PSI - Issue 16

Grzegorz Lesiuk et al. / Procedia Structural Integrity 16 (2019) 51–58 Grzegorz Lesiuk et al. / Structural Integrity Procedia 00 (2019) 000 – 000

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1. Introduction Reliability analysis models of materials and structures consider the ideal material without defects. For a certain group of engineering object such as pipelines, bridges, shafts, rotating elements in machines fatigue is one of the important factors of failures. According to this approach, it is possible to predict fatigue lifetime using stress, strain or energy approach in initiation phase Zhu et al. (2017), Correia et al. (2017, 2018), (as well as fatigue lifetime in propagation phase Rozumek et al. (2018). On the other hand, in many long term operated objects exist cracks and discontinuities as a result of operating time and/or from the technological reason (Nykyforchyn et al. (2016)). For enough good prediction of fatigue lifetime, it is necessary to solve the differential kinetic fatigue-fracture equation. In a general way, it can be represented by an integral form: Here, in Eq. (1) N cr describes the fatigue lifetime in propagation phase, a o represents initial crack length, a cr is the critical crack length,  ext is the external load type and stress level, P fc is the fracture mechanics parameter, so-called crack driving force (CDF), Y represents the geometric constraints, and R (  min /  max ) is the stress ratio – it represents mean stress level. In 60’ of the last century, the first one to correlate fatigue crack growth rates with load fluctuations was P.C. Paris (1961) So far, Paris’ law has been comm only used as a base in fatigue-fracture mechanics:   m da C K dN   (2) where: C, m are constants estimated from the fatigue crack growth rate diagrams. The typical draw of the kinetic fatigue – fracture diagram (KFFD) is shown in Figure 1. This type of diagram is often described by the linear elastic stress intensity factor range  K = K max – K min , corresponding successively to the external load alterations. In Fracture Mechanics, The  K- approach is so called “force approach” and is described in ASTM E647 standard ASTM (2015). ( , , , , ) a P Y R  cr o a cr ext fc a da N f   (1)

Fig. 1. Schematic representation of the kinetic fatigue-fracture diagram.

For engineering calculations, the linear stage II is one of the most interesting regime. This linear regime is often the so-called Paris regime and the Eq. 2 covers this phase of the diagram. However, for better fatigue crack growth