## 3 Results and Discussion
### Four-Point Bending Fatigue Test
#### 3.3.4 Maximum Fatigue Strain Evolution Curve  
In this paper, the Miner criterion [35] was used to define damage variables. First, the following basic assumptions were made:  
1. Assuming that the original miner criterion is valid, the Miner criterion can be simplified under constant amplitude fatigue loading as follows: \(D=\frac{n_{i}}{N_{i}}=1\), where \(n_{i}\) is the number of cycles at the level of the first order stress, and \(N_{i}\) is the fatigue life of order \(i\) stress level;
2. It is assumed that the damage is only related to the maximum strain reached in the history of loading; there is no damage prior to unloading and loading to the maximum strain on the history, and therefore the maximum strain of the cycle is known as the fatigue strain of the cycle, which is referred to as the maximum fatigue strain \(\varepsilon_{max}\). 3. It is assumed that, under different loading conditions, the failure limit strain rate \(\varepsilon^{\prime}\) of the individual specimen is a certain value, which is the material parameter. With the abovementioned basic assumptions and under different loading conditions, the damage amount-fatigue strain curve of the individual test piece was the only option, thus the fatigue strain and the damage amount may have been a one-to-one relationship. The D-\(\varepsilon\) curve of the CNFPUC at different stress levels is shown in Figure 9.  
Figure 9: _Cont._  
As seen in Figure 9, \(\varepsilon_{max}\) represents a change regulation of a power function with the increase of cycle times. With the increase of the stress level \(S\), the deformation growth rate of the specimen was accelerated. This meant that the strain growth rate was proportional to the stress level of \(S\). At the same stress level, the growth rate of the strain increased with the increase of temperature. The maximum fatigue strain under constant amplitude load showed a three-stage strain law independent of the stress ratio. Stage I: In the formation of internal damage, the strain increased rapidly and then slowed down with the increase in the number of cycles, which accounted for approximately 10% of the total fatigue life. Stage II: This was the internal damage stable expansion phase with strain varying at a near constant rate of growth, which accounted for approximately 90% of the total fatigue life. Stage III: The internal damage instability developed, and the strain increased sharply until the specimen was broken, which accounted for approximately 10-15% of the total fatigue life. The idealized curve of the three-stage law of fatigue deformation development is expressed in Figure 10.  
Based on the three-stage development rule of maximum fatigue strain \(\varepsilon_{max}\), a damage variable based on the definition of the maximum fatigue strain is proposed:  
\[D=\left\{ \begin{array}{c}0\left(\varepsilon^{p}\leq\varepsilon_{0}^{p} \right)\\ \frac{\varepsilon^{p}-\varepsilon_{0}^{p}}{\varepsilon_{c}^{p}- \varepsilon_{0}^{p}}\left(\varepsilon_{0}^{p}\leq\varepsilon^{p}\leq \varepsilon_{c}^{p}\right)\end{array} \right. \tag{7}\]  
In the equation, \(\varepsilon_{0}^{p}\) is the longitudinal fatigue initial maximum strain of CNFPUC corresponding to the deformation at the end of Stage I of the curve, which is the fatigue damage threshold. \(\varepsilon^{p}\) is  
Figure 10: Maximum fatigue deformation cycle ratio curve diagram. Figure 9: The \(D\)-\(\varepsilon\) curves of CNFPUC at different stress levels. (a) \(D\)-\(\varepsilon\) curve at stress level 0.6; (b) \(D\)-\(\varepsilon\) curve at stress level 0.7; (c) \(D\)-\(\varepsilon\) curve at stress level 0.8; (d) \(D\)-\(n\)/\(N\) trend diagram. the instantaneous maximum strain after n times fatigue, and \(\varepsilon_{c}^{p}\) is the limit of the maximum strain corresponding to the maximum strain at the end of Stage II (when the specimen began to fail). In the range of 4200-6100 \(\mu\varepsilon\), this value can be used as the ultimate maximum strain of the CNFPUC bending fatigue deformation.