PSI - Issue 38

Jinchao Zhu et al. / Procedia Structural Integrity 38 (2022) 621–630 Author name / Structural Integrity Procedia 00 (2021) 000 – 000

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2.1), i.e. 10 mm and 45°, respectively. The influence of geometrical variability along the weld is therefore not taken into account. The curves corresponding to a survival probability ( P s ) of 2.3%, 50% and 97.7 % are shown in the figure.

Fig. 6. SN-curve without the influence of geometrical variability using the NS method with r ref = 1 mm and FAT 225.

3.2.2 Influence of geometrical variability The probability density function (PDF) of the SCF is computed using MC simulation (Section 2.5), see Fig. 7(a). As can be seen, the PDF is skewed and its maximum value is approximately 2.78 which is obtained for a toe angle of 89°. It is noted that the mean value of the SCF (2.58) is roughly the same as the deterministic SCF ( K t = 2.61) computed using the mean values of leg length and toe angle (Section 3.2.1). The Kaplan-Meier (Kaplan et al. (1958)) estimator is used to calculate the empirical cumulative distribution function (CDF), see Fig. 7b, which corresponds to the probability of failure 1- P s . As can be seen, the difference in predicted fatigue life when using K t = 2.61 and the PDF of K t in Eq. (4) is small at the lower tail of the distribution.

a b Fig. 7. In the NS method with r ref = 1 mm and FAT 225: (a) PDF of K t computed using MC simulations and FEA; (b) CDF of N when the K t in Fig. 7a is used as well as when a deterministic value of K t = 2.61 computed using mean values of geometrical parameters is applied.

3.3. Notch stress approach with r ref = r actual + 1 mm and FAT 200 3.3.1 SN-curve without the influence of geometrical variability

In the NS method with r ref = r actual + 1 mm and FAT 200, an SCF value of K t = 1.85 is determined by using the mean values of leg length (10 mm), toe angle (45°) and toe radius (2 mm). The resulting SN-curve computed using Eq. (4), with Eq. (6) and Eq. (7), is shown in Fig. 8.