PSI - Issue 39

Ilia Nikitin et al. / Procedia Structural Integrity 39 (2022) 599–607 Author name / StructuralIntegrity Procedia 00 (2019) 000–000

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on the loading conditions and mainly on the load amplitude. In the case of relatively high (compare to yield stress of the material) load amplitudes a numerous cracks appear at the structure surface [1] early and the total fatigue life determines by crack propagation stage. When the load amplitude is decreasing lower the yield stress, the rate between crack initiation and propagation durations is permanently changing. At low stress amplitudes the time to crack initiation determines the fatigue life of the structure. This tendency is very clear in the range of very-high cycle fatigue (VHCF) where the time to crack initiation consume about 99 percent of the total fatigue life. This is general tendency for the contribution of crack initiation and propagation processes to the total fatigue life. The developing of the model capable to take this permanent change in these two components of fatigue life as a function of the load amplitude is already not simple task. When the stress state is complex this situation turns to be even more difficult to simulate. It is often observed in service practice that loading conditions are sensitive to the rigidity of the structural element [2]. For example, an element with a high rigidity allows a high frequency vibration due to air flow or non-coaxially of rotating parts. These high frequency vibrations produce the fatigue crack that reduce the rigidity of the element and its loading conditions changing. Such situation can appear in the aircraft turbojet engines. Therefore, the total fatigue life of the element will consist of crack initiation under high frequency vibrations and crack growth under low frequency loading. Nowadays there are no convenient approaches capable to take into an account such a change in loading conditions. The study on the crack initiation and early crack propagation stages shows that some loading regimes (like pure torsion) lead to change in governing mechanism of crack opening [3]. At the initial state the shear or Mode II crack opening mechanism is dominating over the normal crack opening. The observed fatigue cracks in specimens are usually elongated by the specimen axis or perpendicular to it. The stage of Mode II crack growth is determined by stress state and usually depends on load amplitude. However, at a certain crack length the local stress field is turning the crack to propagation in the maximum normal stress planes. At this stage the governing mechanism of crack opening is Mode I. The developing of the model capable to consider the change of crack opening mechanisms is also complex task. Summering the outlined above limitations of the conventional approaches to predict the details of fatigue damage accumulation, a new approach is asking for. The recent investigations are focused on the implementation of the damage function theory in the numerical simulations of fatigue [4]. The use of damage theory makes not obligated the artificial introduction of the crack. However, the presented in the literature results are mainly consider the only one crack opening mechanism. This paper is aimed to introduce the model and numerical procedure capable to take into an account the change in crack opening mechanism, change in loading conditions and progressive change of local stress state due to damage developing. Nomenclature damage function � classical fatigue limit � � VHCF fatigue strength � ultimate tensile strength 2. Model of fatigue damage accumulation and development The multi-mode model is based on the modern advances in the fatigue knowledge. It is assumed that the full SN curve has several branches corresponding to different fatigue domains: low cycle fatigue (LCF), high cycle fatigue (HCF) and very high cycle fatigue (VHCF), fig.1. Each domain is characterized by its crack initiation and growth mechanisms. These ranges are separated by zones of ambiguities or ‘bifurcation areas’ where two mechanisms can be observed, and its appearance have a probabilistic nature. We assume that each branch has its own law, but the structure of the determining equation is similar. This hypothesis of similarity allows us to construct the uniform numerical algorithm for calculating the progressive material degradation due to cyclic loading. The details of this algorithm and model are presented below.