PSI - Issue 5

O. Plekhov et al. / Procedia Structural Integrity 5 (2017) 438–445 A. Vshivkov et al. / Structural Integrity Procedia 00 (2017) 000 – 000

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The energy of plastic deformation in representative volume located near crack tip can be estimated as follow: . 2 1 3 2 3 1      n n e oct oct p n An d U      The energy increment for crack under monotonic loading can be written as , dl d An dU n n      (here K - stress intensity factor, r p – estimation for plastic zone size, r – polar coordinate, f e – function of polar coordinate  determining the relation of octahedral stress versus  ) we can rewrite equation (4) as follow: . dl d d An dU n n   (5) It was shown earlier that plastic zone at crack tip could be divided into two parts: plastically loaded zone (dissipation zone) and elastically unloaded. The geometry of dissipation area would be determined by relation: . cos sin 2 1              e e p e f d df r r f C r f r dl d (6) the areas of plastic uploading and elastic unloading. Figure 7a presents the plastic zone shape under monotonic uniaxial loading. Zone A corresponds to the plastic loading caused by crack advance, zone B - the elastic unloading. a b 2 3 dl e p (4) where - crack length. Using definition 2 1 2 1 3            r r f r Kf p e e e e el oct     2 3 dl      d e p         p e It was shown by Raju (1972) that for p l r  the equation (6) gives two straight lines   79.9    determined

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Figure 7. Structure of plastic zone at crack tip under monotonic loading (a) – uniaxial loading, (b) – multiaxial loading with biaxial coefficient equal to 0.3

For description of crack behavior under mixed mode loading we have to change the function f e in equations (5) and (6). Taking into account elastic solution of the first and second fracture modes at crack tip: , 2 ( , )1 , , I II I II I II xx f r K   