Calculation of the Unsteady Thermal Stresses in Elastoplastic Solids

The one-dimensional boundary problem of the theory of thermal stresses that simulates the shrink fit assembly of cylindrical parts is used to discuss a computational approach to predicting the evolution of the thermal stresses under piecewise-linear plasticity conditions. The solution of the problem is based on the classical maximum shear stress criterion (Tresca–Saint Venant yield criterion), and the maximum reduced shear stress criterion (Ishlinsky–Ivlev yield criterion) is only used to compare the calculation results. The application of piecewise-linear potentials in the theory of plastic flow is shown to allow equilibrium equations to be integrated in both the region of reversible deformation and various parts of a plastic flow region. The dependences thus obtained are important for a time-step calculation algorithm. This algorithm can trace the site and time of both nucleation and completion of plastic flows at each time step. The calculations demonstrate that, following temperature, the stresses in the assembly element materials can pass from correspondence to a certain face of a loading surface to correspondence to its edge and, then, to another face. This circumstance implies the division of the irreversible deformation region into parts, where a plastic flow obeys different sets of equations, which take into account the assignment of the state of stress to various faces and edges of the loading surface. The computational algorithm also makes it possible to trace the beginning of division of a flow region into parts and the motion of the part boundaries through irreversibly deformed materials, including the times of their coincidence (i.e., the disappearance of the parts of the calculation region). A repeated plastic flow is shown to appear. This flow nucleates when an assembly is cooled, i.e., when the assembly element materials return to reversible deformation conditions due to the evolution of the state of stress. Taking into account the change in plastic flow conditions that is caused by the use of piecewise-linear plastic potentials is found to substantially affect the level and the distribution of residual stresses and the final tightness of the assembly.