Title | Mathematical modeling of the process of thermoplastic deformation of a thin circular disk |
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Authors | M. A. Artemov^{1}, E. S. Baranovskii^{1}, I. I. Pereyaslavskaya^{1}^{1}Voronezh State University |

Annotation | Using the Schmidt plasticity condition (plasticity condition of the maximum reduced stress), we give a detailed algorithm for solving the problem of elasto-plastic deformation of a thin circular disk, in the central part of which a uniform temperature field is given, and a constant temperature is maintained on the outer contour. Taking into account the radius of the disk, we determine the temperature at which plastic zones occur. It is shown that for the certain radius of the disk the plastic condition occurs both in the central part and on the boundaries of the disk. The ratios, which establish the relation between the radius of the disk and the temperature of its central part, and which allow to determine the elasto-plastic state of disk, are derived. The algorithm for determining deformations and displacements, which allows to consider any plasticity regime, is presented. Plots for stresses and values of equivalent stress for different regimes of plasticity are given. |

Keywords | theory of plastic flow, plane stress state, elastic-perfectly plastic material, thermoplasticity |

Citation | Artemov M. A., Baranovskii E. S., Pereyaslavskaya I. I. ''Mathematical modeling of the process of thermoplastic deformation of a thin circular disk'' [Electronic resource]. Proceedings of the XIII International scientific conference ''Differential equations and their applications in mathematical modeling''. (Saransk, July 12-16, 2017). Saransk: SVMO Publ, 2017. - pp. 236-247. Available at: http://conf.svmo.ru/files/deamm2017/papers/paper34.pdf. - Date of access: 11.12.2019. |

**© SVMO, National Research Mordovia State University, 2019**

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