# Characteristics of Acoustic Emission Caused by Intermittent Fatigue of Rock Salt
## 4 Results and Discussion  
### Characteristics of Residual Deformation  
Figure 5 shows the strain paths of the first six cycles for the control experiments. \(\Delta\)e(i) is the residual strain produced by the \(i\)th cycle; \(\Delta\)e(2), \(\Delta\)e(4),... are defined as the residual strains before the interval produced by even cycles; \(\Delta\)e(3), \(\Delta\)e(5),... are defined as the residual strains after the interval produced by odd cycles. The cycle before an interval is recorded as a \(\beta\) circle, and the cycle after an interval is recorded as an \(\alpha\) circle.  
This approach was used to understand the development of residual strain in the material (Figure 5). Figure 6 shows the difference in behavior when an interval is inserted into the classic fatigue test: in Figure 6a, the development of the odd and even circles is coincident in the classic fatigue test but are offset when an interval of 5 s is inserted (Figure 6b).  
Figure 4: Stress paths of (**a**) classic fatigue and (**b**) fatigue as a function of time interval.  
Figure 5: Fatigue strain path as a function of time interval.  
An exponential function \(y=\ae^{bx}+C\) was chosen to fit the data of Figure 6b, with \(y=C\) as the horizontal asymptote of the function when \(x\rightarrow+\infty\), which represents the average steady residual strain. In these experiments, fatigue life is defined as the number of completed loading cycles attained when the sample breaks. The fatigue lives of samples subjected to the interval fatigue tests and the C values of the fitted curves of residual strain are listed in Table 1. The value of \((C_{odd}-C_{even})\) is always greater than zero, which means that the residual strain of an \(\alpha\) circle is always larger than that of the adjacent preceding \(\beta\) circle in the interval fatigue tests. The values of \(C_{odd}\) and \(C_{even}\) increase with the duration of time interval, which means that the time interval accelerates the accumulation of residual strain caused by fatigue. The value of \((C_{odd}-C_{even})\) also increases as the interval duration increases. The mathematical manifestation of this phenomenon is that the gap between the fitted curves of residual strain for \(\alpha\) and \(\beta\) circles (Figure 6) increases; physically, this means that the time interval is shorter than the time interval.  
Figure 6: Residual axial strain for each loading circle for (**a**) the classic fatigue experiment and (**b**) the control group experiment with a time interval of 5 s.  
that the longer the interval, the faster the residual strain accumulates. The most important aspect of Table 1 is that a strong correlation between fatigue life and interval duration is demonstrated: the fatigue life decreases as the interval grows. From a macroscopic point of view, the main reason for fatigue fracture of a rock is the accumulation of residual strain [21]. The inclusion of a time interval with no stress accelerates the accumulation of residual strain, which leads to the decrease in fatigue life.  
Another noticeable phenomenon as shown in Table 1 is that when the time interval exceeds approximately 900 s, the fatigue life of the salt no longer decreases, but, conversely, increases with further extension of the interval duration because of the particular self-healing capability of this salt [3; 4; 5; 6; 7].