Page 509 - Marine Structural Design

Chapter 27 Fatigue Reliability 485

Initial crack size: Surface defects are usually more dangerous than embedded defects because
they are often located at stress concentrations, have a crack-like shape and are oriented normal
to the principal stress. The statistical distribution for such defects is the necessary information.
The initial crack size is assumed to be independent and treated as a random variable following
an exponential distribution:

(27.10)

in which, is the distribution parameter of initial crack size.
Crack initiation time: For lack of data about the crack initiation time, a simple model is to
assume that crack initial time is some percentage of crack propagation time Tp, and may be
expressed as,
to =F-T, (27.1 1)

where, 6 is a constant, Tp is crack propagation time.
Crack Propagation Prediction: Considering the effect of stress ratio, the modified Pairs law
can be rewritten as,
da
(27.12)
where a is the crack size, N is the number of stress cycles, C and m are parameters depending
on material and environment, R is the stress ratio, which depends on stress amplitude in
stochastic time history. R is set to 0 in the following analysis. AK is the stress intensity factors
range and can be estimated from Newman's approximation (Newman and Raju, 1981) given
by

AK = Ss,Y(a,X)J;;I; (27.13)
where S is the stress range and Y(a,X) is a geometry function accounting for the shape of the
specimen and the crack geometry, EY is a randomized model uncertainty of geometry function.
By separating variables in Eq(27.12) and introducing Eq. (27.13)

(27.14)
Then, the differential equation can be expressed as:
da N
= Cc (ASi)"'
N 1
am E; -Y(a,X)m I=I = NC-(AS,)" = NE[(AS)"'] (27.15)
,=I N
Since the stress response induced by sea loads is typically a narrow-band process, the number
of stress cycles spent for crack growth N may be defined as
N = ",(ret - to) (27.16)