The method of representing the J-integral during deformation of an elastic-plastic adhesive layer connecting elastic cantilevers using additive components is studied. The additive components of the J-integral are responsible for a specific aspect of deformation: stresses on the end surface of the adhesive layer; the reversible part of the deformations and the irreversible part of the deformations. Two approaches to solving the problems of loading samples connected by overlapping using mixed mode I+II loading of the adhesive layer are analyzed: an analytical solution and the finite element method. The load analysis showed the presence of stress vectors at the boundary of the adhesive layer directly adjacent to the free surface. The results obtained demonstrate a high degree of correspondence in terms of average tangential and diagonal stresses in the elasticity zone, as well as average tangential stresses in the area of elastic-plastic deformation of the adhesive layer. During numerical modeling of problems involving mixed load modes I+II, the components I and II of the J-integral load modes were calculated, and its reversible and irreversible parts were identified. The studies revealed that thinning of the adhesive layer affects all average stresses within the elastic model, as well as the average diagonal components of the stress tensor for elastic-plastic behavior of the layer, with an increase in the length of the zone of irreversible deformations. When the layer thickness is zero, where the J-integral determines the singular stress distribution, a similarity was found between the solutions of problems describing the behavior of a thin adhesive layer in both elastic-plastic and elastic deformation modes.
Glagolev et al. (Mon,) studied this question.