Environmental Engineering Reference
In-Depth Information
specifies equations for the S-N curves for uniaxial repeated compressive loads with
different minimum stresses, the S-N curve for uniaxial repeated tensile loads is only
defined for an effective minimum stress of S
cd,min
¼
0. This is a straight line, see
Equation 4.14 and Figure 4.31. Up to the point log N
¼
6, the line coincides with that
for a uniaxial repeated compressive load. Model Code 90 contains no information
about biaxial fatigue loads. This missing information is therefore derived from the test
results given in [75].
The damage parameters are therefore presented for the stress states at the fatigue limit
state. However, the lines are not dependent on the design condition and so the damage
parameters are not indexed.
fat
Approach for damage variable
k
t
in low-cycle range
As the S-N curves for biaxial repeated compressive loads from the studies of [75] show,
these curves up to a transition range from log N
¼
10
3
to log N
¼
10
4
are comparable, in
qualitative terms, with those for uniaxial repeated compressive loads. Going beyond
this transition range, that is into the high-cycle range, the S-N curves for biaxial
repeated compressive loads diverge noticeably from those for uniaxial repeated
compressive loads. Therefore, on the whole there is no straight line as for the uniaxial
repeated tensile load. After the aforementioned transition range, the S-N curves for
biaxial repeated compressive loads lie between the S-N curves for uniaxial repeated
tensile and compressive loads.
Looking at the course of the damage variable
k
fat
t
for biaxial repeated compressive
loads, we can assume that it coincides with the S-N curves for uniaxial repeated
compressive loads in the low-cycle range and lies between the S-N curves for uniaxial
repeated tensile and compressive loads in the high-cycle range.
Therefore, in order to describe the damage variables, the equations of Model Code
90 [66] for uniaxial repeated tensile loads are modified in such a way that they can
be used to describe the fatigue behaviour for biaxial repeated compressive loads.
Although Model Code 90 contains only one S-N curve for S
cd,min
¼
0, ref. [76] and
others specify that the curves for uniaxial repeated tensile loads related to the
uniaxial strength down to a minimum stress of S
cd,min
¼
0.6 correspond to those for
uniaxial repeated compressive loads and the same equations may be used. The
course of the uniaxial repeated compressive load is used for numbers of fatigue
cycles
<
log N
¼
6.
fat
Approach for damage variable
k
t
in high-cycle range
In the high-cycle range, the curve for numbers of fatigue cycles
log N
¼
6 is chosen
such that it lies between the uniaxial repeated tensile and compressive loads. The
criterion specified is that the course of the tension meridian for S
cd,min
¼
0at
logN
¼
12 leads to a failure envelope that just still satisfies the convexity conditions
of the failure model of [41]. This means that the tension meridian is embrittled so
severely under fatigue loads that the strength reached under biaxial repeated
compressive loads for log N
¼
12 lies noticeably below the uniaxial compressive
fatigue strength. A biaxial compressive load increases the strength. However, not
