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FRACTURE MECHANICS

FRACTURE MECHANICS. Energy approach.  0. r. . x. a. H.M.Westergaard, 1939, N.I.Muskhelischvili, 1943 – 2D analysis of the stress field around the notch tip.  A.  y. Dla. Singularity !. Stress intensity factor.

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FRACTURE MECHANICS

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  1. FRACTURE MECHANICS Energy approach

  2.  0 r  x a H.M.Westergaard, 1939, N.I.Muskhelischvili, 1943 – 2D analysis of the stress field around the notch tip A y Dla Singularity ! Stress intensity factor

  3. Stress intensity factors for different orientation of crack plane and loading has been calculated around 1960 (G.Sih) To stystemise above, three cases are distinguished: KII KI KIII Mode I - Tearing; crack surfaces open perpendicular to the planes of its movement Mode II – Out-of-plane shear; crack surfacesslide perpendicular to the planes of its movement Mode III - Out-of-plane shear; crack surfacesslide paralel to the planes of its movement

  4. Stress-based approach Safe design requires following conditions to be fulfilled: KI < KIc KII < KIIc KIII < KIIIc KIc , KIIc , KIIIc where are critical values of responsible stress intensity factors, experimentally determined

  5. b a Griffith theory G.V. Kolosow 1910 & C.E.Inglis, 1913 – Thin plate of unlimited width containing an elliptical hole q[Pa] y x σ 3q a  b INDEPENDENT OF THE MAGNITUDE OF a !!! σ  b  0 q[Pa]

  6. if but y x l l where With then c ! for |x|<l w PSS for |x|<l w PSD for |x|>l The work of external load on displacementu(c=1m) u

  7. q Energy required W0 y W0-W u l x l l W Energy supplied q The work of external load on displacementu • Energy required to form a free surface of the length 2x2l (over unit thickness of the plate)  - surface energy of unit thickness [N/m] d(W0-W)/dl=0 lkr Instability point

  8. d(W0-W)/dl=0 For l=lkr LFM:

  9. You will see an experiment showing how elastic energy released with the crack length growth is transferred to the region of final failure

  10. q q

  11. q q

  12. q q

  13. q q

  14. q q

  15. q q

  16. q q

  17. q Even 5-fold reduction of cross section area does not reduce strength of the specimen! q

  18. q 0,5 sec q

  19. q 1 sec q

  20. q 2 sec q

  21. 1 sek q q q q

  22. 1 sek 2lkr q q 2l q q

  23. STOP

  24. FAST ANIMATION

  25. q q

  26. q q

  27. q q

  28. q 1 sek q

  29. 1 sek q q 1 sek q q

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