Abstract
For nearly a century the photoelastic method has been a reference to verify special applications of the theory of elasticity and to provide a solution to cases of loaded structures without theoretical models. Today photoelasticity has been largely replaced by numerical methods, such as finite elements, which provide solutions for any structural problem with great detail and accuracy, and is therefore confined to the role of an illustration tool. This technique is based on an analogy of the optical behavior of transparent amorphous bodies; this fact limits the applications but its capability of analyzing the general field and, at the same time, clarifying details, is still very useful, and applications of photoelastic techniques continue to be presented in the most qualified international venues. It is therefore still logical to present an overview of the theory and to discuss some applications. The classical approach remains the best way of understanding the inherent advantages and drawbacks and, thanks to the inverse approach, continues to be a useful investigation method.
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Notes
- 1.
The Society of Experimental Mechanics SEM in the United States included about 80 papers in the annual 2009 conference and comparable numbers in previous years. At the ICEM (International Conference of Experimental Mechanics in 2014) two sessions where dedicated to this method.
- 2.
The light color is determined by the wavelength ; the values of the visible spectrum range from dark red (\(f = 390 \times 10^{12}\) Hz or \(\lambda = 770 \,\mathrm{nm} \)) to violet (\(f = 770 \times 10^{12}\) Hz, or \(\lambda =\; 390\,\mathrm{nm}\)) (\(1\,\mathrm{nm} = 10^{-9}\,\mathrm{m}\)), passing through orange, yellow, green, blue, Indigo-violet . If the light vector is composed of vibrations \({a_1, a_2,\ldots , a_n}\) of the same frequency, light is monochromatic; if the components have different frequencies, the eye perceives them all together as white light.
- 3.
The instantaneous value of the field in planes \( x r \) and \(y r\) is expressed, for Eq. 3.1, by:
$$ a_x = |A_x| \cos \left[ {2 \pi \over \lambda }(r-ct) +\phi _x\right] $$$$ a_y = \pm |A_y| \cos \left[ {2 \pi \over \lambda }(r-ct) +\phi _x\right] $$and instantaneous value of the resulting vector is:
$$ a_r= \sqrt{a_x^2 + a_y^2} = \sqrt{2}|A| \cos \left[ {2 \pi \over \lambda }(r-ct) +\phi _x\right] . $$ - 4.
Currently the employed filters are Polaroid \(\textregistered \) (Polaroid Co., Cambridge, Mass, USA), supplied in sheets of various size; “this material, known as J-sheet, was later replaced by the improved H-sheet. H-sheet is a polyvinyl alcohol (PVA) polymer impregnated with iodine. During manufacture, the PVA polymer chains are stretched such that they form an array of aligned, linear molecules in the material. The iodine dopant attaches to the PVA molecules and makes them conducting along the length of the chains. Light polarized parallel to the chains is absorbed, and light polarized perpendicular to the chains is transmitted” [7].
- 5.
The colors of all wavelengths but the extinct one, are transmitted and perceived as a single color, called the complementary color of the extinguished one.
- 6.
Taken from Prof. Stephen A. Nelson, Department of Earth and Environmental Sciences. EENS 2110, Mineralogy, Tulane University: Interference Phenomena, Compensation, and Optic Sign.
- 7.
Elements can be selected square, to have a ratio equal to \(1\) for the all points.
- 8.
