The state of stress and destruction of an adhesive when joining plates with a lap

The deformation of an adhesive layer of a finite thickness connecting two bodies with an overlap in a linear elastic formulation is considered. The stressed state of the layer is considered on the basis of the average thickness and the associated equilibrium conditions of boundary stresses. The deformed state of the layer is determined by its boundary displacements. Based on the system of variational equilibrium equations for the composite coupled by the displacement field of the adhesive layer, a numerical solution to the problem was obtained using the finite element method. To approximate the displacement field of load-bearing bodies, taking into account tensile and compressive deformations in two orthogonal directions, we obtained an analytical solution to the corresponding problem. The qualitative similarity of solutions for average stresses in the layer is shown in comparison with the solution within the classical plate theory. A comparison is made of the known analytical concepts for this problem, available numerical and simplified analytical solutions. By considering the change along the length of the layer of the average stress, orthogonal to the separation of the layer at a finite thickness, in the proposed formulation of the problem we can affect the value of the boundary tangential stresses. While a change in the average shear stress of the layer leads to a difference in the separation stresses along the boundaries of the adhesive layer. This effect cannot be taken into account in models that use the hypothesis of homogeneity of the stress state throughout the layer thickness without taking into account boundary stresses. When using the boundary stresses of the layer introduced into the model as criterion characteristics, it is possible to simulate the detachment of the adhesive from the load-bearing bodies along the mating surfaces. It is shown that for the problem under consideration, the obtaining of the criterion characteristics for detachment and shear results in destruction of the adhesive layer along identical surfaces.