МОДЕЛИРОВАНИЕ УСТАЛОСТНОЙ ДОЛГОВЕЧНОСТИ ПОЛИКРИСТАЛЛИЧЕСКИХ КОНСТРУКЦИОННЫХ СПЛАВОВ ПРИ СОВМЕСТНОМ ДЕЙСТВИИ МЕХАНИЗМОВ МАЛО- И МНОГОЦИКЛОВОЙ УСТАЛОСТИ

Abstract

Processes of fatigue life of polycrystalline structural alloys under a combined effect of low- and high-cycle fatigue are considered. In the framework of mechanics of damaged media (MDM), a mathematical model is developed, which describes processes of plastic deformation and fatigue damage accumulation. The MDM model consists of three interrelated parts: relations defining cyclic elastoplastic behavior of the material, accounting for its dependence on the failure process; equations describing fatigue damage accumulation kinetics; a strength criterion of the damaged material. The version of defining relations of elastoplasticity is based on the notion of yield surface and the principle of orthogonality of the plastic strain rate vector to the yield surface at the loading point. This version of equations of state reflects the main effects of the cyclic plastic deformation process of the material for arbitrarily complex loading trajectories. The version of kinetic equations of damage accumulation is based on introducing a scalar parameter of damage degree. The construction uses energy-based principles and accounts for the main effects of the process of nucleation, growth and merging of microdefects under arbitrarily complex multiaxial loading regimes. A combined form of the evolutionary equation of fatigue damage accumulation in the regions of low-cycle (LCF) and high-cycle (HCF) fatigue is proposed. It is shown that, under regular cyclic loading of the material, the stress amplitude of the cycle decreases by degrees during the transition from LCF to HCF and depends on the physical interaction of these mechanisms in the transition zone. The condition when the damage degree attains its critical value is taken as the strength criterion of the damaged material. A methodology of numerically determining parameters of the evolutionary equation of fatigue damage accumulation in the conditions of HCF is presented. To assess the reliability and the limits of applicability of the defining relations of MDM, processes of plastic deformation and fatigue damage accumulation in a number of structural alloys in cyclic tests have been numerically studied, and the obtained numerical results have been compared with the data of full-scale experiments. The results of comparison of the numerical and experimental data reveal that the developed model of mechanics of damaged media adequately describes durability of structures subjected to a combined effect of low- and high-cycle fatigue mechanisms. It is shown that the introduced MDM model qualitatively and, accurately enough for practical engineering purposes, quantitatively describes the main effects of the processes of plastic deformation and fatigue damage accumulation in structural alloys under cyclic loading.