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| <!-- EDIT BELOW THIS LINE --> | | <br><br>The line moves rapidly. Is this beginning to sound like a bit of work? It's proven as one of the finest web hosting services; it's an internet service that helps you in creating your own website for your business or any personal interest you might have or just for fun. Reseller Options. If you did your grounding about the reason of your site, then you will have an easy time in influential just how much of these supplies would you need. All in all, it's not that difficult to make the right choice for hosting when you're reading good web hosting reviews - but don't rush it unless it's absolutely necessary, and ensure you're looking at the full picture before making a final decision. So i had to chose own publishing platform and i went with Hostgator. The prices of different plans relate to efficiency of space provided, and the underlying monetary value. You also have the choice on which kind of reseller account you would like, you get the aluminum, copper, silver, gold as well as diamond plan. See that free blogging platforms can shut down your site at any given moment with no alarm, as a result this is in no way a respectable vision in truth, except if you aren't overly fond of your attempt and do not bother losing all with no forewarning.You will acquire a great blog platform such as WordPress, which can with no trouble be activated through your HostGator user dashboard, by means of this you have no limitations without stopping what you could make known and with completely no anxiety of having your website simply erased with no notice.<br><br><br><br>Again, try to build a community within each of these in order to gain the true benefits. Scrubbing bots never sleep. If you have any sort of [http://Dict.Leo.org/?search=inquiries inquiries] concerning where and ways to utilize [http://www.carbondaletimes.com/node/3628 http://www.hostgator1centcoupon.info/], you could contact us at our internet site. A Lot Of Plans And [http://Data.gov.uk/data/search?q=Programs Programs] Are Offered Through Hostgator HostGator delivers a veritable plethora of hosting plans to suit each and every site want. This is primarily because of the ability to use many sub-domains under one account. We ourselves are clients of Hostgator. It's through passion and drive that you'll not only start a blog but become a powerhouse on the web. Currently being stored up-to-date is a really good attribute.With equally the telephone and are living chat purchaser service, I under no circumstances felt I was offered stock solutions. The type of packages HostGator has to offer:The Reseller Hosting plan: this gives you the capability to use your selected hard drive space and bandwidth to host websites on behalf of third parties. |
| [[Image:BiodegradablePlasticUtensils2.jpg|right|thumb|300px|A picture created using photoelasticity, of plastic utensils]]
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| '''Photoelasticity''' is an experimental method to [[stress analysis|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==
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| The photoelastic phenomenon was first described by the [[Scotland|Scottish]] [[physicist]] [[David Brewster]]<ref>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.</ref>
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| .<ref>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.</ref>
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| Photoelasticity developed at the beginning of the twentieth century with the works of [[E.G.Coker]] and [[Louis Napoleon George Filon|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 language|Russian]], [[German language|German]] and [[French language|French]] appeared on the subject.
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| 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.
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| With the advent of digital polariscope using light-emitting diodes, 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 such as fracture of materials.
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| ==Principles==
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| [[Image:Plastic Protractor Polarized 05375.jpg|thumb|Tension lines in plastic protractor seen under cross-polarized light.]]
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| 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 index|refractive indices]]. The property of birefringence (or double refraction) is observed in many optical [[crystal]]s. Upon the application of stresses, photoelastic materials exhibit the property of birefringence, and the magnitude of the refractive indices at each point in the material is directly related to the state of stresses at that point. Information such as maximum shear stress and its orientation are available by analyzing the birefringence with an instrument called polariscope.
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| When a ray of [[Electromagnetic radiation|light]] passes through a photoelastic material, its electromagnetic wave components gets resolved along the two [[Stress (mechanics)|principal stress directions]] and each of these components experiences different refractive indices due to the birefringence. The difference in the refractive indices leads to a relative [[phase (waves)|phase]] retardation between the two components. Assuming a thin specimen made of [[Hooke's law|isotropic]] materials, where two-dimensional photoelasticity is applicable. The magnitude of the relative retardation is given by the ''stress-optic law'':<ref>Dally, J.W. and Riley, W.F., ''Experimental Stress Analysis,'' 3rd edition, McGraw-Hill Inc., 1991</ref>
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| :<math> \Delta = \frac{2\pi t }{\lambda} C ( \sigma_{1} - \sigma_{2}) </math>
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| where Δ is the induced retardation, ''C'' is the stress-optic coefficient, ''t'' is the specimen thickness, σ<sub>1</sub> and σ<sub>2</sub> are the first and second principal stresses, respectively. The retardation changes the polarization of transmitted light. The polariscope combines the different polarization states of light waves before and after passing the specimen. Due to optical [[Interference (wave propagation)|interference]] of the two waves, a fringe pattern is revealed. The number of fringe order ''N'' is denoted as
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| :<math> N = \frac{\Delta}{2\pi}</math>
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| which depends on relative retardation. By studying the fringe pattern one can determine the state of stress at various points in the material.
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| For materials that do not show photoelastic behavior, it is still possible to study the stress distribution in such materials. The first step is to build a model using photoelastic materials, which has similar geometry as the real structure to be investigated. The loading is then applied in the same way to ensure that the stress distribution in the model is similar to the stress in the real structure.