References
Ajovalasit A, Barone S, Petrucci G (1998) A review of automated methods for the collection and analysis of photoelastic data. J Strain Anal 33(2):75–91
Asundi A (1998) Recent advances in photoelastic applications. School of Mechanical and Aerospace Engineering. http://www.ntu.edu.sg/home/masundi/optical-methods/photoelasticity/recent_advances.html
Diaz FA, Patterson EA, Siegmann P (2009) A new experimental method for calculating KI and KII using photoelasticity. In: SEM (ed) Proceedings of the 2009 annual conference, SEM, Bethel
Patterson EA (2002) Digital photoelasticity: principles, practice and potential. Strain 38(1):27–39
Ramesh K (2000) Digital photoelasticity: advanced techniques and applications, vol 1. Springer, Berlin
Ajovalasit A (2009) Analisi sperimentale delle tensioni con la fotomeccanica: fotoelasticita, moire, olografia, speckle, correlazione immagini, vol 1. Aracne Roma, Roma
Polaroid filter on Wikipedia (2014). http://en.wikipedia.org/wiki/Polaroid_(polarizer)
Jones RC (1941) A new calculus for the treatment of optical systems. J Opt Soc Am 31(7):488–503
Dally JW, Riley WF (2005) Experimental stress analysis, 4th edn. McGraw-Hill, New York
Föppl L, Mönch E (1959) Praktische Spannungsoptik, vol 1, 2nd edn. Springer, Berlin
Frocht MM (1948) Photoelasticity, vols 1 and 2. Wiley, New York
Jessop HT, Harris FC (1949) Photoelasticity, vol 1. Hume Press, London
Kuske A, Robertson G (1974) Photoelastic stress analysis, vol 1, 1st edn. Wiley, London
Mondina A (1958) La Fotoelasticità, vol 1. Rivista di Meccanica, Milano
Wolf H (1961) Spannungsoptik. Springer, Berlin
Nelson SA (2014) Earth and environmental sciences 2110 mineralogy. Syllabus 1, Tulane University, Tulane, USA, http://www.tulane.edu/sanelson/eens211/index.html
Post D (1966) Fringe multiplication in three-dimensional photoelasticity. J Strain Anal Eng Des 1:380–388
Kenny B, Hugill JW (1967) Comparison of fringe multiplication and Tardy compensation methods for a frozen stress investigation. Strain 3(1):3–7. doi:10.1111/j.1475-1305.1967.tb00857.x, http://dx.doi.org/10.1111/j.1475-1305.1967.tb00857.x
Borbas L (2004) Some problems of data evaluation of photoelastic coating technique in case of small-size, fibre-optics fitted equipment. In: Advances in experimental mechanics, vol 1. ICEM 12, Bari, McGraw-Hill, pp 595–596. ISBN 88 386 6273-8
Borbas L, Thamm F, Olah L (2006) Comparison of strain gage technique and photoelastic coating method in the investigation procedure of femur prostheses. J Comput Appl Mech 7(1):3–12
Gyökös F, Borbas L, Thamm F (2005) Following the process of failure during fatigue testing of a bus frame structure by photoelastic coating, vol XII, Slovakian Academy, Zilina, pp 7–12. ISSN 1335-0803
Ramakrishnan V, Ramesh K (2014) Influence of thermal cycling on residual stress generated in glass using digital photoelasticity. In: Proceedings of ICEM 16, EURASEM and BSSM, Cambridge UK, see http://www.icem16.org/contenu.php?page=prog
Gotkhindi T, Simha KRY (2014) Force analysis in porous media. In: Proceedings of ICEM 16, EURASEM and BSSM, Cambridge UK, http://www.icem16.org/contenu.php?page=prog
Huang MJ, Huang ZW (2014) Temporal phase unwrapping works at stress concentration zones. In: Proceedings of ICEM 16, EURASEM and BSSM, Cambridge UK, http://www.icem16.org/contenu.php?page=prog
Tomlinson R, Taylor Z (2014) Novel photoelastic materials and methods for validation of biomechanics models. In: Proceedings of ICEM 16, EURASEM and BSSM, Cambridge UK, http://www.icem16.org/contenu.php?page=prog
Noselli G, Bigoni D et al (2014) Stress singularity and neutrality around a stiffener revealed by photoelasticity. In: Proceedings of ICEM 16, EURASEM and BSSM, Cambridge UK, http://www.icem16.org/contenu.php?page=prog
Surendra KVN, Simha KRY (2014) Analysis of obliquely oriented edge cracked semicircular ring (OECSR). In: Proceedings of ICEM 16, EURASEM and BSSM, Cambridge UK, http://www.icem16.org/contenu.php?page=prog
Shreesudha B, Abhinav T, Ramesh K (2014) Photoelastic study of an inclined crack from a fillet of a biaxially loaded cruciform specimen. In: Proceedings of ICEM 16, EURASEM and BSSM, Cambridge UK, http://www.icem16.org/contenu.php?page=prog
Antony SJ, Barakat T (2014) Processing behaviour of particulate materials using photo stress analysis technology. In: Proceedings of ICEM 16, EURASEM and BSSM, Cambridge, UK, http://www.icem16.org/contenu.php?page=prog
Photoelastic coating materials (2014). http://www.vishaypg.com/micro-measurements/photo-stress-plus/category/coating/?subCategory=materials
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Freddi, A., Olmi, G., Cristofolini, L. (2015). Introduction to Photoelasticity. In: Experimental Stress Analysis for Materials and Structures. Springer Series in Solid and Structural Mechanics, vol 4. Springer, Cham. https://doi.org/10.1007/978-3-319-06086-6_3
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