The objective of the present work is to investigate the interaction between interfaces and cracks in metal/ alumina bi-materials. The behaviour is analyzed by the determination of the J integral and the plastic zone at the crack tip using the finite-element methods. Different orientations of the crack according to the bi-materials interface were examined such as cracks parallel and perpendicular to the interface and inclined cracks. The effects of the mechanical properties of the joint materials, the crack length and the metal thickness on the extent of plastic zone and the J integral at the crack tip were also highlighted. The obtained results allow us to deduce mathematical relations giving the variation of the J integral and the plastic zone according to the crack position.

eigenfunction expansion technique. Zak and Williams [1] showed that the stress field singularity at the tip of a crack perpendicular to an interface or terminating at the interface is of order r −λ , where λ is the real part of the eigenvalue and depends on the elastic properties of the bi-material. Bogy [2] investigated the stress singularity of an infinite crack terminating at the interface with an arbitrary angle of different material components. Cook and Erdogan [3] used the Mellin transform method to derive the governing equation of a finite crack perpendicular to the interface and obtained the stress intensity factors (SIFs). The authors found that the power singularity of stress around the crack tip is not −1/2. Erdogan and Biricikoglu [4] solved the problem of two bounded half planes with a crack going through the interface. Wang and Chen [5] used photoelasticity to determine the stress distribution and the stress intensity factors of a crack perpendicular to the interface [6-8], and also used finite element to analyze cracks perpendicular to bimaterial in a finite elastic body. Chen [9] used the body force method to determine the stress intensity factors for a normal crack terminating at a bi-material interface. Chen et al.[10] used the dislocation simulation approach to investigate the crack tip parameters for a crack perpendicular to an interface in a finite solid. He and Hutchinson [11] also considered cracks approaching the interface at oblique angles. Lin and Mar [6] presented a finite element analysis of the stress intensity factors for cracks perpendicular to the bi-material interface. Chang and Xu [12] presented the singular stress field and the stress intensity factors solution for an inclined crack terminating at a bi-material interface. A theoretical description of the stress singularity at an inclined crack terminating at an anisotropic bi-material interface was proposed by Lin and Sung [13]. Wang and Stahle [14,15] used the dislocation simulation approach to investigate a crack perpendicular to and terminating at the Abstract The objective of the present work is to investigate the interaction between interfaces and cracks normal to and terminating at a metal/alumina interface. The behavior is analyzed by the determination of the J integral and the plastic zone at the crack tip using the three-dimensional finite element methods. The effects of the thickness of the metal/alumina were highlighted. The obtained results allow us to deduce mathematical relations, giving the variation of the J integral and the plastic zone as a function of the crack position and the bi-materials thickness.