Fatigue Design of Wind Turbines - Wind Turbine Technology: Fundamental Concepts of Wind Turbine Engineering - page 706

Defining a threshold stress as the stress producing the threshold stress intensity with
the initial crack and an R-ratio of zero, we obtain from Equations (12-14), (12-17e), and
(12-18)

Q = 1.200 - 0.714 (0.050/0.125) 2 = 1.086 (12-19a)

S TH = 5,000 / sqrt [1.086 p x 0.050] = 12,100 psi (12-19b)

where

S TH = threshold stress (psi)

Crack depths vs . operating time can now be calculated by setting the maximum stress in
the spectrum equal to values larger than the threshold stress since, in accordance with Equa-
tion (12-17a), no crack growth takes place if S maxmax is less than or equal to S TH .
Typical results of the forward-integration of Equations (12-17) for an overload ratio, R OL ,
of unity are shown in Figure 12-20 for increasing values of S maxmax . Here we see the sensitiv-
ity of crack growth to the amount by which S maxmax exceeds S TH when the number of fatigue
cycles is very high, as it is in this case. When the maximum stress in the spectrum is only
4 percent larger than the threshold stress, the crack will grow to the specified final depth of
0.500 in. after 30 years of operating time. If this is increased to 8 percent, the same crack
depth is reached in about 15 years. The effect of overloads between load spectra is shown in
Figure 12-21, which is the solution to this sample problem. As the overload ratio increases
from 1.0 to 2.0 the fatigue design allowable stress increases from 12,100 psi to 13,600 psi for
the given design parameters.

Figure 12-20. Typical crack growth histories for the sample problem.