Issue 48

O. Plekhov et alii, Frattura ed Integrità Strutturale, 48 (2019) 451-458; DOI: 10.3221/IGF-ESIS.48.43 455 where 0 , , A n  – material constants, 0 0 , , n e oct e e GA B                – elastic limit. The energy of plastic deformation in representative volume near the crack tip can be estimated as follows 1 0 3 3 . 2 2 1 n n e oct p oct oct e e An U d n                         (3) The energy increment caused by crack advance under monotonic loading can be written as 0 3 , 2 n n e p e d dU An dl dl             (4) where l - crack length. Using definition 1 1 2 2 3 el p e oct e e e r f Kf r r              (here K – stress intensity factor, r p – estimation for plastic zone size, r,  – polar coordinates, f e – function of polar coordinate  , we can rewrite Eqn. (4) as 0 3 . 2 n n e p e d d dU An dl d dl               (5) where 1 sin cos . 2 p e e e p e r df d f C f dl r d r f r                    (6) To analyse plastic deformation at the crack tip under cyclic loading we need to divide energy dissipation in cyclic and monotonic plastic zones at the crack tip . tot cyc mon p p p U U U   (7) The energy of representative volume at cyclic zone can be estimated as 3 2 cyc p ec pc U    , (8) where ec  – characteristic size of the yield surface,   , 1 1 pc oct c ec s G G             – amplitude of plastic deformation under an assumption of the validity of Ramberg-Osgood relationship ship, , oct c  – stress change in the representative volume. The full energy of cyclic plastic zone can be calculated as a double integral over the region (S) bounded on the outside of the monotonic plastic deformation zone and inside of the fracture zone , 2 0 3 1 1 2 1 2 oct c cyc p ec s ec S U rdrd G G                    (9) The simple approximation of plastic zone boundary can be given by , p c e r r f  , for cyclic-fracture zone boundary –