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| ==Isoclinics and isochromatics==
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| Isoclinics are the loci of the points in the specimen along which the principal stresses are in the same direction.
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| Isochromatics are the loci 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.<ref>Ramesh, K., ''Digital Photoelasticity,'' Springer, 2000</ref>
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| ==Two-dimensional photoelasticity==
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| [[File:Photoelasticimetry1.JPG|thumb|Photoelasticity]]
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| 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 or 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.
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| The working principle of two-dimensional photoelasticity allows the measurement of retardation, which can be converted to the difference between the first and second principal stress and their orientation. To further get values of each stress component, a technique called stress-separation is required.<ref>Fernandez M.S-B., Calderon, J.M.A., Diez, P.M.B and Segura, I.I.C, Stress-separation techniques in photoelasticity: A review. ''The Journal of Strain Analysis for Engineering Design'', 2010, 45:1 [doi:10.1243/03093247JSA583]</ref> Several theoretical and experimental methods are utilized to provide additional information to solve individual stress components.
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| ==Plane polariscope==
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| The setup consists of two linear [[polarizer]]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. (e/_)
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| 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.
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| [[Image:Transmission Circular Polariscope.svg|right|thumb|400px|Transmission Circular Polariscope<br />The same device functions as a plane polariscoe when quarter wave plates are taken aside or rotated so their axes parallel to polarization axes]]
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| ==Circular polariscope==
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| In a circular polariscope setup two quarter-[[wave plate]]s are added to the experimental setup of the plane polariscope. The first quarter-wave plate is placed in between the polarizer and the specimen and the second quarter-wave plate is placed between the specimen and the analyzer. The effect of adding the quarter-wave plate after the source-side polarizer is that we get [[circular polarization|circularly polarized light]] passing through the sample. The analyzer-side quarter-wave plate converts the circular polarization state back to linear before the light passes through the analyzer.
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| 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.
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| ==Applications==
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| 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.<ref>Frocht, M.M., ''Photoelasticity''. J. Wiley and Sons, London, 1965</ref> Digitization of polariscopy enables fast image acquisition and data processing, which allows its industrial applications to control quality of manufacturing process for materials such as glass<ref>Ajovalasit, A., Petrucci, G., Scafidi, M., RGB photoelasticity applied to the analysis of membrane residual stress in glass, ''Measurement Science and Technology'', 2012, 23-2, no. 025601</ref> and polymer.<ref>Kramer, S., Beiermann, B., Davis, D., Sottos, N., White, S., Moore, J., Characterization of mechanochemically active polymers using combined photoelasticity and fluorescence measurements, ''SEM Annual Conference and Exposition on Experimental and Applied Mechanics'', 2010, 2, pp.896-907.</ref> Dentistry utilizes photoelasticity to analyze strain in denture materials.<ref>Fernandes, C.P., Glantz, P.-O.J., Svensson, S.A., Bergmark, A.
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| Reflection photoelasticity: A new method for studies of clinical mechanics in prosthetic dentistry
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| ''Dental Materials'', 2003, 19-2, pp.106-117.</ref>
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| [[File:Photoelasticity stiffener.jpg|thumb|300px|Photoelastic model to validate the [[rigid line inclusion|stiffener]] model. Isochromatic fringe patterns around a steel platelet in a photo-elastic two-part epoxy resin.]] | |
| Photoelasticity can successfully be used to investigate the highly localized stress state within masonry<ref>[http://www.ing.unitn.it/~bigoni 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.]</ref><ref>[http://www.ing.unitn.it/~bigoni D. Bigoni and G. Noselli, Localized stress percolation through dry masonry walls. Part II - Modelling. ''European Journal of Mechanics A/Solids'', 2010, 29, pp.299-307.]</ref>
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| <ref>Bigoni, D. Nonlinear Solid Mechanics: Bifurcation Theory and Material Instability. Cambridge University Press, 2012 . ISBN 9781107025417.</ref> or in proximity of a [[rigid line inclusion (stiffener, anticrack)|rigid line inclusion (stiffener)]] embedded in an elastic medium.<ref>[http://www.ing.unitn.it/~bigoni 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.]</ref> 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. Dynamic photoelasticity integrated with high-speed photography is utilized to investigate fracture behavior in materials.<ref>Shukla, A., High-speed fracture studies on bimaterial interfaces using photoelasticity - A review, ''Journal of Strain Analysis for Engineering Design,'' 2012, 36-2, 119-142.</ref>
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| ==See also==
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| * [[Acousto-optic modulator]]
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| * [[Photoelastic modulator]]
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| * [[Polarimetry]]
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| ==References==
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| <references/>
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| ==External links==
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| *[http://www.doitpoms.ac.uk/tlplib/photoelasticity/history.php University of Cambridge Page on Photoelasticity.]
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| *[http://public.fotki.com/ROBERT1010/scitech/photoelasticstress4.html Photograph of photoelastic stress pattern using plane-polarized white light.]
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| *[http://ssmg.ing.unitn.it Laboratory for Physical Modeling of Structures and Photoelasticity (University of Trento, Italy)]
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| *[http://www.photostress.com Reflection Photoelasticity Appartus.]
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| [[Category:Mechanics]]
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| [[Category:Mechanical engineering]]
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| [[Category:Materials science]]
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| [[Category:Optics]]
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