Equilibrium of a prestressed elastic body weakened by a plane elliptical crack

Abstract

The problem of normal pressure loading of the edges of a plane elliptical crack is considered. The crack subjected to the load is in the open state. The medium in which it is located is frist subjected to homogeneous biaxial tension or compression along the plane of the crack. A model of incompressible neo-Hooke material is considered /1/. The problem is reduced to solving a singular integral equation of the first kind. In the case when the intensity of the initial loading is identical in both directions, the problem has an exact solution. If the coefficients of preliminary tension differ slightly, construction of the solution of the problem is possible by an asymptotic method /2/. It is shown that as in the case of equal coefficients /3/ ∗∗, the initial stress does not alter the order of the singularity of the stress field near the crack edge and only affects the normal stress intensity factor. Analogous problems are considered in /4, 5/ for the case of equal prestrain coefficients in a body containing a circular crack. A solution /4/ is constructed for the axisyametric problem for a layer under different conditions on its faces, and it is shown /5/ that it is possible to use the solution of the problem concerning a crack in an anisotropic material. A solution of the axisymmetric problem is constructed /6/ in the case of radial finite prestrain. An asymptotic solution /7/ is obtained for the spatial contact problem for a prestressed elastic body.