To the problem of determination of the residual strength of beams, damaged by cracks

Abstract

The evaluation of the residual strength of structures already damaged by cracks  is an extremely important scientific problem today. This is due to the fact that during prolonged use in the elements of the structure cracks appear both from the fatigue of the material and from the presence of certain stress concentrators in their design. As a result, the initial design strength, which did not take into account the presence of cracks, begins to decline significantly. In order to avoid the destruction of such a structure, a corresponding reduction in the design load is required.

The problem of determining the stress-strain state of an anisotropic beam with an inclined crack, in the formulation of a flat problem of the theory of elasticity, is considered by S. Serensen and G. Zaitsev in a well-known work [1]. The problems of isotropic strip with a transverse and a longitudinal crack using the linear conjugation method are solved in the writings of V. Panasyuk, B. Lozovyi and other authors [2,3,4,5]. Authors G. Kit, O. Sushko and B. Lozovyi [6] considered bending of strips of rectangular or elliptical sections, which are damaged inside by a circular crack, with a different load. The stress-strain state in the vicinity of cracks was investigated in this work as well as dependence of SIF (stress intensity factor) from the load and location of the crack. The method of boundary integral equations with complex potentials by M. Mushelishvili was used. In another paper [7], the authors investigate the net bending of a beam with a crack, taking into account the plastic zones near its vertices, where an analytic solution is obtained in the class of functions restricted to the ends of the plastic strips.

The methodology for determining the residual strength of composite beams damaged by the edge crack in the area of tensile stress is developed. Such calculations use a non-classical bending model of composite beams, which takes into account the effect of shear and compression deformations. Formulas for the limit loads of a composite beam, which is loaded by a distributed load and damaged by a small boundary crack at the lower surface of the beam, have been obtained. Numerical results for different thicknesses and materials are given.The results obtained are analyzed and compared with the results for the beams without damage.