The J-integral at Dugdale cracks perpendicular to interfaces of materials with dissimilar yield stresses

The J-integral is applied to a Dugdale crack perpendicular to an interface of materials with equal elastic properties but different yield stresses. It is shown that the integral is path independend with certain limitations to the integration path. Three essentially different paths can be distinguish ed. The first integration path is totally within the first material, it pro vides the local crack driving force. Performing the integral around the pla stic zone in both materials gives the global crack driving force. An interf ace force can be defined by evaluating the integral along both sides of the plastically deformed region of the interface. A comparison of these three integrals reveals that the global crack driving force is equal to the sum o f the local crack driving force and of the interface force. The derived exp ression for the J-integral are compared with the crack tip opening displace ment published recently. This reveals that the local J describes the plasti c deformation at the crack tip. Therefore it represents the crack driving f orce in bimaterials as it does the conventional J-integral in case of homog eneous materials. The analyses are also extended to cyclic plasticity, wher e an out-of-phase effect is observed. Finally it is discussed how these res ults can be used to explain fatigue tests at bimaterial specimens.