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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3.2 Results and discussion

A – Influence of the crack shape development To clarify the influence of crack shape variation on estimated reliability index is carried out by comparing results from reliability analysis with equal crack growth rate in deep and surface points C c =C A with results of the assumption of Newman Newman and Raju (1981) C c =0.9 m C A . Figure 2 represents the variation of reliability index according to the above cases C c =C A and C c =0.9 m C A . Based on the presented results, for a law number of cycles, there is no pronounced difference in reliability index. In the other hand a difference is noticed with the increasing of cycles number where a relative difference of 5% is found for a number cycles of 6*10 5 . This latter can be interpreted by a difference in finale crack dimensions. These results are supported by those obtained in Hosseini et al study Hosseini and Mahmoud (1985) were the authors compared crack dimensions a and c of cracked plate under tension with consideration of the two cases with experimental results.

Fig 2. Variation of reliability index with different and equal crack growth rates C a and C c

It’s well recognized that initial semi elliptical crack still have this propriety or tend to be semicircular in final stage of stable propagation according to their initial shape ratio Görner et al. (1983), this imply that shape ratio is in continues change during fatigue propagation. The assumption of constant shape ratio in many research papers and codes Leander and Al-Emrani (2016, JCSS (2011) can lead to a fault estimation of crack dimension evolution. To show the lack of precision associated with a constant crack shape, we consider tow cases of growth: 1-Shape ratio is constant during the propagation 2- Shape ratio is variable according to 2D model of Paris law presented in equation (2) Figure 3 presents the variation of reliability index with fatigue cycles number of a pipeline. Initial shape ratio is 0.5. The use of constant shape ratio overestimate the growth in surface direction, hence reliability index is underestimated. The variation of crack shape favorite in first a growth in direction where the shape ratio reaches a value of 0.7 to 0.8 .

Fig 3. Effect of variation of shape ratio on reliability index