This work is devoted to durability prediction at high-cycle irregular loading of materials. The process of brittle failure is considered as a hierarchical stochastic process at the micro-, meso-, and macro-structural levels. The initiation of defects at each level occurs as a result of the sequential generation, growth and merging of defects at previous levels. Constitutive relations for the brittle failure probability at the micro-, meso-, and macro-structural levels on the basis of Hilbert-Schmidt integral operator are proposed. High-cycle fatigue curves on defect levels for one-frequency loading of variable amplitude and asymmetry are obtained. These curves correspond to the lines of the microhardness levels. The results of calculations correspond to experimental data for aluminum alloy 2024-T42 and steel S25C at symmetric loading of two and three blocks. The analysis results shows that durability alloy 2024-T42 doesn’t depend practically from the order of amplitude application at the same maximum stress values. The calculations for steel S25C show a dependence on the order of application of loading amplitudes, namely, the maximum stresses differ on 10% and the durability can be changed in six times. For an aluminum alloy the correspondence of defect level fatigue curves to experimental lines of microhardness levels is shown.
Zavoichinskaya et al. (2025) studied this question.