## 3 Results and Discussion
### Rheological Properties  
Strain amplitude sweep tests were performed to investigate the change in the dynamic viscoelastic modulus of the MREs under cyclic shear fatigue. Figure 3 shows the storage modulus (G\({}^{\prime}\)\({}_{0}\)) and loss factor (tan(\(\delta_{0}\))) of the NR sample as a function of the strain amplitude in the zero-field after 0, 300,000, and 500,000 fatigue cycles. As shown in Figure 3a, the G\({}^{\prime}\)\({}_{0}\) of the NR sample decreased with increasing strain amplitude owing to the Payne effect and decreased with fatigue. In addition, tan(\(\delta_{0}\)) increased as the number of fatigue cycles increased, as shown in Figure 3b. These results are consistent with the generally known behaviour, that is, the remarkable decrease in the storage modulus. As the number of cycles increased, damage gradually propagated, thereby decreasing G\({}^{\prime}\)\({}_{0}\) and increasing tan(\(\delta_{0}\)) because the friction inside the material causes more energy dissipation [(41; 42)]. Figure 4 shows the rheological properties of the MRE sample in the absence (off-state) and presence (on-state) of the magnetic field under cyclic shear fatigue. After 300,000 cycles, the G\({}^{\prime}\)\({}_{0}\) of the MRE sample was lower than that of the initial sample, exhibiting a behaviour similar to the NR sample. After 500,000 cycles, G\({}^{\prime}\)\({}_{0}\) increased again. This trend can be attributed to the increase in the maximum load during the cyclic shear fatigue test. The MRE sample has more pronounced hysteretic heating and crystallisation accumulation, resulting in its higher stiffness. In contrast, the G\({}^{\prime}\)\({}_{0}\) value of the MRE sample before and after being subjected to fatigue under a magnetic field exhibits a slightly different trend, \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Number of Fatigue Cycles**} & \multirow{2}{*}{**0**} & \multicolumn{2}{c}{**Zero-Field**} & \multicolumn{2}{c}{**Magnetic Field (300 mT)**} \\ \cline{3-6}  & & **300,000** & **500,000** & **300,000** & **500,000** \\ \hline Specific gravity (g/cm\({}^{3}\)) & 2.586 & 2.581 & 2.583 & 2.577 & 2.565 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Specific gravity of the MRE sample before and after cyclic shear fatigue in the absence or presence of a magnetic field. Figure 3: (a) G\({}^{\prime}\)\({}_{0}\) and (b) tan(\(\delta_{0}\)) of the NR before and after cyclic shear fatigue. as shown in Figure 4b. After 500,000 cycles under a magnetic field, the G\({}^{\prime}\)\({}_{0}\) of the sample decreased more than that of the sample after 300,000 cycles. This trend can be ascribed to the relative movement of the CIPs limited by the magnetic field and loss of CIPs. In particular, the limited relative movement of the CIPs can suppress the increase in stiffness of the MRE by reducing the energy loss in the strain cycle. In addition, this decreases the softness of the MRE because of the CIPs lost during the cyclic shear fatigue test. Figure 4: Off-state G\({}^{\prime}\)\({}_{0}\) of the MRE sample before and after being subjected to cyclic shear fatigue in the (**a**) absence and (**b**) presence of a magnetic field. On-state G\({}^{\prime}\) of the MRE sample before and after cyclic shear fatigue in the (**c**) absence and (**d**) presence of magnetic field. (**e**) Absolute and (**f**) relative MR effects of the MRE samples. The on-state G\({}^{\prime}\) trend of the MRE before and after being subjected to cyclic shear, as shown in Figure 4c,d, is similar to that of the off-state G\({}^{\prime}\)0 in Figure 4a,b, respectively. However, the difference of the G\({}^{\prime}\)0 values before and after being subjected to fatigue is larger. This suggests the effect of fatigue on the modulus stored in the restrained matrix generated by the interparticle forces. Therefore, the magnetorheological (MR) performance of an MRE can be altered by cyclic shear fatigue as it is dependent on the capacity of the modulus stored in the restrained matrix [43].