Page 512 - Marine Structural Design

488 Part IV Structural Reliabiliw

Uncertainty measures: For the Wirsching's S-N lognormal reliability model, it's necessary to
specify the mean and COV of K, B and A, which are assumed to be lognormal distributed
variables.
The variables B and A are used to quantify the modeling error associated with assumption
made in the stress analysis and the description of the fatigue strength.
For random variable A describing the modeling error associated with Miner-Palgrem
-
hypothesis, the following values for h and C, are widely used, A = 1.0 and C, = 0.3.
For random variable K, it is associated with the uncertainty in the S-N relationship. For the S-
N curves established from the fatigue tests, the median value is determined by the
experimental tests for different S-N categories while the COV is derived as 0.3-0.6 based on
experimental data analysis.

27.4 Calibration of FM Model by S-N Approach

Both S-N curve approach and FM approach have been applied to calculate failure probability:
Based on the S-N curve and Miner's rule, the LSF can be written as Eq.(27.7), where A is
the Miner's sum at failure, NO is the number of cycles over the design lifetime that causes
initiation and propagation. 1rK is modeled as a normal distribution.
Alternatively, a and to used in the FM based LSF Eq. (27.21) can be combined together by
neglecting to in the expression and substituting by which is an equivalent initial
crack size accommodating crack initiation time.
Accordingly, there is a correlation between these two approaches. This means that the initial
crack size used in the FM model may be calibrated to the S-N approach (Song & Moan, 1998).
The numbers of stress cycles to failure can be written as

N=KS-" =Ni +N, =Ni + da (27.28)
a. C(EYY(a,~)G)"'
where a0 corresponds to the crack size after Ni cycles of crack initiation.
Assuming that N+N, the calibration of initial crack size a can be done according to

(27.29)

The median value of the initial crack size a can be calibrated by other variables from Eq.
(27.29). It is generally believed that the calibrated a will also depend on the crack initiation
period indicated by 6. In the calibration, m may be modeled as a fixed value or a random
variable of normal distribution.
In a similar way, the S-N approach can also be calibrated against FM approach. In another
word, the crack size can be explicitly included in a S-N curve. No matter which approach is
going to be calibrated, the principle of calibration is that the different approaches should yield
consistent fatigue life.