Issue 49

A. Guillalet alii, Frattura ed Integrità Strutturale, 49 (2019) 341-349; DOI: 10.3221/IGF-ESIS.49.34 347 In case 1, the letter A is used to refer to deep point. It is clear that reliability index is strongly influenced by shape factor. For the same depth ratio, reliability index decreases with increasing of the crack length. This trend is accentuated with increasing depth ratio from 0.2 to 0.8. A direct consequence is that a lack of precision during crack geometrical identification can lead to a considerable error in reliability estimation in advanced stage of growth (a/t = 0.8) comparing to initial stage (a/t = 0.2) In case 2, the letter C is used to refer to surface point. For (a/t ≤ 0.4), reliability index is approximately steady for the shape ratio (a/c > 1) and increase with decreasing (a/c). For (a/t > 0.4), the inverse is happening, where β is decreasing for (a/c ≥ 1) and approximately steady for (a/c < 1). This means that the influence of crack shape factor is not same for all configurations of cracks when SIF is calculated in surface point. Although, comparing values of reliability index for different depth ratio, it seems that β decrease with increasing depth as showed in Fig. 5. As consequence, calculation of reliability index in deep point illustrates a monotonic effect of shape factor variability on structural reliability analysis. Another point should be noted, for high shape ratio (a/c ≥ 1), reliability index in surface β A is lower than those in deep point β C ; while β A for surface point is higher than β C for (a/c < 1). This Remarque implies that considering SIF in surface point results in high or less conservatism then deep point according to the considered crack shape ratio. Figure 6 : Variation of reliability index with different cases of shape factor at constant a/t b- Reliability fatigue assessment In this second part, the fatigue life time of cracks with two different shape factors is calculated based on Paris crack growth expressed in Eqn. (6): * * m a a m c c da C K dN dc C K dN          (7) where: C a =C c are Paris crack growth rates in deep and surface directions, they are assumed to be equal. ∆K a , ∆K c are the change in applied stress intensity factor in deep and surface point respectively. Paris crack growth expressed in Eqn. (6) considers tow dimensional crack growth. Simultaneous evolution of crack depth and length can reflect the crack shape evolution. Tow configurations of initial shape are presented in Tab. 2. The first is a small crack with semicircular shape, the second is a shallow crack with an aspect ratio a/c=0.2. An applied 150 MPa equivalent cycles is used to represent the stress severity indicator in term of number of cycle during fatigue life of the pipeline.