Piecewise Linear Plastic Potentials as a Tool for Calculating Plane Transient Temperature Stresses

Abstract

A numerical-analytical solution of a one-dimensional problem of the theory of temperature stresses on the evolution of plane stress states under conditions of heating and subsequent cooling of a round plate made of an elastoplastic material is constructed. The plate is heated in such a way that the level of the bell-shaped temperature distribution increases in proportion to the time up to the set maximum value. After that, the heating source is removed and then cooling occurs in natural conditions. It is shown that following the conditions of piecewise-linear plastic potentials at any calculated time of the deformation process, integration of the equilibrium equation establishes dependences connecting reversible and irreversible deformations and stresses with the temperature distribution. The yield point is assumed to be quadratically dependent on temperature; elastic moduli, specific heat and thermal expansion coefficient are considered constant. It was found that the problem under consideration in the framework of the Tresca-Saint Venant plastic potential has no solution, but it can be solved in the framework of the Ishlinsky – Ivlev plastic potential.