Fracture of the adhesive layer (AL) of finite thickness with elastoplastic properties in a layered composite is considered in this article. The expression of the J C -integral is obtained as the sum of values of the products of the layer thickness and the increments of the specific free energy and specific dissipation. Based on the variational formulation, a solution to the model problem of shear action on a thin elastoplastic layer is obtained. From the analysis of the solution obtained, it follows that in the case of a layer degenerating into a mathematical section, the main contribution to the representation of the J C -integral is made by the term responsible for the energy dissipation, and the energy product tends to zero. In this case, it is not pure dissipation that is considered, this is the product of specific dissipation and layer thickness. The expression of the J C -integral is obtained in terms of the quantities measured in a possible experiment.