Mechanical Properties of Materials in the Calculations of a Low-Cycle Deformation of Structures

Standard strength calculations for bearing units of extremely loaded structures, including nuclear power plants, allow an inelastic deformation of the materials of these units. At the same time, the calculations of the low-cycle fatigue require taking into account the factors that are not observed upon single loading, i.e., kinetics of cyclic strains, cyclic creep, and the effect of change in the modes of the inelastic cyclic deformation under normal operating conditions. It is known that, in this case, a material can be cyclically hardened, softened, or stable. For the first type of materials under soft loading with constant amplitude of stresses in cycles, the range of strains decreases with an increase in the number of cycles, but increases for the second one. Under hard loading with constant strain amplitude, the maximum stresses in a cycle increase for a hardened material and, on the contrary, decrease for a softened one. In addition, the soft loading of a softened material with an increased number of loading cycles results in one-sided accumulation of plastic deformations. These phenomena must be taken into account both in the analytical description of the kinetics of deformation diagrams and in the corresponding calculation equations used in the strength standards. At early stages of developing the calculation techniques for these conditions, the stresses were calculated under the assumption of perfect elasticity of a material. This approach was used owing to the lack of available calculation techniques for the problem of an inelastic cyclic deformation, which is complicated in the formulation. The subsequent development of the theory of the cyclic elastoplastic deformation and the analytical and numerical solutions of cyclic boundary-value problems and the development of numerical computational methods and powerful computer software codes fundamentally changed the situation, providing the possibility of analysis and modeling of the physically and geometrically nonlinear deformation processes. It is shown that the transition from the elastic adaptability (with an elastic deformation of the structure in a stable cycle) to a sign-alternating flow is smooth and continuous and is similar to the transition from the elastic to plastic deformation under a single loading. This mechanism is similar to the conditional boundary of the transition from low-cycle to high-cycle fatigue under a cyclic strain. In this case, we propose to use in calculations the existing rather simple models and experimentally determined parameters of the cyclic deformation diagrams of materials. In the modern formulation of the considered problems, it is of fundamental importance to take into account both the kinetics of cyclic and one-sided accumulated deformations and make allowance for the occurrence of creep effects in cycles. This approach also makes it possible to take into account the acceleration of unsteady cyclic creep as a result of the previous plastic deformation of the other sign, which can be rather significant.