Equilibrium State of a Straight-Line Internal Crack Near the Corner Point of an Elastic Region Reinforced along the Contour

The problem of plane deformation of an elastic isotropic wedge-shaped region weakened by an internal defect in the form of a crack is considered. The boundaries of the investigated region are supported by a thin flexible coating. The boundary conditions determining the influence of the coating are modeled by special relations based on the asymptotic analysis of the problem solution for the strip. The adequacy of the mathematical model of the coating is verified by a series of numerical experiments in the authors' previous studies. The problem solution was carried out by the method of integral transformations. The Mellin transformation allowed reducing the problem to a system of ordinary differential equations of the second order. Its general solution is constructed. To determine the unknown coefficients in the found general solution, a system of linear algebraic equations is obtained. The conjugation condition on the crack location line allowed us to obtain a singular integral equation with a Cauchy kernel, which is characteristic of the problems of stress concentration at the crack ends in the plane formulation. Its numerical solution was carried out, providing the possibility of calculating the values of the normal stress intensity factors at the crack ends. The concept of the indicator of the coating restraining effect is introduced, its behavior for coatings with different parameters is studied, the influence of physical and mechanical characteristics of the coating. We investigated its thickness and stiffness, as well as the crack size, its location relative to the corner point of the area, the angle of opening of the wedge-shaped area on the crack opening. The assessment of how the coatings influence the stress-strain state of sections of products weakened by stress concentration zones contributes to the development of new design approaches to the structural component of products, allowing us to enhance the strength and wear resistance of machine parts and elements of building structures.