## 3 Results and Discussion
### Rheological Properties
When cyclic shear fatigue is applied under a magnetic field, the decrease in G\({}^{\prime}\) is more pronounced owing to agglomeration caused by the migration of the CIPs, as shown in Figure 2f. This is ascribed to the increased distance between the CIP aggregates as the CIPs move, which can weaken the interparticle forces or reduce the area of the restrained matrix around the magnetised CIPs. The performance of the MRE sample is usually evaluated by the absolute and relative MR effects, which represent the change in the storage modulus under a magnetic field [44; 45; 46; 47]. The absolute MR effect (\(\Delta G^{\prime}\)) represents the difference between G\({}^{\prime}\) and G\({}^{\prime}\)0. The relative MR effect is the percentage of \(\Delta\)G\({}^{\prime}\) and G\({}^{\prime}\)0, as:  
\[\text{Relative MR effect }=\frac{\Delta\text{G}^{\prime}}{\text{G}^{\prime} 0}\times 100\%. \tag{1}\]  
Figure 4e,f shows the absolute and relative MR effects of the MRE sample before and after subjecting it to fatigue, respectively. Except for the sample after 500,000 cycles in the zero field, which has the highest G\({}^{\prime}\), the \(\Delta\)G\({}^{\prime}\) values of all samples after fatigue were lower than that of the initial sample. Similar to the results of the G\({}^{\prime}\) values, lower \(\Delta\)G\({}^{\prime}\) values were obtained for the samples after fatigue. As G\({}^{\prime}\)0 decreased with increasing strain amplitude owing to the Payne effect, the relative MR effect was strain-dependent, that is, it increased with increasing strain amplitude. The \(\tan(\delta_{0})\) of the MRE increased with increasing energy dissipation after subjecting it to cyclic shear fatigue, as shown in Figure 5a,b, which is consistent with the results of the NR sample in Figure 3. As shown in Figure 5a, the \(\tan(\delta_{0})\) value of the sample after fatigue in the zero field at a lower strain amplitude was slightly lower than that of the initial sample. In contrast, the \(\tan(\delta_{0})\) value of the sample at a lower strain amplitude after 300,000 cycles under a magnetic field was higher than that of the initial sample, as shown in Figure 5b, which can be ascribed to the higher energy dissipation owing to the migration of magnetised CIPs. The \(\tan(\delta_{0})\) behaviour with the strain amplitude of the sample after 500,000 cycles under a magnetic field is expected to vary under the influence of further migration and CIP losses. Figure 5c,d shows the \(\tan(\delta)\) value measured in the on-state condition, which exhibits a different behaviour from that of \(\tan(\delta_{0})\). The loss factor based on the relative movement between the CIPs and matrix in the on-state was lower than that in the off-state because the interparticle forces between the CIPs inside the rubber matrix limit the relative movement of the CIPs, thereby reducing the energy dissipation [18; 38; 39; 40]. Therefore, the \(\tan(\delta)\) values of all samples were lower than of \(\tan(\delta_{0})\). Moreover, the \(\tan(\delta)\) of all samples, except for that after 500,000 cycles in the zero field, was higher than that of the initial sample. The lower \(\tan(\delta)\) of the sample after 500,000 cycles in the zero field is attributed to the reduced sliding between the matrix chains and particles due to the expansion of the separation region and limited relative movement of the magnetised CIPs [31]. The highest \(\tan(\delta)\) was obtained after 500,000 cycles under a magnetic field, as shown in Figure 5d. This can be explained by the agglomerate formation and particle loss due to the migration of the CIPs after cyclic shear fatigue owing to the low G\({}^{\prime}\). The internal changes in the MRE after fatigue increased the distance between the CIPs, thereby weakening the interparticle forces. This reduces the force limiting the relative movement of the magnetised CIPs, thereby increasing energy dissipation.