Issue 30

D.S. Paolino et alii, Frattura ed Integrità Strutturale, 30 (2014) 417-423; DOI: 10.3221/IGF-ESIS.30.50 419 In the literature [9-11], different types of continuous distribution have been proposed for the number of cycles to failure. Usually, either a 2-parameter Weibull distribution or a Log-Normal distribution are used for the cycles to failure rv. Without loss of generality, the conditional fatigue life is supposed to be Normal distributed (i.e., the conditional number of cycles to failure is Log-Normal distributed). Therefore, suppose that the mean values of Y int and Y surf follow the Basquin’s law and that the standard deviations are constant for any value of x , then:   Φ Y int Y int Y int Y int y a x b F              (4) and   Φ Y surf Y surf Y surf Y surf y a x b F              (5) where Y int a , Y int b , Y surf a and Y surf b are four constant coefficients related to the Basquin’s law and Y int  and Y surf  denote the standard deviations of Y int and Y surf , respectively. Fig. 1 shows a schematic of a Duplex S-N curve together with the statistical distributions assumed in each characteristic region: the surface-nucleation and the internal-nucleation regions are described by a randomly variable fatigue life (Eqs. 4 and 5), while the transition and fatigue-limit regions are described by a randomly variable stress amplitude (Eqs. 2 and 3). Figure 1 : Schematic of a statistical Duplex S-N curve with fatigue limit. By taking into account Eqs. 2-5, Y F finally becomes:     Φ Φ Φ Φ 1 Φ t l t t l t Y surf Y surf Y int Y int X X X Y X X X Y surf Y int y a x b y a x b x x x F                                                                     (6) with a number of parameters equal to 10. Transition life: statistical distribution Statistical estimation of the parameters permits to compute the S-N curves corresponding to different probabilities of failure (quantile S-N curves). Eq. (6) can be exploited for the estimation of the  -th quantile S-N curve: if Y F   and