PSI - Issue 22

Abdelkader Guillal et al. / Procedia Structural Integrity 22 (2019) 201–210 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

203

3

= ( + ) ∗ √ ∗

(1) Where S t represents remote uniform-tension stress, S b is the remote bending stress on outer fiber, Q is shape factor for elliptical crack and F is the stress-intensity boundary-correction factor. 2.2. Crack shape variation during fatigue growth Crack growth is now well understood in macroscopic level due to the coupling of experimental observations and analytical concept. Several models have been proposed to predict life time of engineering components subject to time-dependent crack growth such as: fatigue or environmentally assisted cracking (e.g. stress corrosion cracking). The most used models are: S-N model, Cumulative Damage and fracture mechanics. In order to predict lifetime of component with surface crack under cyclic tension, it has been generally accepted to use Paris law in the deepest and surface point of the crack with the assumption of semi elliptical crack shape: In this study, 2D Paris law is adopted, and the crack is assumed to remain semi elliptic during fatigue growth. Crack growth can be characterized using deep and surface points. This assumption has no influence in the general behavior of crack shape development so on stress intensity factor estimationGörner et al. (1983) 2.3 Limit stat functions The performance of cracked pipeline should be evaluated by reliability probability P R or using it complement, the failure probability P f (P f =1- P R ) that can be expressed as follow: P f = P R [LSF(X) ≤ 0] = ∫ f(X)dX LSF(X)≤0 (3) Where X is the vector of random variables and ( ) is the known probability density function of this vector. LSF(X) is the performance function or limit state function BenSeghier et al. (2019). In this paper, tow limit state functions based on LFEM are used. The first one considers pure fracture due to attainment of driving force into limiting value of material resistance to fracture (material toughness). The second considers the R6 curve criteria which define competition between fracture and plastic collapse failure mode Gomes and Beck (2014, Anderson (2017). This competition can be treated using the tow-criterion of failure assessment diagram or FAD diagram. Therefore, limit state functions can be expressed as next: LSF 1 : failure is due to brittle fracture 1 = − (4) Where represents material toughness while represent the stress intensity factor in √ LSF 2 : R6 curve is used as failure criteria 2 = 6 − (5) Where 6 = ( 8 2 { ( 2 )}) (6) Where P c is the collapse pressure in the case of pipe with axial semi elliptical surface crack . P c is given according to the following equationKim et al. (2002) : { = ∗ = ∗ (2)