Main Article Content
Abstract
The advent of digital photoelasticity saw the development of various techniques to get photoelastic data of isoclinics and isochromatics at every pixel in the domain. Unlike in other interferometric techniques, in photoelasticity one gets phase data of two quantities and their mutual dependence and interaction affect their evaluation. For stress separation studies, one requires both isochromatics and isoclinics accurately free of any kinks in the domain. With this in view, a robust approach is evolved to get these parameters. Initially wrapped isoclinics are obtained using a plane polariscope based phase shifting technique. These are unwrapped by a quality guided approach. However, the result has several kinks due to isochromatic-isoclinic interaction. An outlier smoothing algorithm is proposed for getting a smooth variation of the isoclinics. Six-step phase shifting method using a circular polariscope is used for determining the isochromatic data. The smoothed isoclinic values obtained are used in isochromatic calculation to get isochromatic phasemap free of ambiguities. This phasemap is also unwrapped by a quality guided approach and smoothed by the outlier algorithm. These methodologies are validated for two benchmark problems of a disk under diametral compression and a ring subjected to internal pressure. The models are subjected to moderate loads showing a high level of isochromatic-isoclinic interaction.
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References
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References
Ramesh, K., "Digital Photoelasticity: Advanced Techniques and Application", Springer-Verlag, Berlin, Germany, 2000.
Ajovalasit, A., Barone, S. and Petrucci, G., "A Method for Reducing the Influence of the QuarterWave Plate Error in Phase-shifting Photoelasticity", J. Strain Analysis for Eng. Des., Vol.33, No.3, pp.
-216, 1998.
Sai Prasad, V. and Ramesh, K., "Background Intensity Effects on Various Phase Shifting Techniques in Photoelasticity", Proceedings of the Conference on Optics and Photonics in Engineering, New Delhi, pp.183-186, 2003.
Ramji, M., Gadre, V.Y. and Ramesh, K., "Comparative Study of Evaluation of Primary Isoclinic Data by Various Spatial Domain Methods in Digital Photoelasticity", J. Strain Analysis for Eng. Des., Vol. 41, No.5, pp. 333-348, 2006.
Itoh., "Analysis of Phase Unwrapping Problem", App. Opt., Vol. 21, No.14, pp. 2470, 1982.
Sai Prasad, V., Madhu, K. R. and Ramesh, K., "Towards Effective Phase Unwrapping in Digital Photoelasticity", Opt. and Lasers in Eng., Vol. 42, pp.421-436, 2004.
Wang, Z. F. and Patterson, E. A., "Use of Phase Stepping with Demodulation and Fuzzy Sets for Birefringence Measurement", Opt. and Lasers in Eng., Vol. 22, pp. 91-104, 1995.
Ramesh, K. and Mangal, S. K., "Phase-shifting Calculations in 2-D Photoelasticity: Revisited", Journal of the Aeronautical Society of India, Vol. 52, No. 2, pp. 121-136, 1999.
Prashant, P. L., Madhu, K. R. and Ramesh, K., "New Initiatives in Phase Unwrapping in Digital Photoelasticity", Proc. SPIE Vol.5852, pp.192-197, Proc. Int. Conf. on Exp. Mech. and Third Conference of the Asian Committee on Exp. Mech., 29th November -1st December, Singapore, 2004.
Ramesh, K. and Tamrakar, D. K., "Improved Determination of Retardation in Digital Photoelasticity by Load Stepping", Opt. and Lasers in Eng., Vol. 33, pp.387-400, 2000.
Ekman, M. J. and Nurse, A. D., "Completely Automated Determination of Two-dimensional Photoelastic Parameters Using Load Stepping", Opt. Eng., Vol. 34, pp. 1845-1851, 1998.
Madhu, K. R. and Ramesh, K., "New Boundary Information Encoding and Auto Seeding for Effective Phase Unwrapping of Specimens with Cutouts", Strain, Vol. 43, pp. 54-57, 2007.
