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Mathematical modeling of the VHCF resonance loadings with a progressive damage accumulation

One of the most critical in-situ loading modes is resonant. Such loading conditions may lead to premature fatigue damage accumulation and failure. The progressive fatigue damage changes the natural frequency of a structure and causes a permanent modification of loading conditions. This paper considers the model of fatigue damage accumulation regarding its evolution and resonant loading parameters. To describe the evolution of material degradation due to fatigue a complex kinetic model of damage development and numerical algorithm are introduced. The model contains the evolution equation for the damage function depending on stress state. The algorithm is based on a special post proceeding of a numerical solution for an elastic solid mechanics problem that can be also applied for elastic-plastic case. Different loading conditions can be considered by choosing the method of solution for solid mechanics problem. This paper is focused on the comparison between quasi-static and resonant loading conditions used for damage function calculation. It was shown that use of resonant loading solution leads an earlier crack initiation and shorter fatigue life results compared to quasi-static solution. A spatial development of the fatigue damage zone is also different for these two cases. The normal crack opening mechanism is discussing in this paper.