PSI - Issue 5

Bahman Hashemi et al. / Procedia Structural Integrity 5 (2017) 959–966 Author name / Structural Integrity Procedia 00 (2017) 000 – 000

965

7

× 1.5 × 0.8 = 1.2 3.1 × 0.8 = 2.48 3.8 × 0.8 = 3.04 4.3 × 0.8 = 3.44 11 × 10 −2 6.6 × 10 −3 1.2 × 10 −3 2.9 × 10 −4 Partial Factors 0.88 1.17 1.32 1.43

Table 3. Values of the partial factors

Simulation

5.31 × 10 6 6.13 × 10 6 4.76 × 10 6 4.71 × 10 6

S-N, EN1993 S-N, BS7608

0.89 0.79 0.78

1.18 1.06 1.09

1.33 1.19 1.25

1.45 1.31 1.36

LEFM, Simplified law LEFM, Bilinear law

⁄ = 3.8 = 1 5 0.8 ℎ

Table 4. Description of the simulations for sensitivity analysis and their effects on partial factors Simulation Description

LEFM model

S-N model

SN, EN1993

SN, BS7608

FM, Simplified

FM, bilinear

S1 S2

Deterministic initial crack size, Deterministic threshold value for ∆ Without considering the threshold value for ∆ Deterministic model parameters 1 & 2 - Considering model uncertainty factors on loads - - -

- -

- -

0.96 1.07

0.96 1.06

S3

-

-

1.07

1.06

S4

-

-

1.00

0.98

S5

Considering model uncertainty factors on loads Deterministic material parameters 1 & 2 0

1.16

1.17

2.21

2.11

S6

-

0.97

0.98

-

-

The results of each simulation in the terms of failure probability and reliability index trends are presented in Fig. 3 and Fig. 4. In case of S-N models, considering a deterministic value for material parameters has a small effect on partial factors because in the region around the target reliability index, simulation S6 behaves similar to the reference case. But in the zone with higher failure probability, the differences become more considerable. On the other hand, introducing the model uncertainty factors to loads has a substantial effect in any case. In Fig. 4, it can be observed that curves related to simulations S2 and S3 coincide completely. The reason is that for this particular stress spectrum, the minimum value of ∆ for each CMCS sample is higher than the characteristic value of ∆ ℎ .

Fig. 3 Failure probability trend (Left) and Reliability index trend (Right) for sensitivity analysis of S-N models