Напружено-деформований стан клейового з’єднання, що має поздовжній дефект

Abstract

In adhesive joints, one has to face the phenomenon of non-adhesive. It is known that non-adhesive reduces the strength of such joints. Analytical models known today for calculating the stress-strain state of adhesive joints have certain defects that appear as a result of simplification (one-dimensional models), and the realization of numerical methods requires a large resource of computing equipment. The subject of study in this article is a mathematical model of the stress-strain state of an adhesive joint of two plates. The purpose of this research is to study the stress-strain state of an adhesive joint with non-adhesives and to develop methods for studying the stress state of adhesive lap joints. Methods: a simplified two-dimensional analytical model of the stress state of the adhesive joint was used to construct an analytical solution to the problem of the stress state of the joint, which contains a defect in the adhesive layer along the side edge of the bonding area. The simplification of the model consists of the fact that the transverse displacements of the base layers are considered to be zero. This assumption can be interpreted as the presence of base layers of high stiffness in the transverse direction, and it allows reducing the problem of the stressed state of the joint to a system of two partial differential equations with respect to the longitudinal movements of the base layers and obtaining the solution of the problem in an analytical form. The obtained solution is written in the form of functional series. The eigenfunctions are not orthogonal. Using the least squares method, the solution of the problem is reduced to a system of linear equations. The model problem for joining two aluminum plates of the same size has been solved. The results showed that the presence of non-adhesive area can significantly increase the stress near the edge of the adhesive layer. Corner points in the adhesive layer are especially dangerous from the strength point of view. The results were compared with the results of finite element modeling. The comparison showed that the proposed mathematical model has high accuracy for engineering calculations. This model can be developed to solve similar problems, for example, to study the stress state of the joint of coaxial pipes, which has defects in the adhesive layer.