Thermal Stresses in an Elastoplastic Tube Depending on the Choice of Yield Conditions

We use the solution of a one-dimensional problem of the theory of thermal stresses in an elastoplastic tube heated on its interior surface and maintained at a constant temperature on the exterior surface as an example to make a comparison of both the results and solution methods depending on the choice of each of three conventional yield criteria: piecewise linear criteria of maximum shear and maximum reduced stresses and a smooth criterion of maximum octahedral stresses. It is established that while the transition of stresses from the face of the Tresca prism to its edge (change in the flow regime) in the first of the piecewise linear yield criteria takes place at the plastic flow onset, in the second one, this transition occurs on the elastoplastic boundary. The yield stress is assumed to be temperature dependent.