The influence of the relationship between yield strength and temperature on the stress state in a thin hollow disk

A thin hollow elastoplastic or perfectly plastic disk placed in a rigid cylindrical container and subjected to the action of a temperature field is considered. The conditions of plane stress state are assumed. The Mises yield condition is satisfied in the plastic zone. The main feature of the problem formulation is in the relationship between yield strength and temperature, taken in arbitrary form. A parametric analysis of the solution is carried out for the linear relationship. It was shown that the relationship between yield strength and temperature needs to be taken into account for some materials to define the stress-strain state in the disk and to estimate the conditions of the transition of the whole disk to the plastic state.