Page 414 - Wind Energy Handbook

388 COMPONENT DESIGN
ó
å d (ó, N) ¼ å 0d N 1=m 1 (7:7)
ó cd
where å 0d ¼ å 0k =ª mf , ó cd ¼ ó ck =ª mu , å 0 is the value of å given by the å–N curve when
log N is zero, ó is the mean stress for the loading cycles under consideration, and
ó cd is the design compressive stress. ª mf is the partial safety factor for fatigue
strength, ª mu is the partial safety factor for ultimate strength, and the suffices d and
k signify design and characteristic values respectively.
Equation (7.7), together with its equivalent for mean tensile loading, can be used to
calculate the permissible number of load cycles, N i , for each strain range in the fatigue
loading spectrum for the point in the blade cross section under examination –
incorporating the appropriate partial safety factor for the consequences of failure.
Thesearethencombinedwiththepredictednumberofcyclesforeachstrainrange, n i ,to
P
yieldMiner’sdamagesum, i (n i =N i ),whichisnormallyrequiredtobelessthanunity.
There is inevitably a degree of uncertainty as regards the accuracy of Miner’s rule
in predicting the fatigue damage due to variable amplitude loading from constant
amplitude test data. In order to investigate this, fatigue test programmes have been
carried out using the WISPER (Wind SPEctrum Reference) and WISPERX variable
amplitude fatigue load spectra, which have been devised to be representative of
those experienced by wind turbine blades. (WISPERX is a modification of WISPER
in which the large number of small cycles, accounting for approximately 90 percent
of the total, are omitted to reduce test durations.) For each test specimen, the
WISPER (or WISPERX) load sequence is scaled to give a chosen maximum stress
level and applied repeatedly until the specimen fails.
Van Delft, de Winkel and Joose (1996) analysed the results of a series of tests carried
out at ECN and Delft Technical University on a 08, 458 laminate and found that, for a
maximum stress of about 150 MPa, the actual fatigue lives of specimens subjected to
repetitions of the WISPER or WISPERX load sequences were about 100 times less than
predicted for these sequences on the basis of constant amplitude, reverse loading test
data and Miner’s rule, with the effect of mean stress allowed for using the linear
relation described above. The R ¼ 1 test data led to an S–N curve given by
N ¼ (ó=ó tu ) 10 , where ó is the amplitude of the stress cycles and ó tu is the ultimate
tensile strength, so the number of cycles to failure for constant amplitude loading at
other R values was taken as N ¼ (ó=ó tu (1 ó=ó tu )) 10 for a tensile mean and
N ¼ (ó=ó tu (1 ó=ó cu )) 10 for a compressive mean in calculating the Miner’s damage
sum. The difference in fatigue lives at the stated maximum stress level quoted above
translates to an approximate ratio of 1:1.5 between actual and predicted maximum
stress levels of the WISPERsequenceto causefailureover the design fatigue life,which
would clearly use up a substantial proportion of the safety factors used in design.
However,otherinvestigatorsworkingwith differentlaminateshavefoundreasonable
agreement between measured and predicted fatigue lives under WISPER loading.

Material safety factors

Limit-state design requires that the characteristic strength of a material be divided
by a partial safety factor for material strength. In the case of GFRP, this factor needs