Abstract
Stress measurement around the edge of a circular hole at the center of a tensile-loaded plate was performed using an improved hybrid method. Phase-shifting method by Fourier transformation (PSM/FT) in laser speckle interferometry was utilized to measure micro-scale displacement of points away from the edge of the hole. Using few x-displacement and location data only, least-squares method integrated with a Laurent series representation of the stress function and local collocation was used to do reliable stress evaluation on the hole boundary. Traction-free conditions are satisfied at the geometric discontinuity using conformal mapping and analytic continuation. The results of the present improved hybrid method agree well with that of finite element method using commercial software, ABAQUS. Different values of number of term (m) in the complex stress functions were tested to see its effect. In the comparison between input x-displacement data and calculated the hybrid method is effective with an error below 1% in all values of m. On the other hand, it came out that at point of high stress concentration (θ =90°), well-comparable results was attained at decreasing value of m. The best value of m is consistently known to be equal to 1 which results are accurate by less than one percent. Results showed that the method is accurate and reliable as compared with the widely-used ABAQUS.
Similar content being viewed by others
References
Kobayshi, A. S., “Handbook on Experimental Mechanics, Second Revised Edition,” Society for Experimental Mechanics, VCH Publishers, Inc., 1993.
Pilkey, W. D. and Pilkey, D. F., “Peterson’s Stress Concentration Factors,” John Wiley & Sons, Inc., 2008.
Lekhnitskii, S. G., Tsai, S. W. and Cheron, T., “Anisotropic Plates,” Gordon and Breach, 1968.
Baek, T. H. and Rowlands, R. E., “Hybrid Stress Analysis of Perforated Composites using Strain Gages,” Experimental Mechanics, Vol. 41, No. 2, pp. 194–202, 2001.
Baek, T. H., Kim, M. S., Rhee, J. and Rowlands, R. E., “Hybrid Stress Analysis of Perforated Tensile Plates using Multiplied and Sharpened Photoelastic Data and Complex-Variable Techniques,” JSME International Journal, Series A: Solid Mechanics and Material Engineering, Vol. 43, No. 4, pp. 327–333, 2000.
Baek, T. H. and Rowlands, R. E., “Experimental Determination of Stress Concentrations in Orthotropic Composites,” Journal of Strain Analysis, Vol. 34, No. 2, pp. 69–81, 1999.
Baek, T. H. and Kim, M. S., “Computer Simulation of Photoelastic Fringe Patterns for Stress Analysis,” Lecture Notes in Computer Science, Vol. 3398, pp. 214–221, 2005.
Baek, T. H., Koh, S. K. and Park, T. G., “An Improved Hybrid Full-field Stress Analysis of Circularly Perforated Plate by Photoelasticity and Finite Element Analysis,” Key Engineering Materials, Vol. 326–328, pp. 1209–1212, 2006.
Baek, T. H., Chung, T. J. and Panganiban, H., “Full-Field Stress Determination Around Circular Discontinuity in a Tensile-Loaded Plate using x-displacements Only,” Journal of Solid Mechanics and Material Engineering, Vol. 2, No. 6, pp. 756–762, 2008.
Steinzig, M. and Takahashi, T., “Residual Stress Measurement Using the Hole Drilling Method and Laser Speckle Interferometry, Part IV: Measurement Accuracy,” Experimental Techniques, Vol. 27, Issue 6, pp. 59–63, 2006.
Creath, K, “Phase-measurement interferometry techniques,” Progress in Optics, Vol. 26, pp. 349–393, 1988.
Schwider, J., “Phase shifting Interferometry: reference phase error reduction,” Applied Optics, Vol. 28, Issue 18, pp. 3889–3892, 1989.
Baek, T. H., Kim, M. S., Na, E. G. and Koh, S. K., “Application of ESPI to Measurement of Out-of-plane Displacement in a Spot Welded Canti-levered Plate,” International Journal of the Korean Society of Precision Engineering, Vol. 4, No. 5, pp. 41–46, 2003.
Kim, M. S. and Baek, T. H., “Measurement for In-plane Displacement of Tensile Plates with Partly Perforated and Through-thickness Circular Holes by Speckle Interferometry,” Key Engineering Materials, Vol. 321–323, pp. 77–80, 2006.
Gerhardt, T. D., “A Hybrid/Finite Element Approach for Stress Analysis of Notched Anisotropic Material,” ASME Journal of Applied Mechanics, Vol. 51, No. 4, pp. 804–810, 1984.
Stanford, R. J., “Application of the Least-Squares Method to Photoelastic Analysis,” Experimental Mechanics, Vol. 20, No. 6, pp. 192–197, 1980.
Morimoto, Y., Seguchi, Y. and Higashi, T., “Application of Moire Analysis of Strain by Fourier Transform,” Optical Engineering, Vol. 27, No. 3, pp. 650–656, 1988.
Morimoto, Y. and Fujisawa, M., “Fringe Pattern Analysis by a Phase-Shifting Method using Fourier Tranform,” Optical Engineering, Vol. 33, No. 11, pp. 3709–3714, 1994.
Kim, M. S., Baek, T. H., Morimoto, Y. and Fujigaki, M., “Application of Phase-shifting Method using Fourier Transform to Measurement of In-plane Displacement by Speckle Interferometry,” Journal of the Korean Society for Nondestructive Testing, Vol. 25, No. 3, pp. 171–177, 2005.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Baek, T.H., Rudolphi, T.J. A hybrid stress measurement using only x-displacements by phase shifting method with fourier transform (PSM/FT) in laser speckle interferometry and least squares method. Int. J. Precis. Eng. Manuf. 11, 49–54 (2010). https://doi.org/10.1007/s12541-010-0006-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12541-010-0006-3