About the influence of the elastoplastic properties of the adhesive on the value of the $${\varvec{J}}$$-integral in the DCB sample

On the basis of the general variational formulation of the problem of the deformation of two bodies connected by a thin layer, a system of differential equations of equilibrium of the double-cantilever beam is obtained, taking into account the shear deformations of the cantilevers, both in the interface section and in the free section, taking into account also the elastoplastic properties of the layer. In this work, we use the connection representation of the J-integral in terms of the energy product and the energy product of dissipation. For purely elastic deformation, on the basis of the analytical solution of the system, an expression is obtained for the stress state of an extremely thin layer connecting the cantilevers, which is dependent on the material properties of both the layer and the cantilevers. The obtained expression for the elastic energy flux is compared with the known ones. The energy product at the top of the layer is found, the value of which depends only on the material properties of the consoles. With the elastoplastic behavior of the layer, the energy product of dissipation was found, which turned out to be dependent on the yield stress of the adhesive. The energy product in this case is proportional to the layer thickness. For adhesives with pronounced plastic properties, taking into account the dissipative mechanism of energy release leads to fundamental differences in the J-integral in comparison with the elastic calculation. The dependences of the DCB sample compliance with subcritical growth of the plastic deformation region in the adhesive are plotted.