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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3. Application and results 3.1. Case study In order to apply the above methodology, problem of semi elliptical crack located on the surface of pipeline is considered where the geometrical configuration of the crack is illustrated in figure (1)

Fig.1. Geometry of crack in the pipeline Tables 1 represent the statistical proprieties of the random variables involve in the limit state functions. To illustrate the influence of crack shape development and the effect of correlation parameter of Paris law (C, m) 4 cases are considered as follow and detailed in table 2: 1- C and m are deterministic. 2- C is log-normal and m is deterministic. 3- C is log-normal and m is obtained based on Cortie correlation 4- C is log-normal and m is normal with correlation factor = −0.997 To take in consideration the variation of crack shape during fatigue crack growth, the simple suggestion of variability of material resistance along the crack front of (Newman and Raju) Newman and Raju (1981)is used. This variation is modeled by an empirical equation = 0.9 where C c and C A are crack growth rate in surface and deep point. Table 1. Input random variables Variables mean Standard deviation Distribution a 4 mm 0.4mm Normal c 20mm 1mm Normal t 15.88 mm 0.794 mm Normal D 1219.2 mm 3.65mm Normal P (MOP) 8 MPa 0 deterministic K ic 137 MPa.m 1/2 13.7 MPa.m 1/2 (1) Normal Sigma (Re) 555 MPa 26 Normal

Table 2. Paris law parameters variability in considered 4 cases

cases

Mean value of C (mm/cycle)

Standard

distribution

Mean value

Standard

Distribution

deviation

of m

deviation

Case 1

5*10 -9

/

deterministi

3.1

/

deterministic

c

case 2 Case3 Case 4

5*10 -9 5*10 -9 5*10 -9

8.5*10 -10 8.5*10 -10 8.5*10 -10

Log-Normal Log-Normal Log-Normal

3.1 3.1

/

deterministic

0.62

Normal Normal

Cortie correlation

Cortie correlation