Within the framework of the theory of small deformations, using the example of the problem of a rapidly rotating thin disk, a comparison is made of the fields of stresses, displacements, and deformations determined for various mathematical models of an isotropic ideal elastic-plastic body, which include smooth or piecewise-linear plasticity functions. The general principles of plane stress state are discussed. All material parameters are considered to be constant values. It is shown that when choosing piecewise-linear plasticity functions, singular modes occur at the boundary separating regions where regular plasticity modes are realized. It has been established that as the load parameter increases, the boundary for the occurrence of the singular mode shifts. For this reason, the relationships of the associated law of plastic flow in the region of the shifting boundary are integrated numerically. Since, during loading in the plastic region, the change in the position of the boundary between zones of regular modes is small, in this work, instead of the associated law of plastic flow, the associated law of plastic deformation is chosen. In determining the stress and strain state of the disk, the power condition of plasticity by Karafillis-Boyce is considered, which is one of the generalizations of von Mises’ plasticity condition. Moreover, as the exponent increases, the deviatoric stress components transition to Ishlinsky’s plasticity condition. The processes of increasing and removing load are examined. Graphs of stresses, displacements, deformations, and the stress vector hodograph are presented.

Mikhail A. Artemov, Dr. Sci. Phys. & Math., Professor; e-mail: artemov_m_a@mail.ru; AuthorID: 8282

Alexandr A. Verlin, Senior Lecturer; e-mail: alexandrverlin@mail.ru