PSI - Issue 22

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

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1. Introduction Over the last three decades, probabilistic approaches have gained much interest and application to model and solve engineering structures problems Keshtegar and Benseghier (2018). In oil and gas industry, production and transportation structures whether offshore or onshore structures, especially pipelines subject to random loading are among the most critical ones that take the attention of researchers Kirkemo (1988), BenSeghier et al. (2018). Currently, integrity management program of onshore/offshore pipelines proceeds to reliability fatigue based assessment in order to control the cyclic pressure loading, which induce fatigue problems. The fluctuating of internal pressure coupled with stress concentration due to localized damages such as dents or residual stress in welding joints can be the origin of fatigue loading and alter pipeline integrity Straub (2004). Fatigue crack growth can be modeled using 2D crack growth laws; this model is widely used in academic research and standards as BS7910 (2000).This model is well adapted to surface cracks, it allows to take in consideration The variation of Paris crack growth rate among crack front, the effect of crack dimensions in initial stage and crack shape development. Several approaches are proposed in order to model the development of crack shape. Mahmoud (1988) compared various methods to predict crack shape development during fatigue crack growth in tension plate based on experimental data. The applied approach involves analytical and empirical equations. where the comparison of this latters with real test results shows that analytical method have the best fitting over the full range of initial crack shape values compared to experimental data with standard deviation less than 0,07 . Noting that this method is based on local SIF ( K loc ) calculated according to Newman and Raju (1981) with assumption of C c =0.9 C a ( C c and C a are fatigue crack growth rate in surface and deep point). Wu (2006) proposed to determine the crack shape according to a given distribution of stress intensity factor based on numerical simulation. Hou (2011) also has used numerical approach and has considered closer effect to simulate crack shape development. Another proposed alternative is to use the mean square root of stress intensity factor ( RMS SIF ) instead of local intensity factor Chahardehi et al. (2010). Most of these methods are compared to Newman assumption. The existence of correlation between Paris law parameters and its physical basics have been subject to disagreement for years. Many studies were focused also on parameters that have the most influence on crack growth rate C and m such as: load ratio R . Cortie and Garrett (1988) proposed linear correlation in the form of ( ) = + and argued that C-m correlation have no fundamental basic and its purely the results of: 1- The logarithmic method used to plot data of C-m values. 2- The nature of the dimensions of the physical quantities used in the Paris equation. Carpinteri et al Carpinteri and Paggi (2007) tried to propose a C-m correlation based on both self-similarity concepts and condition where the Paris law instability corresponds to the Griffith-Irwin instability at onset of rapid crack growth. This correlation used fracture toughness of the material, crack growth rate at onset of crack instability, and loading ratio. The objective of this paper is to use reliability – fatigue based assessment approach on case of study represented by an onshore pipeline subject to induced cyclic loading. The influences of key aspects of probabilistic model (crack growth model, limit stat, input random variable and correlation of Paris law parameters) were assessed. Reliability analysis of pipeline with surface semi elliptical cracks using importance-sampling method is discussed. Various cases of C-m correlation are also investigated to show their influence on analysis results. Finally, sensitivity analyses were performed to clarify the effect of different concepts on the probabilistic analysis.

2. Problem formulation 2.1. Stress Intensity factor

As mentioned above, the linear elastic material crack tip conditions can be characterized by one single element called Stress Intensity factor ( SIF ) where all stress components are proportional to it. A lot of research have been published to compute this parameter analytically or using finite element method. well-known formula developed by Raju and Newman (Newman and Raju (1981)) is widely used. It was obtained empirically based on extensive results of 3D FEM results of different crack configurations in structural components. In the case of plate with semi elliptical surface crack, SIF can be expressed by equation (1):