Issue 49

A. Guillalet alii, Frattura ed Integrità Strutturale, 49 (2019) 341-349; DOI: 10.3221/IGF-ESIS.49.34 344 by this record is the fluctuating pressure range and number of times that take place. To make this information useful as a constant amplitude pressure change events during time period, a cycle counting method as rain flow method can applied to obtain the Pressure Range Histogram. To easily asses and compare the cyclic severity of a given pressure time history, Stress Severity Indicator (SSI) is efficient tool. SSI is the number of cycles of a given pressure range required to grow a crack the same amount as the actual pressure time history over one year. An example is illustrated in Fig. 2 where SSI of 150 MPa equivalent cycles is used. Figure 2 : Spectrum Severity Indicator. Limit state function of cracked pipeline Reliability problem related to fatigue cracks in pipelines can be expressed using limit state function (LSF) that separate the failure region (LSF ൑ 0) (e.g. plastic collapse, fracture) and the safe region (LSF>0). The considered limit state in this work is based on LEFM where it defines the failure as fracture that the crack growing force represented by stress intensity factor K i reaches a critical value equivalent to fracture toughness K ic , therefore the limit state function can be represented as follow: I IC LSF K K   (3) From above the considered problem is modeled as probability of failure estimation where the goal is to calculate failure probability of each crack configuration based on simulation or analytical methods such as the Monte Carlo Simulation or FORM method. The Eqn. (2) can be expressed as:   0 f IC I P LSF K K    (4) ௙ ሺ ሻ represents the failure probability and the results are expressed in term of reliability index. This later is related to the probability of failure according to Eqn. 4:   1 β Φ f P    (5) where Φ ିଵ ሺሻ is the inverse of standardized normal distribution function. R ELIABILITY METHODS robabilistic methods are widely used when evaluating the structural performance of pipeline due to theirs advantages[13, 14]. Comparing to deterministic method or assessment again target reliability using calibration safely factor, it gives many advantages. Due to the large number of input parameter involved in structural analysis, P