PSI - Issue 43

A.D. Nikitin et al. / Procedia Structural Integrity 43 (2023) 53–58 A.D. Nikitin et al. / Structural Integrity Procedia 00 (2022) 000 – 000

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propagation. The crack growth rate is a function of the evaluated stress state. The crack growth stage is longer for high stress amplitudes. The last step is final fracture that is not contributed to the total fatigue life. Therefore, to predict the total fatigue life, the model considering the material degradation and evaluation of the stress state is required. The degradation of the material under cyclic loading can be described by the damage function. Many stress-based criteria are based on a direct generalization of the S- N Wöhler - curves described by Basquin type relations. These criteria are divided into two large groups. Criteria that are based on invariant characteristics of the stress tensor can be referred as a group 1. The second group includes criteria that consider the amplitudes of the tangent and/or normal stresses on the so-called critical plane. These criteria required to find an extremum of the equivalent stress on the arbitrary orientated plane. The detailed information about the criteria with a critical plane can be found in works Karolczuk et al. (2016), Bourago et al. (2011). To study the progressive development of fatigue damage, the two different approaches can be introduced. The first one is based on the common fracture mechanics concepts and considering the fatigue cracks development as a function of stress intensity factors (SIF) at the crack tip. The relation between crack growth rate and SIF was proposed by Paris and Erdogan, and nowadays it has many modifications. The second approach is considering the description of damage under external loads. The earliest works can be referred as Kachanov (1958) and late developed by Altenbach et al. (1999), Lemaitre et al. (1994). These damage theories are usually not considering the cyclic loading but some modification allowing the applying such theories to fatigue failure was introduced in Nikitin et al. (2020). The present investigation is considering the damage theory proposed in Kachanov (1958). This theory was successfully applied to cyclic loading and fatigue failure problems in works Altenbach et al. (1999), Lemaitre et al., (1994). Withing present investigation the kinetic equation for damage function description was assumed together with one of stress based multiaxial criteria. 2. Mathematical model and numerical method The present model of fatigue failure is based on the recent advances in structural integrity of metallic material subjected to cyclic loading. According to the numerous experimental results Shanyavskiy et al (2022), Sakai (2009) the full distribution of fatigue life is considering as multi-mode complex SN curve. Nowadays there are three ranges of fatigue: low cycle fatigue (LCF), high cycle fatigue (HCF) and very high cycle fatigue (VHCF), fig.1. There are no sharp borders or a separation criterion between these fatigue ranges. The switch between two neighboring ranges has a probabilistic nature and can be described by bifurcation area model proposed by Shanyavskiy et al (2022).

Fig. 1. The full SN curve for metallic material with multi-regime fatigue life distribution.

Considering two different mechanisms (mechanisms 1 and 2) of fatigue fracture we can introduce a probability to get a specimen failure by a given mechanism. This probability will be a stress amplitude depended. The bifurcation area is considering as a stress range where the two mechanisms have a high enough probably to be found in experiment. Due to a probabilistic nature of the mechanisms change, a high dispersion of fatigue life can be observed for many structural materials in this stress range. Such fatigue behavior of structural materials allows several different