Issue 49

A. Guillalet alii, Frattura ed Integrità Strutturale, 49 (2019) 341-349; DOI: 10.3221/IGF-ESIS.49.34 342 I NTRODUCTION ne of the strategic energy resources are oil and natural gaz. they have the advantage to ensure a continues and reliable energy supply with an acceptable cost. An important reason behind this success is the reliability of system transmission via pipeline from zone of production to market zone. Pipes carrying such hazardous products are subject to different type of defects. Crack growth in pipelines is an inevitable problem due to its nature. Cracks in pipeline can have different origins such as pipe manufacturing defect, welding defect or external damage. Crack growth may lead to a real concern about structural performance and failure of system production. The reliability and the fracture prediction of such piping systems are primordial given their impact on the economic plan and safety. Several researchers studied the fracture behavior of pipes containing semi elliptical surface cracks and the change of crack shape during fatigue crack growth. Zhang and Ferguson [1] developed model to predict crack shape development, under fatigue. Induced cyclic fatigue is due to service fluctuating pressure in pipeline based on API579 Stress Intensity Factor calculation and Paris law. For given initial a/c and a/t, final crack length with the crack propagation to through-wall thickness can be predicted. They found that crack shape development is strongly influenced by initial crack shape and depth ratios. The BS 9710 standard proposes an approximate integration method for fatigue life estimation. Mahmoud [2] compared different methods used to predict crack shape development during fatigue crack growth in tension plate with experimental data. The used methods are based on analytical and empirical equations. The comparison shows that analytical method based on local SIF (K loc ) calculated according to Newman and Raju formula [3] and the assumption of C c =0.9C a (C c and C a are fatigue crack growth rate in surface and deep point) is the best solution over the full range of initial crack shape values compared to experimental data with standard deviation less than 0,07. Boukharouba [4] reviewed proposed prediction model of crack shape factor evolution with depth ratio in fatigue cracking test for the following cases: tension plate, three point bending plates and tube under internal pressure. For the last case, they conclude that a/c ratio passes by maximum (growth in deep direction is more rapid comparing to surface direction) then remains steady following horizontal asymptote during crack growth. Another important conclusion is that behavior of a/c evolution is similar in thick plate under tension and thick tube under internal pressure. This finding can be supported by the work of Zhu and Tao [5] where they found that stress distribution and stress intensity factor in plate and pipe are similar for the same magnification load. Probabilistic methods are widely used when evaluating the structural performance due to theirs advantages. Different mechanisms failure are studied using Probabilistic methods such as corroded pipelines in [6-8] in comparing to deterministic methods or assessment again target reliability using calibration safely factor, it gives many advantages. The large number of input parameter involved in structural analysis, evaluation of failure probability can be optimized using probabilistic methods. Use of worst case input parameters and very pessimistic estimations can be avoided. In probabilistic fatigue calculation many authors take into consideration crack growth in depth direction only for simplification purpose [9] or assume basic Paris crack growth in depth and surface direction where crack growth rates are equal : C a =C c [10]. Leander and Al-Emrani [11] published reliability fatigue assessment of steel bridge. They illustrated the effect of initial crack aspect ratio on fatigue lifetime. They found that for a target reliability of 3.1 and Gumbel distribution of stress range, crack with initial a/c=1 had longer fatigue life then crack with initial a/c=0. However, the effect of shape factor variability on the estimation of reliability index is a point not well illustrated. The Influence of random character of initial shape ratio on crack shape development, during probabilistic analysis has to be more clarified according to proposed crack shape prediction model. In this work, the effect of crack shape factor on reliability index calculation is considered. The aim is to show the lack of precision associated to inaccurate estimation of shape factor during crack growth. The variation of reliability index with crack shape factor is illustrated with plots at constant crack depths. This paper is structured as follow. Probabilistic model based on liner elastic fracture mechanics was established. A developed reliability method called “Importance sampling at the design point “was used to generate simples. This method is a simulation method based on crude Monte Carlo method. Then a case study of pipeline with axially external defect is applied. P ROBABILISTIC MODEL Liner elastic fracture mechanics iner Elastic Fracture Mechanics (LEFM) is widely used to evaluate structural reliability of onshore pipelines. Early model of LEFM simplify the relation modeled using triangle in Fig. 1. Therefore , three main parameters are involved as load, defect size and fracture toughness. In real situation, the problem is more complex; where many O L