1113 Stiffness Controlled ScN Fatigue Design Curves

Based on stiffness degradation data, already discussed in Section 1.10.2.2, stiffness-controlled Sc-N curves, corresponding to specific EN/E1 values, were calculated by means of Eq. (1.20). Fatigue strength curves were also defined at predetermined survival probability levels based on the parameters of the statistical model from Table 1.14 and were plotted in Figs. 1.15-1.21. Comparing these two sets of fatigue design curves, it was concluded that they could be correlated as follows. To any survival probability level, Ps(N), corresponds a unique stiffness degradation value, EN/E1, which can be determined from the cumulative distribution function, F(EN/E1), of the respective data. It is this value of En/E1, for which F(EN/E1) = Ps(N); see Fig. 1.35. Observing the two different curves derived as stated above, it was concluded that they are similar for all cases considered in this work, with the Sc-N being slightly more conservative in general. Therefore, one can use in design an Sc-N curve bearing information on both issues: survival probability and residual stiffness.

The derivation procedure of an Sc-N curve is schematically demonstrated in Figs. 1.35 and 1.36 for the data of 15° off-axis coupons under R = 0.1. In Fig. 1.36 both design curves, for 50 and 95% survival probability, are plotted together along with experimental failure data. It is observed indeed that Sc-N and S -N curves from each set lie very close, and that the former type of design curve is slightly more conservative. Using as design allowable the Sc-N at En/E1 = 0.96, as seen from Fig. 1.35, a 95% reliability level is at least guaranteed while stiffness reduction will be less than 5%. Similar comments are also valid for Figs. 1.37-1.40, where results are shown for coupons cut at different off-axis angles and tested under different R ratios. It has to be mentioned that this good correlation between stiffness-based and reliability S-N curves is the rule followed by all other types of coupon, tested under different loading conditions. In Table 1.16, S-N curve equations are given for 95% reliability level for all data sets used in this study and compared to the corresponding stiffness-based Sc-N curve equations.

FIGURE 1.36 Sc-N vs. S-N curves. R = 0.1, 15° off-axis.
FIGURE 1.37 Sc-N vs. S-N curves. R = -1, 0° on-axis.

These results strongly recommend that despite the observed discrepancies, which are not significant in most of the cases, stiffness-based Sc-N curves be used instead of reliability S-N curves in design. Curves of the former type refer to two design parameters, reliability and stiffness degradation level. Thus, they can be used in design to cover requirements of design codes and regulations. In addition, Sc-N curves can be determined much faster, as stiffness degradation trends are readily captured with only a small number of coupons tested.

FIGURE 1.38 Sc-N vs. S-N curves. R = 10, 30° off-axis.
FIGURE 1.39 Sc-N vs. S-N curves. R = 0.1, 45° off-axis.

To demonstrate this, the procedure for the determination of stiffness-based Sc-N curves was repeated by using half of the coupons. A fraction of 50% of the coupons from each set was randomly selected and the calculations were repeated. The Sc-N curves, determined that way, were then compared to the original ones. Probability cumulative distributions were almost identical in most of the cases studied, for example, see Fig. 1.41. Thus, Sc-N curves were similar to those determined by using the full data set as shown, for example, in Fig. 1.42 for 30° off-axis coupons, tested under alternating stress, R = —1.

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