The paper is concerned with the fracture process zone at the tip of a crack at the nonsmooth interface between isotropic elastic media. A plane symmetric problem is formulated. The zone is modeled by lines of discontinuity of the normal displacement at the interface. The exact solution of the elastic problem is found by the Wiener-Hopf method Keywords: fracture process zone, interface, crack, Wiener-Hopf method Introduction. The high crack resistance of composites is due to crack growth inhibition at the interfaces between the components of these materials [15,16]. This is why studies of cracks growing to reach the interface of dissimilar media are of current importance. While problem solutions describing the growth of cracks located at interfaces of various media are addressed in the extensive literature [1,2,4,5,8,13,17,20,21], studies of cracks growing to reach such interfaces are much fewer.A crack reaching the interface between media with different mechanical properties may cause partial separation of the materials (fracture process zone) because of the high stress intensity at its tip, which was demonstrated in many studies. Such fracture process zones are usually modeled by discontinuity lines of the normal displacement in the case of brittle matrix (generalized Leonov-Panasyuk model [1,8,11]) or plastic slip lines in the case of plastic matrix (Cherepanov's modified model [3,5,17]). To gain insight into the failure mechanism of piecewise-homogeneous media, it is important to know the stress intensity at the crack tip, the type of its singularity, the size of the fracture process zones, and the way it affects the stress intensity. Knowing the singularities of stresses at the tip of a crack reaching an interface, we can more efficiently develop numerical methods for determining the stress state of compound piecewise-homogeneous bodies with cracks. Solving such problems is also needed for the development of the theory of failure of adhesive joints with allowance for the rheological properties of adhesives (plastic, brittle, viscoelastic, etc.) Symmetric plane solutions describing the fracture process zone at the tip of a crack reaching the nonsmooth interface of media that comprise a piecewise-homogeneous elastoplastic body were found in [3, 18] using plastic slip lines as models. We will solve a similar problem considering that the fracture process zone (partial separation zone) is modeled by discontinuity lines of the normal displacement at the interface (brittle matrix).1. Problem Formulation. Consider a piecewise-homogeneous isotropic elastic body under plane strain. It consists of different homogeneous parts with a thin binder interlayer between them. The interlayer is more brittle than the bonded parts. Let the tip of a rectilinear crack be at a corner point of the nonsmooth interface between two parts of the body. This domain is considered symmetric about the crack line.As the external load increases, a fracture process zone appears and grows at the crack tip. We will study only the initial stage of...
