Properties of the J, L and M integrals, proposed by knowles and Sternberg for homogeneous materials are explored for bimaterial interfaces. The integrals are shown to satisfy the conservation law under suitable conditions such as the interfaces of perfect bond, frictionless contact, separation with no-slip or separation. Relations between the stress intensity factors and the conservation integrals for interfacial cracks in isotropic, linear-elastic materials are derived. The conservation integrals for some interfacial cracks are applied to get the stress intensity factors in a very simple way without solving the complicated boundary value problems. For interfacial cracks in finite-sized medium some numerical computations are carried out to verify the usefulness of the conservation integrals. It is also found that the use of the conservation integrals is more advantageous than the use of the stress intensity factors since the latter quantities are very sensitive to the local stress field, the nature of which is not clear as yet.
An interfacial crack model is proposed to include the effect of plastic deformation in an interface crack, where plastic zones are assumed to have the form of a strip lying along the interface at each end of the crack and a frictionless contact zone is assumed to exist in order to prevent overlapping of the crack faces. This model is applied to a crack subjected to normal and shear loads at infinity, which is lying along the interface of two semi-infinite planes with different material properties. The crack and the plastic zones are represented by a continuous distribution of edge dislocations. The sizes of the plastic zones and the contact zone, and the contact stresses in the contact zone are obtained. The relation between the size of the plastic zone and the relative displacement at the crack tip is investigated. The J integral in this model is compared with the energy release rate of purely elastic solution. Out-of-plane shear loads are also considered in this model, where the size of the plastic zone, the crack tip opening displacement and the J integral are obtained in a closed form.
Assuming the plastic zones spreading out on each slip plane of the two materials under out-of-plane shear loading, the size of each plastic zone is computed. It is found that the size of the plastic zone in each material is the same if we have the same frictional shear stress. The effect of the different frictional shear stresses in the two materials on the sizes of the plastic zones is also studied.
