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from which
S
1
= 15,610 psi (107,600 kN/m
2
). For the required 30-year design life,
N
f
= 30
yr
´ 8, 760
hr
yr
´
19,105
cyc
= 5.6 ´ 10
8
cyc
(12-13c)
9.0
hr
From Table 12-1,
36
1
n
i
s
-1/ (- 0.0676)
36
1
n
i
= 19, 105
cycles
= 1, 618
cycles
(12-13d)
i
Substituting the factors calculated in Equations (12-13) into Equation (12-12) then gives
S
maxmax
=
4
,
230 psi
(
32
,
590 kN
/
m
2
)
Again, this stress represents the average fatigue strength of laboratory specimens and
therefore
must not be used directly for a fatigue allowable stress
. It must first be mul-
tiplied by one or more so-called
knock-down factors
(each less than 1.0) to account for (a)
scatter in the laboratory test data and (b) several conditions that can reduce fatigue strength
in full-scale structures below that of laboratory specimens.
Fiberglass Blade Fatigue
Fiberglass composites (also termed
glass fiber-reinforced-plastics
or
GRP
) are currently
the most common materials used in the manufacture of modern wind turbine blades [Ancona
and McVeigh 2001, Griffin 2001]. The fatigue properties of fiberglass have been studied
extensively and databases of S-N curves have been compiled [Mandel and Samborsky 1997,
Delft
et al.
1997, Wahl 2001, Wahl
et al.
2002].
Because fiberglass is a non-homogeneous material, like the laminated fir-epoxy material
discussed previously, its fatigue resistance is sensitive not only to the selection of its constituent
materials and the processing variables used to combine these materials, but also to the ratio of
applied tensile and compressive stresses.
A
Goodman diagram
of the type shown in Figure 12-18 [Sutherland and Mandel 2005] is
the conventional method for displaying the dependence of fatigue life on cyclic stress combined
with various amounts of mean stress. The asymmetry evident in Figure 12-18 illustrates the
significantly different effects that tensile and compressive mean stresses have on the fatigue re-
sistance of this composite material. An extensive amount of fatigue testing of material samples
is normally required to produce a complete Goodman diagram for fiberglass. To reduce the
required amount of testing, Sutherland and Mandell [2005] verified that fatigue tests at the 5
R-ratios shown in Figure 12-18 are sufficient to capture the essential features of this material's
fatigue resistance in a Goodman diagram.
Fracture-Mechanics Method
A fracture-mechanics model of the fatigue damage process is more complex than the
S-N linear damage model, but it is considered by many fatigue specialists to be the most rep-
resentative model of the physical processes leading to fatigue failure [
e.g.
, see Broek 1982,
Tada
et al.
1985, Suresh 1991]. Fracture-mechanics analysis is a standard, validated tool of
structural engineering, and its application to wind turbines is straight-forward [Finger 1980,
Finger 1985]. As with any fatigue design methodology, experience and verification by field
testing are much more critical to success than the level of complexity.
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