## 0

FIGURE 1.11 Stiffness degradation data. R = 0.1, 90° off-axis.

Kolmogorof-Smirnof (KS) goodness-of-fit tests were performed for each one of the hypotheses. KS test results, that is, the DN statistic and its probability, P(Dn), for all the aforementioned distributions are given in Table 1.13. Values of P(Dn), greater or equal to 0.05 correspond to goodness of fit at a significance level of 5% or higher. Calculations for the KS test were performed using the method described in Press et al. [42].

LogN

FIGURE 1.12 Stiffness degradation data. R = 10, 45° off-axis.

LogN

FIGURE 1.12 Stiffness degradation data. R = 10, 45° off-axis.

As seen from the results of Table 1.13, stiffness degradation data, at a specific R value and off-axis angle 0, can be modeled by a single statistical distribution for the whole range of stress levels considered for an S-N curve determination. Notice that for the cases studied herein, the number of experimental points taken into account was at least 80.

An example of favorable and unfavorable comparison between experimental data and theoretical distributions is given in Figs 1.13 and 1.14, respectively, for different material configurations. The upper and lower 95% confidence interval bounds correspond to the less satisfactory distribution, which for the case of Fig. 1.13 is the two-parameter Weibull distribution, whereas for Fig. 1.14 is the lognormal distribution. In this latter case, since the experimental sampling distribution intersects the 95% confidence bounds, the respective null hypothesis, that is, the lognormal distribution, is not accepted at the significance level of 5% [43].

At noted from the results of Table 1.13, the best performing distribution is the two-parameter Weibull distribution, which succeeds in 14 of 16 treated cases to fit the data at a significance level greater than 5%. The statistical distributions are sorted, in this table, according to their fitting capability and, therefore, the second best performing function is the normal. It must be emphasized that in all cases treated except that of R = 10 at 0 = 90°, stiffness degradation data are satisfactorily fitted by a single statistical distribution, at a significance level of 5% or higher, irrespective of stress level in the same S -N curve.

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