Plouzennec, N., Dupre, J.C. and Lagarde, A., "Whole Field Determination of Isoclinic and Isochromatic Parameters", Exp. Tech., Vol. 23, pp. 30-33, 1999.
Aben, H., Ainola L. and Anton, J., "Half-fringe Phase-stepping with Separation of the Principal Stress Directions", In Proc. of Estonian Academic Science Engineering, Estonia, , Vol.5, No.3, pp. 198211, 1999.
Ramji, M. and Ramesh, K., "Isoclinic Parameter Unwrapping and Smoothening in Digital Photoelasticity", Proc. Int. Conf. Opt. and Optoelectronics, Instruments Research and Development Establishment, Dehradun, 12th - 15th December, 2005.
Quiroga, J. A. and Gonzalez-Cano, A., "Separation of Isoclinics and Isochromatics from Photoelastic Data Using Regularized Phase-tracking Technique", App. Opt., Vol. 39, No.17, pp. 2931-2940, 2000.
Ghiglia, D. C. and Pritt, M. D., "Two-Dimensional Phase Unwrapping: Theory, Algorithms and Software", Wiley-InterScience, US, 1998.18. Siegmann, P., Backman, D. and Patterson, E. A., "A Robust Approach to Demodulating and Unwrapping Phase-stepped Photoelastic Data", Exp. Mech., Vol.45, No.3, pp. 278-289, 2005.
Ramji, M., Nithila, E., Devvrath, K. and Ramesh, K., "Assessment of Autonomous Phase Unwrapping of Isochromatic Phase Maps in Digital Photoelasticity", Sadhana, 2008 (In Print).
Barone, S., Burriesci, G. and Petrucci, G., "Computer Aided Photoelasticity by an Optimum Phase Stepping Method", Exp. Mech., Vol. 42, No. 2, pp. 132139, 2002.
Ramji, M. and Ramesh, K., "A New Six Step Phase Shifting Technique Using Mixed Polariscope in Digital Photoelasticity", Proc. Int. Conf. on Exp. Mech., Lotte Hotel, Jeju Island, Korea, 26th - 29th
September, 2006.
Tamrakar, D. K. and Ramesh, K., "Simulation of Errors in Digital Photoelasticity by Jones Calculus",
Strain, Vol. 37, No. 3, pp. 105-112, 2001.
D’Acquisto, L., Petrucci, G. and Zuccarello, B., "Full Field Automated Evaluation of the Quarter Wave
Plate Retardation by Phase Shifting Technique", Opt. and Lasers in Eng., Vol. 37, pp. 389-400, 2002.
Mangal, S. K. and Ramesh, K., "Use of Multiple Loads to Extract Continuous Isoclinic Fringes by
phase-shifting", Strain, Vol. 35, No. 1, 1999, pp. 15-17, Errata 1999, Vol. 35, No. 2, pp.76.
Nurse, A. D., "Full-field Automated Photoelasticity by Use of Three-wavelength Approach to Phase
Stepping", App. Opt., Vol. 36, pp. 31-32, 1997.
Petrucci, G., "Full-field Automatic Evaluation of an Isoclinic Parameter in White Light", Exp. Mech.,
Vol. 37, No. 4, pp. 420-426, 1997.
Kihara, T., "An Arctangent Unwrapping Technique of Photoelasticity using Linearly Polarized Light at
Three Wavelengths", Strain, Vol. 39, pp. 65-71, 1997.
Math Works Inc., "Curve Fitting Toolbox Ref. User’s Guide", Math Works, Inc., Natick, MA,
Ashokan, K., Ramji, M., Raja Guruprasath, R. and Ramesh, K., "Autonomous Phase Unwrapping by
Domain Masking in Digital Photoelasticity", In CD Proc. Int. Conf. Photonics, 13th-16th December, Hyderabad, India, 2006.
Timoshenko, S. P. and Goodier, J. N., "Theory of Elasticity", McGraw - Hill, Singapore, 1987.