When the crack tip in ductile parent body reaches near the interface of another elastically matched but strength mismatched ductile body, the plasticity or yield zone at the tip spreads to interface body which triggers the effect of strength mismatch between the bodies over the tip by way of plasticity induced load transfer. The interface effect is best quantified by the value of J integral, J(interface), obtained over a path around the interface of the bodies in the yield zone. The paper presents finite element analysis of minute yield zone, formed at Mode I crack tip in linear elastic regime, across a strength mismatched interface to determine J(interface). The yield zone, treated as Dugdale's cohesive zone, is isolated from the bimetallic body domain and modeled alone under the action of cohesive stresses. Effect of farfield load at the interface is obtained separately. Such an uncomplicated approach is first tested successfully over theoretical results of cohesive zone across a thin interface of weak ASTM 4340 alloy and strong MDN 250 maraging steels under monotonic load. Subsequently, it is verified vis-a-vis experimental results of cyclic cohesive zone developed across the weld interface in bimetallic compact tension specimen by subjecting the crack in alloy steel near the interface of ultra strong weld between the stated steels to high cycle fatigue. .