Correlation between the hierarchical structure evolution and Mullins effect of filled rubber under variable amplitude loading

Aiming to investigate the correlation between structure evolution and Mullins effect of filled silicone rubber, deuterated chain labeling and in situ small-angle neutron scattering (SANS) under variable amplitude loading have been conducted. The mechanical properties provide stress (σmax′) at the maximum strain (εmax), energy loss and recovery hysteresis (Es and Erh), etc. While the macrostructure such as radius of gyration Rg of aggregate covered with the bound rubber and the orientation can be obtained from SANS. All the parameters demonstrate consistently pattern in the two conditions of variable amplitude loading process. The evolution of crosslinking modulus Gc, the number of chain segment between entanglements ne/Te, amplification factors of filler X, etc. extracted from constitutive model further confirm such manners. With repeating cycles, the values reflecting mechanical properties such as σmax′ and Erh all exhibit a variation of less than 10%. Additionally, parameters related to microstructural evolution, such as X0 and Rg, also demonstrate a small variation of less than 10%. This implies that the system is in a state of stable equilibrium. With the εmax further increase, the amplitude of variation in orientation of bound rubber (th/tv-1) reaches 30%，ranging from 0.48 at S0.5C5 to 0.62 at S1.0C1, along with the variation of σmax′ around 75%, indicating the reversible deformation might transform into irreversible inelastic destruction and tend to an updated equilibrium.