plasticity, hardening, elasticity, perturbation method, temperature stresses.

As you know, when heated, solids, in particular metals, experience thermal deformations associated with the effect of linear expansion. Moreover, in spite of the fact that these strains are small, the corresponding stresses can be quite large, often exceeding the yield stress of the material. In this regard, to describe the stress-strain states of bodies exposed to high temperatures, it is necessary to take into account the inelastic behavior of materials. Determination of stresses and strains in elastoplastic problems has been the subject of many works, including studies [1–10]. Some of them [1], [5–10] consider the temperature effect on bodies of various configurations. In this work, we solve the problem of determining the axisymmetric stress field in a flat disk when exposed to a point heat source (for example, spot welding). The disc material is modeled by a hardening elastoplastic medium. The problem was solved within the plane-stressed state by the method of small perturbations. In an analytical form, relations are obtained that describe the distribution of stress fields in elastic and plastic deformation regions. The conditions of continuity of the radial and circumferential components of the stress tensor and the radial component of the displacement vector were used as conditions for conjugation of solutions on the elastoplastic boundary.

Maria Mikhailovna Visloguzova, student, Voronezh State University, Voronezh, Russia. Dmitry Viktorovich Gotsev, Professor, Doctor of physical and mathematical Sciences, Voronezh state University, Military training and research center of the air force “Air force Academy named after prof. N.E.Zhukovsky and Yu.A.Gagarin”, Voronezh, Russia.

Alexey Viktorovich Kovalev, Professor, Doctor of physical and mathematical Sciences, Voronezh State University, Military training and research center of the air force “Air force Academy named after prof. N.E.Zhukovsky and Yu.A.Gagarin”, Voronezh, Russia.

Alexandr Ivanovich Shashkin, Professor, Doctor of physical and mathematical Sciences, Voronezh State University, Voronezh, Russia