The use of piecewise linear plastic potentials in the nonstationary theory of temperature stresses

Under the conditions of a piecewise linear plastic potential defining in the space of principal stresses the plasticity condition for the maximum reduced tangential stresses, a solution is obtained for a one-dimensional quasistatic problem of the theory of temperature stresses about the local heating of a circular plate made of an ideal elastoplastic material. The yield point is assumed to be temperature dependent. A comparison is made in the distribution of the current and residual stresses during heating and cooling of the plate metal obtained both with the dependence of the elastic models on the temperature, and without taking this dependence into account. It is shown that, depending on the rate and temperature of heating, the regime of plastic flow can change under the transition of stressed states from one face of the loading surface to another. In this case, the possibility of an inclined prism of fluidity on the edge is excluded, the surface of which in the space of principal stresses is the loading surface.