A plane problem for a crack between two anisotropic semi-infinite spaces under remote tensile-shear loading is considered. In the framework of the assumption that the crack faces are free of stresses an exact analytical solution of the problem is given on basis of the complex potentials approach. This solution possesses oscillating square root singularities in stresses and in the derivatives of the displacement jumps at the crack tips. To remove these singularities a new model founded on the introduction of the shear yield zones at the crack tips is suggested. This model is appropriate for the cases where interface adhesive layer is softer than the surrounding matrixes. Under this assumption the problem is reduced to the nonhomogeneous combined Dirichlet-Riemann boundary value problem with the conditions at infinity. An exact analytical solution of this problem is presented for the case of a single yield zone. The length of this zone is found from the finiteness of the shear stress at the end point of the zone. Due to such simulation the shear stress becomes finite at any point and the normal stress possesses only square root singularity at the crack tip. Therefore, the conventional stress intensity factor of the normal stress at the crack tip is used. The numerical illustration of the obtained solution is given.

PRE-FRACTURE ZONE MODELING FOR AN INTERFACE CRACK IN AN ISOTROPIC BIMATERIALAn interface crack in an infinite bimaterial space under remote combining loading is considered. The complex potentials approach is applied and an exact analytical solution of this problem is presented. To remove the oscillating singularities which occur in this solution a model based on the introduction of the shear stress pre-fracture zones at the crack tips is suggested. In the framework of this assumption the nonhomogeneous combined Dirichlet-Riemann boundary value problem with the conditions at infinity is formulated and its analytical solution is presented. The length of this zone is found from the condition of restriction of the shear stress at the end point of the zone. In this case the shear stress becomes finite in the right hand side of the pre-fracture zone while the normal stress has a square root singularity at the crack tip. The energy release rates (ERR) at the crack tip and also along the pre-fracture zone are found and their total values are compared the ERR of the classical model. For the case of a similar problem, but for finite sized body the finite element method is applied. The crack length is assumed to be much smaller then characteristic body size. The finite element net with two levels of concentration is constructed. The first level provides the uniform concentration from the boundaries of the body to the crack and the second level assumes the similar concentration at the singular points of the pre-fracture zone. The different values of the shear stress in the pre-fracture zone are considered and the local ERR at the singular points as well as the global energy release rate is found. It is shown that for different values of the mentioned shear stress the global energy release rate remains almost invariable and is in a a good agreement with the analytical solution.

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