PSI - Issue 28

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L.R. Botvina et al. / Procedia Structural Integrity 28 (2020) 1686–1693 L.R. Botvina et al. / Structural Integrity Procedia 00 (2019) 000–000

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where F(x) – cumulative probability, x – the value (number of cycles N f in our case), and γ, α and β are its parameters. The results of using original Weibull method is given on fig. 4 (a). On the fig. 4 (b) the cumulative curves plotted using the alternative method based on eq. 1 are given.

Fig. 4. (a) Three-parameter Weibull cumulative distributions (Sakai and Fujitani, 1989); (b) cumulative distributions in inverse axes N f - P f .

As in original work, the exponential functions with meaningful slope coefficient γ were used for description of lifetime distributions. As a result, it was proved that γ fully depends on stress amplitude as linear function (fig. 5) with R 2 =0.913: 26.04 0.087      (5), where is the slope coefficient of cumulative lifetime distributions and σ is stress amplitude.

Fig. 5. Relationship between statistical parameter γ and stress amplitude σ.

3.2. Fatigue fracture of SUJ2 steel The alternative statistical approach in fatigue failure was also used for SUJ2 steel experimental results (Sakai et al., 2001, Harlow, 2006). Same as in previous section, the authors analyzed the data using three-parameter Weibull's distribution (eq.4), (fig. 6 a), and we applied the alternative approach (fig. 6 b).