FIGURE 2 Damage equivalence
Figure 2 shows that cycles at high loading have exactly the same damage
state as cycles at low loading . However, in view of the rationality of
fatigue damage equivalence under different stress levels,
studies18-19 point out that the traditional damage
equivalence state does not exist under different stress levels.
According to this point of view, in the fatigue driving stress model,
equivalence according to equation (6) is not sufficient as well. In
particular, for the high-low loading sequence, it tends to speed up the
damage evolution process under low loading, whereas for the low-high
loading sequence it is the reverse. At the same time, the greater the
difference between the stress levels applied, the greater the effect.
This phenomenon (loading interactions) is usually described in terms of
load ratio and has been reported by Corten and
Dolan20, Freudenthal and Heller21,
Morrow22, and Huang23 et al.
More recently, targeting the flaws of traditional damage equivalence
methods, Peng16 proposed a fatigue damage equivalence
rule by considering the loading interaction effects. Generally,
according to the principle of damage equivalence, points A and B in
Figure 3 have the same damage state, which can be represented by the
concept of fatigue damage state as:
The damage evolution path is then OABE, but the loading of the second
stage retains its damage evolution trend under constant amplitude
loading, ignoring the interaction effects between the loadings. After
undergoing high-loading cycling, the damage evolution curve under
low-loading cycling will be shifted based on its damage evolution curve
of constant amplitude loading and this shift has a promoting effect on
damage accumulation, while the opposite is true for low-high loading.
The damage curve after the offset can be assumed to be AN, and the
damage curve AN is shifted and extended to give an equivalent damage
curve OFE with low loading applied alone, as shown in
Figure 3. Unlike the OBE, this
damage curve OFE takes into account the interactions between high and
low loadings.
Thus, by considering the load interaction effects, the damage
accumulation path is OA→AF→FE, and the corresponding equivalent state of
fatigue damage can be described as
The function represented by curve OBE has the same starting point and
ending point as that represented by curve OFE, and curve OFE can be
transformed by curve OBE. In general, this transformation relation is
power exponential. Peng16 modified Ye’s model with the
proposed method by taking loading interactions into account, and in
comparison to Miner’s rule and Ye’s model, the modified model has a more
satisfactory forecasting result .