Stress state and conditions for crack initiation in the adhesion layer of the composite

The paper deals with the elastic deformation of a composite consisting of plates connected with an adhesive layer on the basis of the interaction layer concept. The layer thickness is taken as a linear parameter. Under loading by the normal separation in the case of plane deformation, the triaxial stress state of the adhesive layer is taken into account. From the general variational setting, by using the hypothesis of flat sections, the problem is formulated in a differential form. Within the framework of a simplified formulation, an analytical solution is found that agrees with the numerical solution obtained by the finite element method. It is shown that Poisson's ratio of the adhesive layer significantly affects its stress state, in which there is a coincidence of the two principal stresses. For weakly compressible adhesion layers, a stress state close to hydrostatic tension is realized. In order to analyze the stress state of the adhesion layer, which is singular at extremely small values of the linear parameter, it is proposed to use the energy product (EP), local stresses (LS) and local deformations (LD). EP is determined as the product of the specific free energy of the layer and the linear parameter, and LS (LD) is determined as the product of stresses (deformations) and the square root of the linear parameter. It is shown that these characteristics are not singular with respect to small layer thicknesses and do not depend on the linear parameter. It was found that the value to which the EP converges at a fixed external load and the linear parameter tends to zero does not depend on the mechanical properties of the adhesive, and the LS (LD) values depend on the properties of the adhesive. At the critical load of crack initiation in the adhesive, the LD in the direction of the separation is significantly (by several orders of magnitude) higher than the LD in the orthogonal direction. In this case, the LS and LD of separation make the main contribution to the formation of the EP. A method is proposed for determining the critical value of the EP corresponding to crack initiation in the adhesive based on the use of the maximum external load from the experimental R-curves.