Page 510 - Marine Structural Design

486 Part IV Structural Reliability

where vo is the average zero-crossing rate of stress cycles over the lifetime of the ship, r is the
fraction of service time for the ship.
The crack size at the ith ship structural detail location at time t can be derived from the above
equations with R=O (Song and Moan, 1998)), as

(27.17)

where Y(.) is the auxiliary function, which is monotonically increasing with the crack size a,
expressed as

(27.18)

and

(27.19)

Assuming that lnA\i follows normal distribution.
Fatigue failure criterion: When the critical crack size a~ is defined, which may be considered
according to the serviceability, the fatigue failure criterion at cycle number N is defined as

a, -a(t) < 0 (27.20)
Limit State Function: Based on fracture mechanics, the failure criterion is Written in terms of
the crack size at time t. The limit state hction (LSF) for the ith ship structural detail location
can thus be Written equivalently as (see, e.g. Madsen, 1986)

(27.21)

where Z is a set of random variables of material and stress parameters, geometry function,
initial crack size, crack growth time, etc. ~i is the critical crack size of the ith potential crack
site, is the initial crack size at the ith crack site which can be calibrated with respect to
crack growth part of S-N curve.
Uncertainty in fracture mechanics model: Uncertainties associated with the probabilistic
fracture mechanics model include the follows
initial crack size,
long-term loading,
. material parameters
geometry correction factor in stress intensity factor computation, and
critical crack size.
Initial crack size depends mainly on the material microstructure and fabrication process and
the welding quality. Thus, large uncertainty in initial crack size is obvious. In general, the