On the calculation of unsteady thermal stresses in elastoplastic solids

The features of estimated prediction of thermal stress evolution are considered in terms of the one-dimensional boundary problem of the theory of thermal stresses, in which a shrink fit assembly of cylindrical parts is simulated on the assumption of piecewise linear plasticity conditions. The problem solution is principally based on the classical maximum shear stress criterion (Tresca-Saint Venant yield criterion), whereas the maximum reduced shear stress criterion (Ishlinsky-Ivlev yield criterion) is used only for comparison of calculation results. It is shown that the use of piecewise linear potentials makes it possible to integrate an equilibrium equation in both reversible deformation area and various irreversible deformation areas. Dependences thus obtained are used in a time-step calculation algorithm. Calculations have shown that, as the temperature changes, stresses in the materials of the assembly can change plastic flow pattern. It means that the correspondence of plastic flow to a certain facet of loading surface passes into the correspondence to an edge and then to other facet. These circumstances cause irreversible deformation areas to be divided into parts in which the plastic flow obeys different sets of simultaneous equations, which take into account the assignment of the stress states to different facets and edges of the loading surface. The designed algorithm makes it possible to trace the moments of appearance and disappearance of such plastic flow areas, as well as their propagation in the deformed material. The calculations demonstrate the possibility of occurrence of a repeated plastic flow during unloading in a certain area of the assembly after return of the process to reversible deformation conditions on cooling. It has been established that taking into account the change of plastic flows caused by the use of piecewise linear plastic potentials has an essential impact on the distribution of current and residual stresses and on the final tightness of the assembly.