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Determination Of Geometric Stress Intensity Factor For A Photoelastic Compact Tension Specimen

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Experimental and analytical studies with finite elements was done on a polycarbonate transparent material as a forerunner to a similar study on transparent glass -epoxy composites

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Determination Of Geometric Stress Intensity Factor For A Photoelastic Compact Tension Specimen

  1. 1. Determination of geometric stress intensity factor for a photoelastic compact tension specimen Me 823 project Presented by Anupam dhyani
  2. 2. objectives <ul><li>To determine Geometric Stress Intensity Factor (K I ) for modified C(T) specimen with </li></ul><ul><li>- Experimental work </li></ul><ul><li>- Analytical ( ASTM methods) </li></ul><ul><li>- Finite Element modeling </li></ul><ul><li>Use of the J approach </li></ul><ul><li>Comparison of these techniques </li></ul>
  3. 3. Organization <ul><li>Background </li></ul><ul><li>Experimental Set-up and procedure </li></ul><ul><li>Finite Element Model </li></ul><ul><li>Calculation of J( ASTM E 1820) </li></ul><ul><li>Conclusions and Recommendations </li></ul>
  4. 4. background <ul><li>With advance of fatigue crack-plastic deformation at the crack tip is associated. </li></ul><ul><li>In additions of residual stresses ahead of the crack tip, these deformations produce effects behind the crack tip-have profound effect on the crack growth. </li></ul><ul><li>Elber concluded that the premature recontacting (crack closure) of crack faces was a direct result of permanent deformation left in the wake of the advancing crack. </li></ul>
  5. 5. background <ul><li>When the load is removed the presence of fringes show that the stresses at the crack tip are non zero </li></ul><ul><li>The crack has closed and plasticity is the most probable cause of this closure </li></ul><ul><li>Also there is an affect of geometry and loading.( since the specimen is loaded off center so it is basically loading in bending) </li></ul><ul><li>There must be a transition zone from tensile to compressive loading, where the fringe order is zero. </li></ul><ul><li>When lower loads are applied the loops move away from the crack tip as the crack tip stresses become stronger </li></ul>
  6. 6. Experimental work <ul><li>Sample (C(T)) was cut to ASTM standard </li></ul><ul><li>Loaded the sample in a Tensile testing machine </li></ul><ul><li>Cyclically loaded the sample to tensile load </li></ul><ul><li>Fatigue crack grown to 6 mm from notch </li></ul><ul><li>Image captured at different loads </li></ul><ul><li>Image analysis </li></ul>
  7. 7. Specimen-modified C(T) <ul><li>Annealed Polycarbonate </li></ul><ul><li>Thickness  2mm </li></ul><ul><li> y = 65 Mpa </li></ul><ul><li>Note: All measurements in mm. </li></ul>
  8. 8. Experimental Set-up Polarizer Testing machine Analyzer Specimen
  9. 9. Experimental Set-up <ul><li>Cyclic load ( tensile) applied ( 0 – 150 Newton) with a frequency of .5 Hz (0-150 in 1 sec) </li></ul><ul><li>Initial crack appeared at 9000 cls. </li></ul><ul><li>Crack increased to 6 mm at 22000 cls. </li></ul>After 9000 cls 21890 cls
  10. 10. Images at various loads 0 LOAD 80 N 90 N 100 N 110 N 120 N
  11. 11. Image analysis <ul><li>Recorded images were used to calculate the Stress Intensity Factor with </li></ul><ul><li>- Apogee Method </li></ul><ul><li>- Differencing Method </li></ul><ul><li>- Taylor Series Correction Method </li></ul>
  12. 12. APOGEE METHOD
  13. 13. Differencing method
  14. 14. Taylor series correction method (TSCM)
  15. 15. Analytical method ( ASTM- 399)
  16. 16. error chart 16.76 2.87 14.31 120 21.2 4 5.54 16.95 110 28.40 7.76 22.10 100 22.30 10.86 22.53 90 58.68 11.62 28.39 80 TSCM(% error) Differencing(% error) Apogee(% error) LOAD (Newton)
  17. 17. Comparison chart
  18. 18. Finite element modeling <ul><li>Used Radial meshing using ABAQUS </li></ul><ul><li>Used Quad 8 node elements </li></ul><ul><li>Collapsed elements near the crack area </li></ul><ul><li>Obtained Value of K I at different loads </li></ul><ul><li>Refined the mesh to get better results </li></ul>
  19. 19. Finite element modeling-initial mesh 2387 Elements
  20. 20. results 15.87 54.87 120 14.34 49.89 110 14.16 44.25 100 14.09 40.08 90 13.98 35.34 80 Error (%) K (Mpa  mm) LOAD (Newton)
  21. 21. Finite element modeling-next mesh
  22. 22. results 15.87 54.87 120 14.34 49.89 110 14.16 44.25 100 14.09 40.08 90 14.336 35.45 80 Error (%) K (Mpa  mm) LOAD (Newton)
  23. 23. Finite element modeling- final mesh 5228 Elements
  24. 24. results 15.67 53.8 120 14.29 49.87 110 14.49 44.35 100 14.99 40.16 90 14.98 35.50 80 Error (%) K (Mpa  mm) LOAD (Newton)
  25. 25. Finite element modeling- final mesh- refined 7642 Elements
  26. 26. results 15.87 54.87 120 14.34 49.89 110 14.16 44.25 100 14.09 40.08 90 14.336 35.45 80 Error (%) K (Mpa  mm) LOAD (Newton)
  27. 27. Comparison chart( all methods)
  28. 28. deduction <ul><li>The % error between the analytical and the FE Model was because of the stress concentration the model assumes at the notch </li></ul><ul><li>Also as you move away from the notch the effect of this stress concentration is reduced and significant changes in % error </li></ul>
  29. 29. J- CALCULATION <ul><li>To compare the K value from J calculations (ASTM E1820) the value of J IQ was obtained. </li></ul>
  30. 30. J calculation <ul><li>J IQ value could not satisfy the conditions in part A 6.2.2 and A9 hence this was not J C or J U value that could be compared. </li></ul>
  31. 31. conclusions <ul><li>The Differencing Method gives a better value for the Stress Intensity Factor among all the methods </li></ul><ul><li>In Apogee Method limited photoelastic sensitivity and localized 3-D effects near tip restrict number of usable fringes </li></ul><ul><li>Except the TSCM method in all other the % error decreases with increasing load as the stress field is better visible and more number of usable fringes are available </li></ul><ul><li>The Finite Element Modeling gives improved results after refining the mesh however the difference b/w the analytical model and FEM is attributed to the stress concentration model assumes at the notch </li></ul><ul><li>J Value does not qualify to become J IC in this case. </li></ul>
  32. 32. Recommendations/Future work <ul><li>Use of Finer mesh and triangular elements around the crack tip </li></ul><ul><li>Repetition of work for varying geometries </li></ul><ul><li>Fracture toughness can also be calculated for the material </li></ul>
  33. 33. acknowledgements <ul><li>Dr. Dahsin Liu </li></ul><ul><li>Chiara Colombo </li></ul><ul><li>Roz-ud-din Nassar </li></ul><ul><li>Amol Patki </li></ul>

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