Evaluation of Fatigue Steel Damage Stages in Stress Concentrators Considering Inelastic Strain Kinetics

An application of the proposed model of ultimate exhaustion of cyclic plasticity is considered for the calculation of fatigue damage stages of structural elements in the elastoplastic statement and kinetics of the stress-strain state (SSS) under conditions of stress concentration. The paper outlines the defining equations of the model of ultimate exhaustion of cyclic plasticity. The basic difference between the model solutions and the current model lies in the use of cyclic stress–strain diagrams dependent on the number of loading cycles, which is attained via the introduction of the function reflecting the variation of inelastic strains into the plastic part of the Osgood–Ramsberg equation. Based on the experimental data under symmetric tension–compression on smooth specimens, refinement of the function parameters and the introduction of ultimate values are performed. Then, these results are employed in the development of the approach to calculating the lifetime of structural elements with the presence of a stress gradient in the elastoplastic statement. The approach is used to determine the fatigue life of cylindrical specimens with stress concentrators. With this aim in view, the processes of damage to thin layers of the material with the required value of their discretization are stepwise determined by the model of ultimate exhaustion of plasticity. To define the kinetics of elastoplastic SSS within the minimal section of the specimen, a hybrid numerical-analytical scheme of calculation is proposed applying the method of finite elements (FEM) at the points of support and weight functions. To consider the variations of the numerical solution depending on the change of elastoplastic properties with the increase of the number of loading cycles at various levels of stress amplitude, FEM solutions are standardized (the same as for equations of equilibrium). The solutions to these equations allow one to determine the kinetics of distribution diagrams of the elastoplastic SSS, fatigue damage to the specimens with stress concentrator and their lifetime for the material with non-stabilized cyclic deformation. The lifetime of fatigue damage to the specimens with stress concentrators is defined via the criterion of nucleation and propagation of the short crack of the specified size. The results of the comparison between the experimental and calculated lifetimes for steels 45 and 1Kh2M demonstrate a good correlation between the results.