Hybrid Photoelastic Stress Analysis Around a Central Crack Tip in a Tensile Loaded Plate Using Isochromatic Data

등색프린지 데이터를 이용한 인장하중 판재 중앙 균열선단 주위의 하이브리드 광탄성 응력장 해석

  • 백태현 (군산대학교 기계공학부) ;
  • 첸레이 (군산대학교 대학원 기계공학과)
  • Published : 2007.12.01


An experimental test is presented for photoelastic stress analysis around a crack tip in tensile loaded plate. The hybrid method coupling photoelastsic fringe inputs calculated by finite element method and complex variable formulations involving conformal mappings and analytical continuity is used to calculate full-field stress around the crack tip in uniaxially loaded, finite width tensile plate. In order to accurately compare calculated fringes with experimental ones, both actual and regenerated photoelastic fringe patterns are two times multiplied and sharpened by digital image processing. Regenerated fringes by hybrid method are quite comparable to actual fringes. The experimental results indicate that Mode I stress intensity factor analyzed by the hybrid method are accurate within three percent compared with ones obtained by empirical equation and finite element analysis.


Stress Analysis;Hybrid Stress Analysis;Photoelasticity;Stress Intensity Factor;Complex Stress Function;Least Squares Method;Digital Image Processing;Fringe Multiplication;Fringe Sharpening


  1. Smith, C. W. and Kobayashi, A. S., 1993, 'Experimental Fracture Mechanics' in Handbook on Experimental Mechanic, edited by A. S. Kobayashi, VCH Publishers, Inc
  2. Murakami, Y., 1987, Stress Intensity Factors, Vol. I & II, Pergamon Books Ltd
  3. Shin, K. B., Kyung, W. M., Kim, C. G., Hong, C. S. and Park, H. Y., 1996, 'Stress Analysis of Fir-Tree Root in Turbine Rotor Using Photoelastic Technique,' Transactions of the Korean Society for Mechanical Engineers (A), Vol. 20, No. 6, pp. 1784-1797
  4. Gerhardt, G. D., 1984, 'A Hybrid/Finite Element Approach for Stress Analysis of Notched Anisotropic Materials,' ASME Journal of Applied Mechanics, Vol. 51, pp. 804-810
  5. Rhee, J., He, S., and Rowlands, R. E., 1996, 'Hybrid Moire-Numerical Stress Analysis Around Cutouts in Loaded Composites,' Experimental Mechanics, Vol. 36, No. 4, pp. 379-387
  6. Baek, T. H. and Rowlands, R. E., 1999, 'Experimental Determination of Stress Concentrations in Orthotropic Composites,' Journal of Strain Analysis, Vol. 34, No. 2, pp. 69-81
  7. Hawong, J. S., Lin, C. H., Lin, S. T., Rhee, J., and Rowlands, R. E., 1995, 'A Hybrid Method to Determine Stresses in Orthotropic Composite using only Isochromatic Data,' Journal of Composite Materials, Vol. 29, No.9, pp. 236-2387
  8. Baek, T. H., Kim, M. S., Rhee, J. and Rowlands, R. E., 2000, '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
  9. Baek, T. H., 2006, 'Photoelastic Stress Analysis by Use of Hybrid Technique and Fringe Phase Shifting Method,' Journal of Experimental Mechanics, University of Science and Technology of China, Vol. 21. No. 1, pp. 87-95
  10. Rhee, J., 1995, Geomertic Discontinuities in Orthotropic Composites, Ph. D Dissertation, Department of Engineering mechanics and Astronautics, University of Wisconsin-Madison, USA
  11. Dally, J. W. and Riley, W. F., 1991, Experimental Stress Analysis, 3rd ed., McGraw-Hill, New York, USA
  12. Photoelastic Division, Measurement Group, Inc., Raleigh, NC 27611, USA
  13. Baek, T. H. and Lee, J. C., 1994, 'Development of Image Processing Technique for Photoelastic Fringe Analysis,' Transactions of the Korean Society for Mechanical Engineers, Vol. 18, No. 10, pp. 2577-2584
  14. ABAQUS Analysis User' Manual, 2003, ABAQUS Inc., Providence, RI 02909, USA
  15. Baek, T. H., 1993, 'Digital Image Processing Technique for Photoelastic Isochromatic Fringe Sharpening,' Journal of the Korean Society for Precision Engineering, Vol. 10, No. 3, pp. 220-230
  16. Baek, T. H. and Burger, C. P., 1991, 'Accuracy Improvement Technique for Measuring Stress Intensity Factor in Photoelastic Experiment,' KSME International Journal, Vol. 5, No. 1, pp. 22-27
  17. Anderson, T. L. 1995, Fracture Mechanics Fundamentals and Applications, 2nd ed. CRC Press Inc., pp. 53-64
  18. Baek, T. H., Koh, S. K. and Park, T. G., 2006, 'An Improved Hybrid Full-field Stress Analysis of Circularly Perforated Plate by Photoelasticity and Finite Element Analysis,' Key Engineering Materials, Vols. 326-328, pp. 1209-1212
  19. Baek, T. H. and Rowlands, R. E., 2001, 'Hybrid Stress Analysis of Perforated Composites using Strain Gages,' Experimental Mechanics, Vol. 41, No. 2, pp. 194-202
  20. Savin, G. N., 1961, Stress Concentration Around Holes, Pergamon Press, New York, USA
  21. Sanford, R. J., 1980, 'Application of the Least Squares Method to the Photoelastic Analysis,' Experimental Mechanics, Vol. 20, No. 6, pp 192-197
  22. Baek, T. H., Panganiban, H. and Chung, T. J., 2007, 'A Hybrid Photoelastic Stress Analysis Around Holes in Tensile-Loaded Plates Using Isochromatic Data and Finite Element Method,' Lecture Series on Computer and Computational Sciences, Brill Academic Publishers, Vol. 8, pp. 21-25