Issue 30

D.S. Paolino et alii, Frattura ed Integrità Strutturale, 30 (2014) 417-423; DOI: 10.3221/IGF-ESIS.30.50 421 Figure 2 : Experimental fatigue data plot [13]. Quantile S-N curves Parameter estimates given in Eq. (9) can be used for computing quantile S-N curves. In particular, if the  -th quantile S- N curve is of interest, the following equation:     Φ Φ Φ Φ 1 Φ t l t t l t Y surf Y surf Y int Y int X X X X X X Y surf Y int y a x b y a x b x x x                                                                                  (10) must be solved with respect to y for different values of x . Fig. 3 shows the S-N plot together with the 10%, 50% and 90% quantile S-N curves. Figure 3 : Quantile S-N curves. As shown in Fig. 3 the region between the 10% and 90% quantile S-N curves includes about the 86% (which is close to the expected 80%) of the failure data; while the 50% quantile S-N curve is almost median between failure data at each stress amplitude. Statistical distribution of the transition life If parameters are substituted by their estimates, Eq. (8) can be used for numerically computing the statistical distribution of the transition life. To this aim, Eq. (8) must be solved with respect to , t y  for different values of  ranging from zero to one. It is worth noting that for a given value of  , , t x  in Eq. (8) is a known quantity and is equal to t t X X z       , being z  the  -th quantile of a standardized Normal distribution. Fig. 4 shows the computed statistical distribution of the transition life.