Page 421 - Marine Structural Design

Chapter 21 Application of Fracture Mechanics 397

21.5.2 Crack Growth due to Variable Amplitude Loading
The equations presented in Section 21.5.1 may be applied to risk-based inspection in which the
crack growth is predicted using Paris Law. Predicting the number of cycles for the crack
propagation phase for variable amplitude loading is compIex and needs a computer program to
do numerical integration of Eq.(21.9). The number of occurrence ni in a block for stress range
Si for crack depth from a,to a,,, may be estimated as (Almar-Naess, 1985),
1 P,., da
(2 1.12)

and the fatigue life Ni at a constant amplitude stress Si is given by

(21.13)

Hence, the accumulated fatigue damage may then be estimated using the Miners Law, which
is:

(21.14)

21.6 Comparison of Fracture Mechanics & S-N Curve Approaches for Fatigue
Assessment
As compared in Table 21.1, the Paris Equation may be transformed to the equation of an S-N
curve. Eq(21.10) may be written as

(21.15)

where I in Eq.(21.15) is an integral. The total number of cycles N is close to Np because the
number of cycles to the initiation of crack propagation is small. Hence the above equation may
be further written to:
I
m
N = - (S)- (21.16)
Cl

Fracture Mechanics S-N Curve
Region I Threshold Region (no crack growth) Fatigue Endurance Limit (infinite life)
Region IT Paris Equation S-N Curve (high cycle fatigue)
Region III: Final Fracture (yielding) Low-cycle fatigue, failure region