EQUILIBRIUM LONGITUDINAL INTERNAL CRACK IN A STRIP WITH A THIN COATING

Abstract

The static problem of the theory of elasticity on stress concentration in the vicinity of tips of an internal crack of finite length in a strip reinforced with a thin flexible coating is considered. The crack is located parallel to the boundaries of the strip, its sides do not interact. The problem is symmetric with respect to the crack line. The study is based on the method of integral transformations, which made it possible to reduce the problem to the solution of a singular integral equation of the first kind with a Cauchy kernel. As a model of the coating, special boundary conditions were used, formulated based on an asymptotic analysis of the solution of the problem for a thin elastic strip whose bending stiffness can be neglected. The regular part of the kernel is investigated depending on the ratio of the physical characteristics of the strip and coating materials, as well as such geometric parameters as the size of the crack and the thickness of the strip and coating. The solution of the integral equation is constructed by the collocation method in the form of an expansion in terms of Chebyshev polynomials with a pre-selected singularity. The convergence of the method is analyzed depending on the ratio of the values of the parameters of the problem. The values of the influence factor, the reduced intensity factor of normal stresses in the neighborhood of crack tips for various combinations of geometric and physical parameters of the problem are obtained. In particular, it was found, that increasing the thickness and hardness of the coating leads to a decrease in the magnitude of the influence factor. Increasing the length of the crack or decreasing the width of the strip entails an increase in the magnitude of the influence factor. We consider certain special cases of the problem under consideration. In particular, in the absence of coverage, the results are compared with the data available in the literature.