PSI - Issue 68

Evgeniia Georgievskaia et al. / Procedia Structural Integrity 68 (2025) 559–565 Evgeniia Georgievskaia / Structural Integrity Procedia 00 (2025) 000–000

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Fig. 2. Effect of HF-loads on the crack growth rate.

All cracks in HU lifetime-determining components are divided into two groups (Figure 2): non-hazardous and hazardous. Cracks are considered safe when there is no growth under the influence of external operating loads. HU can work with such cracks throughout its lifetime. Cracks that exceed the crack length threshold are considered hazardous, they will grow during normal HU operation but the growth rate will vary significantly depending on the spectrum and amplitudes of external loads. Among the hazardous cracks are the most hazardous cracks with a high growth rate, which can lead to rapid destruction of the HU component under consideration. LF loads determine the growth rate of hazardous cracks during the first stage. At this stage, the crack from the initial value ℓ 0 grows slowly and steadily according to the Paris law during several years or even decades. At the end of the first stage, the crack reaches a threshold value ℓ th , the SIF at its tip reaches the threshold value K th , from which the crack growth is influenced by HF loads with low amplitudes. The influence of HF loads is manifested in changing the nature of crack growth and accelerating its development. Duration of stage 2 from Т th till the moment of T f , corresponding to the destruction, is significantly shorter than the duration of stage 1 and usually takes no more than a few months. Therefore, in practice it is critical to adequately determine the crack transition time from stage 1 to stage 2, i.e. the moment of the crack transition into a very hazardous state when the growing crack becomes sensitive to high-frequency loads. To determine the point of Т th it is necessary to solve both problems: the slow growth of the crack under LF loads, during stage 1 and the rapid crack growth during stage 2 with the combined LF and HF loads. The HU lifetime estimation (determining the point at which the runner will be destroyed) depends on the measurement of crack length based on fracture mechanics methods according to the principle of making sure the inability of brittle fraction (crack resistance criterion). Residual lifetime ( Т res ) determines itself from the condition of reaching the limit state. Т res – is the time period during which the crack length will reach the operational limit-permissible length ℓ cr for the given scenario of HU modes for the forecast period. ℓ cr variable complies to the numerical evaluation according to the recommendations BS 7910 taking into account the margin factors for crack length and material fracture toughness according to Georgievskaia (2019). 5. Results For demonstration purposes the proposed approach uses the 5.5 m diameter runner residual lifetime numerical simulation of a vertical 220 MW HU. Its rotation speed equals approximately 2.1 Hz. The numerical simulation task involves determining the time of the next major repair, required due to the possibility of hazardous cracks in the runner blades. Figure 3 shows the numerical simulation results: to the left is the crack growth kinetic diagram, to the right is the threshold value definition ℓ th for stage 2. Table 2 displays quantitative lifetime indicators. Formula for determining ℓ 1 , ℓ 2 , ℓ cr are as follows below: