| Abstract: | Use of the fact that a singular operator transforms a polynomial again into a polynomial permitted obtaining substantially new results in 1], devoted to wing theory. This property of singular operators is used to solve the plane problem of elasticity theory for a plane weakened by cracks. The criterion for the beginning of crack growth is related in the linear theory of fracture to the stress-intensity factor at its end. An investigation of the influence of the mutual arrangement of cracks on the intensity factor is of considerable interest. The intensity factor is zero in the stretching of a plane weakened by a longitudinal slit, but this factor grows in the presence of a transverse slit and may even exceed the intensity factor at the end of the transverse slit. In this case stratification of the material, the development of cracks located along the loading line, starts. Fractures of this kind have been observed in experiments. To solve the problem of determining the stress-intensity factor at the end of a longitudinal crack in the presence of a transverse crack, the consideration of a periodic system of longitudinal-transverse cracks turns out to be effective. Introduction of symmetry simplifies the construction of the solution of the problem, on the one hand, and is a good approximation to the problem of the mutual influence of two cracks for a sufficient mutual removal of the slits, on the other. |
