On predicting material and structural resources under cyclic loading

Mathematical modelling of elastoplastic deformation and accumulation of material damage under proportional and non-proportional, isothermal and non-isothermal cyclic loading is considered. On the basis of the version of the theory of plasticity (which is a particular version of the theory of inelasticity and class one-dimensional flow theories) with combined hardening. The range of applicability of the version of the theory of plasticity is limited to small deformations of initially isotropic metals at temperatures when there are no phase transitions and strain rates, when dynamic and rheological effects can be neglected. A set of material functions closing the version of the theory of plasticity is given, and a basic experiment, based on the results of which material functions are determined. On the basis of the integration of the evolution equation for microstresses (deviator of the displacement of the loading surface center) with a rigid symmetrical cyclic loading with a constant swing of plastic deformation under conditions of the uniaxial stress state, the equation of the curve of low-cycle fatigue (from up to cycles) is obtained. To determine the parameters entering the equation of the curve of low-cycle fatigue, the results of the basic experiment are sufficient. For SS304 stainless steel, a low-cycle fatigue curve is constructed, which is compared with the experimental data in the range from up to cycles to failure. Also for SS304 stainless steel, processes of non-linear summation of damages are analyzed for two-block rigid cyclic loads. It is shown that the transition from a larger swing of deformations to a smaller one significantly reduces the overall durability. The results of the calculations are compared with the results of the experiments. Further, the fatigue of SS304 stainless steel is considered under proportional and disproportional hard cyclic loads ranging from up to cycles to failure. It is shown that the greatest damaging effect belongs to loading along the trajectory of deformations in the form of a circle. The calculated fatigue curves for different deformation trajectories are compared with the results of the experiments. Predicting the structural material resource under nonisothermal cyclic loading is carried out on the basis of the durability analysis of the edge of the combustion chamber of the diesel piston and the uncooled conical nozzle of the LPRE nozzle under heat changes. In the first case, a uniaxial stress state (simple non-isothermal loading) is realized at the edge of the combustion chamber, and in the second case a biaxial stress state (complex non-isothermal loading) is realized too. We predicted the resource on the basis of the kinetic equation of damage accumulation, included in the equation of the theory of plasticity, and also on the basis of the deformation-kinetic criterion of low-cycle fatigue. Estimation of the resource on the basis of the deformation-kinetic criterion gives overestimated results (by a factor of 5-6) in comparison with the results obtained on the basis of the kinetic equation of plasticity theory and the corresponding experimental results with a good agreement of the latter.