An interface crack with a frictionless contact zone at the right crack tip between two semi-infinite piezoelectric/piezomagnetic spaces under the action of a remote mechanical loading, magnetic and electric fluxes as well as concentrated forces at the crack faces is considered. Assuming that all fields are independent on the coordinate x 2 co-directed with the crack front, the stresses, the electrical and the magnetic fluxes as well as the derivatives of the jumps of the displacements, the electrical and magnetic potentials are presented via a set of analytic functions in the (x 1 , x 3 )-plane with a cut along the crack region. Two cases of magneto-electric conditions at the crack faces are considered. The first case assumes that the crack is electrically and magnetically permeable, and in the second case the crack is assumed electrically permeable while the open part of the crack is magnetically impermeable. For both these cases due to the above-mentioned representation the combined Dirichlet-Riemann boundary value problems have been formulated and solved exactly. Stress, electric and magnetic induction intensity factors are found in a simple analytical form. Transcendental equations and a closed form analytical formula for the determination of the real contact zone length have been derived for both cases of magnetic conditions in the crack region. For a numerical illustration of the obtained results a bimaterial BaTiO 3 -CoFe 2 O 4 with different volume fractions of BaTiO 3 has been used, and the influence of the mechanical loading and the intensity of the magnetic flux upon the contact zone length and the associated intensity factors as well as the energy release rate has been shown.

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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.

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