On the influence of the mechanical characteristics of a thin adhesion layer on the composite strength. Part 1. Elastic deformation

The problem of deformation of a DCB sample, which is a composition of bodies bound by an adhesive layer of finite thickness, is considered. Based on the variational equilibrium equation containing the layer thickness as a linear parameter, a finite element solution of the problem of loading the layer with a normal discontinuity in the plane strain state is constructed. The stresses averaged over the layer thickness are related to the stresses along the layer boundary by the equilibrium equations. The boundary stresses of the layer form the boundary conditions for the mating bodies. In the layer, along with shear stresses, stresses orthogonal to shear are also taken into account. The constitutive relations in the layer are represented in terms of average stresses. With a significant difference in the Young's moduli of the adhesive and mating bodies, the convergence of the value of the J-integral with a decrease in the layer thickness is shown. To find the J-integral, its representation is used as a product of the specific free energy at the end of the layer and its thickness. It has been established that the Poisson's ratio of the bodies affects the value of the J-integral, and the Poisson's ratio of the adhesive layer has almost no effect on the value of the J-integral. Using the theory of plates Mindlin - Reisner at zero Poisson's ratio of the adhesive, an analytical representation of the J-integral is obtained. The representation includes energy terms related to the pull-off stress and the axial stress in the layer. In this case, the term associated with the axial stress in the layer is proportional to the square of the ratio of the Young's moduli of the adhesive layer and the bodies mating with it. From the solution obtained, it follows that the mechanical properties of the adhesive layer with a small thickness compared to bodies do not affect the value of the J-integral if the elastic modulus of the adhesive layer is significantly less than the elastic modulus of the mating bodies. Thus, the use of replacing the adhesive layer with a layer of zero thickness is correct under these restrictions.