Environmental Engineering Reference
In-Depth Information
only is this effect lost at very high load cycles, there is also a significant reduction in
the strength, something that was already indicated by the test results of [75]. For the
fatigue loads relevant in practice, for example for wind turbines with a number of
fatigue cycles log N
9, this approach retains the effect of an increase in strength for
biaxial repeated compressive loads.
At the same time, this approach also leads to isotropic fatigue behaviour up to a number
of fatigue cycles log N
¼
6 because the same results can be presumed for the damage
variables on the compression and tension meridians.
The convexity condition of the Willam-Warnke model [41] results in the S-N curve for
uniaxial repeated tensile loads with an effective minimum stress S
cd,min
¼
0 having to
be changed in such a way that the curve intersects the abscissa not at log N
¼
12, but
rather later, at log N
¼
15. This difference of
D
log N
¼
3 is used for all minimum
stresses with S
cd,min
6¼
0.
The choice of
D
logN can influence the course of the damage in the high-cycle
range. For example, a higher value of
D
log N
¼
6.95 leads to the biaxial compres-
sive fatigue strength corresponding exactly to the fatigue strength as for uniaxial
repeated compressive loads for S
cd,min
¼
0 in the failure model of [41] at logN
¼
12,
and the convexity condition is still clearly satisfied. Consequently, validating the
damage development on the tension meridian requires tests involving biaxial
repeated compressive loads, with numbers of fatigue cycles to failure
>
log N
¼
6
and the ability to derive the development of the damage variable
k
fat
t
in the high-
cycle range.
Figure 4.32 shows the resulting courses of the damage variables
fa
c
and
k
fat
t
k
for the
boundary conditions specified here.
fa
c
and
fat
t
Fig. 4.32 Damage variables
k
k
