Elastic-plastic analysis of crack on bimaterial interface

In this paper are presented solutions for the stress and dis?placement fields for a crack that lies along the interface of an elastic and elastic - plastic material and for a crack between two different elastic - plastic materials. These solutions are obtained using the J2-deformation theory with the power - law strain hardening. In this paper results are described for a small scale yielding at the crack tip. The near tip fields do not have a separable singular form, of the HRR type fields, as in homogeneous media, they do, however bare interesting similarities to certain mixed -mode HRR fields. Under the small scale yielding the elastic fields are specified by a complex stress intensity factor and phase angle loading, while plastic field is characterized by a new phase angle. The size of plastic zone in plane strain and plane stress and displacement fields at the crack tip for the new phase angle are obtained. The crack tip opens smoothly and the crack opening displacement is scaled by the J-integral. The whole analysis is performed by application of the Mathematica symbolic programming routine. U ovom radu su predstavljena resenja za polje napona i deformacije za prslinu koja lezi na interfejsu elasticnog i elasticno-plasticnog materijala i za prslinu izmedju dva razlicita elasticno-plasticna materijala. Ova resenja su dobijena koriscenjem J2 - deformacijske teorije sa stepenim zakonom ojacanja. U radu su opisani rezultati za slucaj malog tecenja oko vrha prsline. Polja oko vrha prsline nemaju poseban singularan oblik tipa HRR polja, kao kod homogenih sredina, mada imaju interesantne slicnosti sa nekim HRR poljima za kombinovani mod. U uslovima malog tecenja elasticna polja se karakterisu kompleksnim faktorom intenziteta napona i faznim uglom opterecenja, dok se plasticna polja karakterisu novim faznim uglom. Dobijeni su velicina plasticne zone pri ravanskom stanju deformacije i napona i polja pomeranja u vrhu prsline za nove fazne uglove. Vrh prsline se otvara ravnomerno i pomeranje otvora prsline je normalizovano J - integralom. Kompletna analiza je uradjena koriscenjem Mathematica paketa za simbolicko programiranje.