On the example of deformation of elastic-plastic adhesive layer binding elastic bearing bodies, the approach to representation of the J-integral value in the form of additive summands responsible for the presence of stresses on the end surface of the adhesive layer, reversible and irreversible parts is considered. Analytical solution and solution by the finite element method with quadratic law of displacement field distribution on the finite element of loading problems of the investigated specimens realizing mixed loading mode I+II of the adhesive layer at overlapping connection of bearing bodies are considered. The problems are considered in the state of plane deformation. It is revealed that the solutions of loading problems lead to the presence of stress vectors on the end surface of the adhesive layer, which is contiguous with the free surface. A good agreement of the considered solutions for average tangential stresses and diagonal stresses in the elastic region and average tangential stresses in the elastic-plastic region of the adhesive layer is demonstrated. At numerical solution of mixed loading problems by mode I+II, the components of I and II loading modes of the J-integral, as well as its reversible and irreversible components, are determined. For a relatively thin adhesive layer without hardening, the effect of yield strength on the dissipative summand is shown. It is shown that a decrease in the thickness of the adhesive layer leads to an increase in all average stresses for the elastic model and average diagonal components of the tensor for the elastic-plastic behavior of the adhesive layer as the length of the irreversible deformation zone increases. In the case of a layer of zero thickness, when the value of the J-integral determines the singular distribution of the stress field, the proximity of partial solutions of problems with elastoplastic behavior of a thin adhesive layer is shown.

Vadim          V.          Glagolev,        Doctor      of                 Physical         and       Mathematical                Sciences,  Professor; e-mail: vadim@tsu.tula.ru; https://orcid.org/0000-0003-0371-7704; AuthorID: 16756

Leonid V. Glagolev, Candidate of Physical and Mathematical Sciences, Senior Researcher; e-mail: len4ic92@gmail.com; https://orcid.org/0000-0003-2313-2084; AuthorID: 662387

Igor M. Lavit, Doctor of Physical and Mathematical Sciences, Professor; e-mail: IgorLavit@yandex.ru;

https://orcid.org/0000-0002-8683-5943; AuthorID: 6507255755 Andrey I. Lutkhov, Postgraduate; e-mail: tip460@mail.ru; https://orcid.org/0009-0009-6196-0076; AuthorID: 1278930

Alexey A. Markin, Doctor of Physical and Mathematical Sciences, Professor; e-mail: markinnikram@yandex.ru; https://orcid.org/0000-0003-1456-8281; AuthorID: 4335