Thin plate effect on stress intensity factor in problems on transverse crack in half-plane and stripe

The solution to the equilibrium problem for half-plane and stripe weakened by straight transverse cracks and reinforced by thin flexible plates is considered. Boundary conditions of a special form are used as a mathematical model of a thin plate. To establish the limits of the model applicability, a numerical study of these conditions is carried out. On the basis of the equilibrium equations, the problem is converted to the solution of the singular integral equation of the first kind with the Cauchy kernel relating to the function derivative of the crack opening. At this, the generalized integral transform method is used. In various ranges of the geometrical and physical problem parameters, solutions to the described above integral equation are constructed by small parameter and collocation methods. The stress intensity factor values in the neighborhood of the crack periphery are obtained. The multivariate analysis of the plate impact on the critical condition of cracks in the substrate is carried out.