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 .