isotropic plane in a non-uniform stress field, rectilinear crack with end zones, cohesive forces.

A homogeneous isotropic plane weakened by rectilinear crack with end zones with bonds between the faces is considered. The model of crack with end zones, in which cohesive forces of the material are act, is used. At the loading of the plane by non-uniform stress field in the end zones the pre-fracture zones will occur, which are modeled as a zone of weakened interparticle bonds of the material. The fracture process zone is a layer of finite length considering as a part of the crack, in which bonds between the individual structural elements of the material is partially broken. The problem of equilibrium of the plane with the crack with bonds between the faces in the end zones under the influence of non-uniform stress field and tractions in the bonds, preventing of crack disclosure is reduced to a system of singular integral-differential equations with Cauchy kernel. From the solution of this system of equations the normal and tangential forces in the bonds are found.

Shahbandaev Elmeddin Huseyn oglu e-mail: mir-vagif@mail.ru, PhD, Senior researcher, Institute of Mathematics and Mechanics of NAS of Azerbaijan, Baku, Republic of Azerbaijan.