Issue 30

D.S. Paolino et alii, Frattura ed Integrità Strutturale, 30 (2014) 417-423; DOI: 10.3221/IGF-ESIS.30.50 418 Two distinct failure mechanisms are generally visible in VHCF data plots and, at a stress value near the conventional fatigue limit, plots show a plateau separating the two failure modes. For this reason, the conventional fatigue limit can be considered as a transition stress that differentiates between the two failure modes [2]. In particular, the plateau separating different failure mechanisms represent a transition stress, while the plateau separating finite lives from infinite lives can be considered as a real fatigue limit, if it exists [3, 4]. Following the experimental evidence, new fatigue life models [2, 5-7] were proposed in the literature for the description of S-N curves characterized by two failure modes. A novel general statistical model, which can take into consideration the two failure modes (Duplex S-N curve) and the possible presence of a fatigue limit is described in [8]. The model differentiates between the two failure modes (surface and internal nucleation) according to the estimated distribution of the random transition stress (corresponding to the conventional fatigue limit). No assumption is made about the statistical distribution of the number of cycles at which the transition between surface and internal nucleation occurs (i.e., the transition fatigue life). In the present paper, the statistical distribution of the transition fatigue life is obtained, according to the statistical model proposed in [8]. A numerical example, based on experimental datasets taken from the literature, is provided. The paper shows results obtained in case of a Duplex S-N curve with fatigue limit. M ETHODS n [8], a unified statistical model for various types of S-N curve was defined. In Subsection Duplex S-N curves: statistical model , the particular case of Duplex S-N curves is recalled. The model is able to take into account the possible presence of a fatigue limit. In Subsection ‘Transition life: statistical distribution’ a procedure for the estimation of the statistical distribution of the transition life is presented. Duplex S-N curves: statistical model In case of Duplex S-N curve with fatigue limit, the cumulative distribution function (cdf) of the fatigue life Y (i.e., logarithm of the number of cycles to failure) can be expressed as [8]:   1 t l t Y X X X Y surf Y int F F F F F F    (1) where Y surf F is the cdf of the fatigue life if crack nucleates superficially (i.e., of the random variable (rv) ) Y surf , Y int F is the cdf of the fatigue life if crack nucleates internally (i.e., of the rv Y int ), t X F is the cdf of the logarithm of the transition stress (i.e., of the rv t X ), l X F is the cdf of the logarithm of the fatigue limit (i.e., of the rv l X ). Y F given in Eq. (1) depends on the cdfs of the continuous rvs l X , t X , Y int and Y surf . According to what proposed in the literature [9-12] for the fatigue strength, both l X and t X can be assumed as Normal distributed (i.e., the fatigue limit and the transition stress are Log-Normal distributed). In particular, let l X have mean value l X  and standard deviation l X  , and t X have mean value t X  and standard deviation t X  , then: Φ l l l X X X x F             (2) and Φ t t t X X X x F             (3) where Φ is the standardized Normal cdf, x denotes the logarithm of the applied stress amplitude. I