative to that in the considered medium....
. The property of birefringence or double refraction is exhibited by many optical crystal
Crystal
A crystal or crystalline solid is a solid material whose constituent atoms, molecules, or ions are arranged in an orderly repeating pattern extending in all three spatial dimensions. The scientific study of crystals and crystal formation is known as crystallography...
s. 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 out of such materials. The model has a similar geometry to that of the structure on which stress analysis is to be performed. This ensures that the state of the stress in the model is similar to the state of 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
Phase (waves)
Phase in waves is the fraction of a wave cycle which has elapsed relative to an arbitrary point.-Formula:The phase of an oscillation or wave refers to a sinusoidal function such as the following:...
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 we get a fringe pattern, which depends on relative retardation. Thus 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 polarizerPolarizer
A polarizer is an optical filter that passes light of a specific polarization and blocks waves of other polarizations. It can convert a beam of light of undefined or mixed polarization into a beam with well-defined polarization. The common types of polarizers are linear polarizers and circular...
s 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.
Circular polariscope
In a circular polariscope setup two quarter-wave plateWave plate
A wave plate or retarder is an optical device that alters the polarization state of a light wave travelling through it.- Operation :A wave plate works by shifting the phase between two perpendicular polarization components of the light wave. A typical wave plate is simply a birefringent crystal...
s 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
Circular polarization
In electrodynamics, circular polarization of an electromagnetic wave is a polarization in which the electric field of the passing wave does not change strength but only changes direction in a rotary type manner....
.
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.Photoelasticity can successfully be used to investigate the highly localized stress state within masonry or in proximity of a rigid line inclusion (stiffener) embedded in an elastic medium. 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.