The main objective here is the understanding of the effect of plastic zone ahead of crack tip on fatigue crack growth (FCG). For that, a numerical simulation of FCG was made, based on cumulative plastic strain, considering a bi-material composed by the 6082-T6 and 7050-T6 aluminium alloys. The first one has a lower yield stress but a higher critical cumulative plastic strain. The values of da/dN are higher for the 6082-T6 which means that the effect of the easier plastic deformation dominates over the effect of the higher critical cumulative plastic strain. The bi-material 6082-7050 showed a pronounced decrease of da/dN near the interface, which starts when the monotonic plastic zone ahead of crack tip reaches the material transition. This indicates that the crack tip deformation is affected by the material inside the monotonic plastic zone. On the other hand, the bi-material 7050-6082 shows an accentuated increase of da/dN, which starts when plastic deformation is observed ahead of transition. The elimination of the contact of crack flanks reduces drastically the transient effects, which indicates that these are linked with plasticity induced crack closure effects. Crack tip blunting was proposed to be the mechanism of plasticity induced crack closure explaining the trends observed.